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Resource management policies in GPRS systems
Performance Evaluation 56 (2004) 73–92
Resource management policies in GPRS systems夽 Michela Meo∗ , Marco Ajmone Marsan Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Abstract In this paper we consider the problem of resource management in GSM/GPRS cellular networks offering not only mobile telephony services, but also data services for the wireless access to the Internet. In particular, we investigate channel allocation policies that can provide a good tradeoff between the QoS guaranteed to voice and data services end users, considering three different alternatives, and developing analytical techniques for the assessment of their relative merits. The first channel allocation policy, voice priority, gives priority to voice in the access to radio channels; we show that this policy cannot provide acceptable performance to data services, since when all the channels are busy with voice connections, data services perceive long intervals of service interruption. The second channel allocation policy is called R-reservation; it statically reserves a fixed number of channels to data services, thus drastically improving their performance, but subtracting resources from voice users, even when these are not needed for data, thus inducing an unnecessary performance degradation for voice services. The third channel allocation policy is called dynamic reservation; as the name implies, it dynamically allocates channels to data when necessary, using the information about the queue length of GPRS data units within the base station. A threshold on the queue length is used in order to decide when channels must be allocated to data. Numerical results show that the dynamic reservation channel allocation policy can provide effective performance tradeoffs for data and voice services, with the additional advantage of being easily managed through the setting of the threshold value. © 2003 Elsevier B.V. All rights reserved. Keywords: GPRS system; Markovian model; Channel allocation
1. Introduction The successes of mobile telephony on one side, and Internet services on the other, are producing very high expectations for the commercial success of wireless Internet access services. Mobile telephony companies in Europe have made huge investments in this sector to acquire UMTS (Universal Mobile Telecommunications System) licenses, and are already offering data services over their existing GSM (Global System for Mobile Communications) networks, so as to start building the market, which will hopefully expand with the advent of UMTS and the proliferation of IEEE 802.11 Wireless LAN islands. 夽
This work was supported by the Center for Multimedia Radio Communications (CERCOM). Corresponding author. Tel.: +39-011-5644167; fax: +39-011-5644099. E-mail addresses: [email protected] (M. Meo), [email protected] (M. Ajmone Marsan). ∗
0166-5316/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.peva.2003.07.002
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The technology that is now becoming available to integrate packet data services into GSM networks is GPRS (Generalized Packet Radio Service). The fact that GPRS exploits the same resources used by mobile telephony raises a number of questions concerning the dimensioning and the management of the GSM/GPRS radio interface. In this paper we tackle this issue, and discuss three possible approaches to manage the radio interface in a GSM/GPRS cell, providing analytical models for their performance analysis, as well as numerical performance results that provide insight into the relative merits of the alternate approaches. The paper is organized as follows. In Section 2 we describe the characteristics of the GSM/GPRS cellular mobile communication network that we consider, together with the probabilistic assumptions that are needed to describe the system dynamics with Markovian models. In the same section we also describe the three channel allocation policies which will be analyzed and compared in the following sections. After a short discussion on related work in Section 3 we present the analytical models and their solutions in Section 4. Some numerical results are shown and discussed in Section 5. Section 6 concludes the paper.
2. System and modeling assumptions Dual-band GSM/GPRS networks exploit two separate frequency bands around 900 MHz and 1.8 GHz. Cells served by frequencies in the 900 MHz band are rather large (up to 35 km around the base station) and are normally called “macrocells,” whereas cells served by frequencies in the 1.8 GHz band are much smaller (typically with a diameter of less than 1 km), due to the much worse propagation characteristics of microwaves in the latter frequency range through the atmosphere. These cells are often called “microcells,” or simply cells. Radio coverage is thus obtained by a two-level hierarchical cellular structure. We focus on a particular area, covered by one macrocell and m cells, where the macrocells are essentially disjoint, and the macrocell overlaps with all cells. This structure is called a cell cluster. Within each cell or macrocell, one or more carrier frequencies are activated, and over each carrier a TDMA frame of Tf = 60/13 ms is defined, comprising eight slots of 15/26 ms each. A circuit (or channel) is defined by a slot position in the TDMA frame, and by a carrier frequency. Since some channels must be allocated for signaling, each carrier frequency can devote to the transmission of end user information from 6 to 8 channels, depending on the cell configuration; we will assume that the TDMA frame allocates seven slots to end users and one slot to signaling. In the model development, we assume that in the considered cell cluster the macrocell is equipped with N(M) user traffic channels, while each cell is equipped with N user traffic channels. We consider two services: telephony and data transfer. Telephony provisioning relies on the usual circuit-based GSM service; data packets are instead transferred according to the GPRS standard, using the same resources deployed for telephony. Based on the provider strategic decisions, different channel allocation policies can be adopted for the simultaneous delivery of telephony and data transfer services. In this paper we consider three different strategies, and we compare their performance. We focus on the telephone call blocking probability (where call blocking may result from the lack of channels to allocate either a new call request or a handover request) as the main QoS parameter for the telephony service. The main QoS parameters for the data transfer service are the data packet loss probability and average data packet transfer delay. The first channel allocation policy is the result of strategic decisions that acknowledge the primary role of the telephony service (telecommunications network operators today still generate most of their
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revenues through voice services). Telephone calls are set up as long as at least one channel is available in the cell of interest. As a consequence, data packets can be transmitted only over the channels which are not used by voice connections. This policy will be called voice priority. A different channel allocation policy is necessary when the telecommunications services provider desires to guarantee at least a minimum QoS level to the data service. In this case, a fixed number R of channels can be reserved to data transfers, while all remaining channels are shared by voice and data connections, with priority to voice. The improvement in the QoS provided to data is obtained at the cost of reducing the resources available for telephony, thus a performance degradation for voice is expected. This policy will be called R-reservation. A yet different channel allocation policy is necessary when the telecommunications service provider expects that the introduction of GPRS may involve a small number of users only, so that a static channel reservation may result in an inefficient use of radio resources, but still some QoS must be provided to data services users. In this scenario, it may happen that during long time intervals no data transfers are required. It is then convenient to dynamically (rather than statically) reserve channels on the basis of the actual data traffic load. This policy will be called dynamic reservation. The decision about when to start reserving channels to data users can exploit a threshold mechanism based on the occupancy of the transmission buffer which stores GPRS packets. In a hierarchical cellular structure, different policies may be employed at different levels of the hierarchy. For the sake of simplicity, we will consider the following scenario. Voice and data services coexist at the microcellular level only, where one of the policies mentioned above is adopted. Macrocell resources, instead, are employed exclusively for voice traffic, and, in particular, they collect the overflow traffic from the microcellular level. Clearly, the models that we describe in this paper can be easily extended to consider other strategies as well. The telecommunications system we consider supports user mobility. Users can roam from a cell to a neighboring cell during active voice calls: an active user (i.e., a user that has established a voice or data call) that roams from a cell to another, must execute a handover procedure transferring the call from the channel in the old cell to a channel in the new cell without interrupting the communication. If no channel is available in the new cell entered by the user, the system attempts to establish the connection employing a macrocell channel. If no channel is available in the macrocell either, the handover fails, and the call must be terminated (or dropped). Since the duration of a data transfer is typically much shorter than the time spent by a user in a cell, we neglect the possibility that a user requests a handover procedure while transferring data. We instead account for handovers of voice connections. As is normally done when modeling cellular telephony systems, we consider one cell at a time [1], and we neglect the impact of signaling (we neglect signaling delays and connection losses due to signaling, but we account for signaling channels). Moreover, in order to model the system, we introduce the assumptions discussed below. As customary in models of telephone systems, we assume that the sequence of new call requests follows a Poisson process with rate λ, and that the duration of calls is an exponentially distributed random variable with mean 1/µ. We also assume that incoming handover requests follow a Poisson process, whose rate is equal to λh (λh is derived by balancing the incoming and outgoing handover flows, as explained below). Thus, the voice call arrival process is Poisson with rate λ v = λ + λh .
(1)
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M. Meo, M. Ajmone Marsan / Performance Evaluation 56 (2004) 73–92 interarrival time (µD) average # of arrivals NP packet arrivals
time
packet call (µC)
reading time (µR)
Fig. 1. Model of GPRS traffic: a packet session.
The time spent by a user within a cell (which is normally called dwell time) is assumed to be exponentially distributed with mean 1/µh and 1/µ(M) h , respectively, for mobility within a cell and a macrocell. The call activity time within a cell (the channel holding time) is thus a random variable with negative exponential distribution with rate µv = µh + µ in the cell, and µ(M) = µ(M) + µ in the macrocell. v h Note that exponential assumptions are generally considered not to be critical in telephony models: telephone systems have been dimensioned using exponential assumptions for almost a century. More recently, these assumptions were used in modeling wireless systems [2–6]. GPRS was conceived for the transfer of packets over a GSM infrastructure, with a simplified allocation of resources over the wireless link, and an IP transport among additional elements of the wired GSM network. In order to cross the wireless link, IP packets are fragmented in radio blocks, that are transmitted in four slots in identical positions within consecutive GSM frames over the same carrier frequency. Depending on the length of the IP packet, the number of radio blocks necessary for the transfer may vary. The allocation of the radio link to radio block transmissions can either use dedicated resources for signaling, or (more usually) the same signaling resources that are available for telephony. In order to describe the GPRS traffic, we adopt the On–Off model of Internet traffic defined by the 3GPP (3rd Generation Partnership Project) in [7]; a sketch of the GPRS traffic model that we use is shown in Fig. 1. Active users within a cell execute a packet session, which is an alternating sequence of packet calls and reading times. According to [7], the number of packet calls within a packet session can be described by a geometrically distributed random variable; however, since we will study the system behavior for a fixed number D of concurrently active packet sessions, we will assume that packet sessions remain active for an indefinite amount of time. The reading time between packet calls is an exponentially distributed random variable with rate µR . Each packet call comprises a geometrically distributed number of packets with mean value NP ; the interarrival time between packets in a packet call is an exponentially distributed random variable with rate µD . According to [7], we shall assume 1/µR = 41.2, NP = 25 and 1/µD = 0.5, all times being expressed in seconds. The average packet call duration, 1/µC , is equal to the average packet interarrival time multiplied by the average number of packets generated during a packet call, so that µC = µD /NP . According to [7], the packet size in radio blocks can have a number of different distributions, some with heavy tail. In our model, for the sake of simplicity, the packet size is equal to either 1 or P radio blocks, with the same probability. Other discrete distributions could be easily introduced in our models in order to approximate heavy tailed distributions of the packet size. The transfer of radio blocks over the radio channel can either be successful, thus allowing the removal of the radio block from the buffer, or result in a failure due to noise, fading, or shadowing. In the latter case, radio block transmissions must be repeated. These events are modeled by a random choice: with probability c a radio block transfer is successful, and with probability 1 − c it fails.
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3. Related work Many papers in the literature propose and analyze channel reservation schemes. In the context of cellular networks, channel reservation is typically proposed in order to favor handover requests over new call requests in accessing the system resources, see for example, [8–12]. The rationale behind the idea of channel reservation for handovers is that the forced termination of an active call has a much worse impact on the QoS perceived by the user than the failure in a new connection set up. Some schemes account also for the introduction of traffic classes with different bandwidth requirements and QoS constraints, see for example, [13–16]. The possibility to dynamically degrade the service is considered in [17]. In [18], four channel allocation schemes are proposed for GPRS systems dealing with voice and data transmission requests, with the assumption that voice calls can be queued while waiting for a packet transmission to complete. A continuous-time Markovian model similar to the one proposed here for the R-reservation scheme is presented in [19]. While the idea of static and dynamic channel reservation was widely investigated in the literature, in this paper we propose a dynamic scheme based on a threshold mechanism on the data packet buffer occupancy. In order to evaluate and possibly compare the performance of the three considered schemes (the traditional voice priority, R-reservation and the proposed dynamic reservation) we develop a Markovian model of the system. Since the model explicitly accounts for the radio block buffer occupancy, it can be used to assess the QoS perceived by data service users. The model is flexible and simple enough to be easily adapted to describe the three considered schemes.
4. Analytical model In describing the analytical model, we first focus on the model of a single cell which adopts the voice priority channel allocation policy. We then describe how to derive, from the model of a cell, the behavior of the system which includes the hierarchical cell structure. Finally, we present the extensions to be introduced in the model in order to deal with the other considered channel allocation policies. 4.1. Model of a cell Each cell can be modeled by a queue with N servers, which represent the N available channels. Two classes of customers enter the queue. Customers in the first class represent voice connections. They arrive at the system according to a Poisson process with parameter λv and require a negative exponential service time with rate µv ; these users do not queue waiting for service: if no channel is available to set up the connection, i.e., if no server is free when the customer joins the queue, the request fails, and the customer is lost. The second class of customers represents GPRS radio blocks. The GPRS traffic representation in Fig. 1, is an On–Off traffic source. The time spent in state Off represents the reading time, while state On describes packet calls. In the latter state the GPRS user generates packets according to a Poisson process with rate µD . Packets can be short or long, with the same probability; a short packet is composed of one radio block, a long packet is segmented into P radio blocks. Radio blocks are queued waiting to be served in a transmission buffer whose capacity is equal to B radio blocks.
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A radio block is transmitted over the wireless link if a channel is available (i.e., it is not used by voice connections), hence if a server is idle. The radio block is removed from the buffer if the transmission is successful, with probability c. In the analytical model we assume that the transmission time of a radio block is a random variable with negative exponential distribution with mean value equal to four GSM frames, 1/γ = 4Tf . Of course, the radio block transmission time is constant and equal to 4Tf , rather than exponential. However, the impact of this assumption on the system performance was shown to be very limited, due to the variability introduced by the possible retransmissions. This phenomenon was studied in [20] by comparing the results obtained from a model which includes the exponential assumption for radio block transmission times against the results obtained from a discrete time model with constant radio block transmission times. The exponential assumption was observed to produce quite accurate results. Given the assumptions introduced above, we develop a continuous-time Markov chain (CTMC) model of the system, whose state is defined as s = (d, b, v), where 1. d is the number of active packet calls, d varies between 0 and the number of data sessions, D; 2. b is the number of radio blocks in the buffer, b varies between 0 and the buffer capacity, B; 3. v is the number of active voice calls, v varies between 0 and the number of channels in the cell, N. Let S be the state space of the CTMC model. The number of states in S is equal to (D + 1)(B + 1)(N + 1). Transitions from state s to all possible successor states are reported in Table 1 together with their rates and, possibly, with the condition under which the transitions exist; the last column indicates the type of event to which a transition refers. Changes of the state variable v are determined by the dynamics of voice connections. The state variable d increases when a GPRS packet call begins, and decreases when a packet call terminates. Whenever a packet is generated, the buffer occupancy b increases by one or P radio blocks, depending on the packet size. When no free positions are available in the buffer, some radio blocks are lost. Finally, transitions reported in the last row of the table refer to the removal of radio blocks from the buffer. A radio block is successfully transmitted with rate cγ. The factor r accounts for the number of radio blocks which can be transmitted during the same set of four frames; radio blocks are transmitted employing all the resources not used by voice connections: N − v channels are used if at least N − v radio blocks are in the buffer. Using standard techniques for the solution of Markov chains, we compute the steady-state probabilities of the CTMC. Let π(s) be the steady-state probability of state s (we will also use the notation π(d, b, v) for π(s)). The value of the arrival rate of incoming handover requests, λh , as in (1) is derived by balancing incoming and outgoing handover flows for voice users in a fixed point procedure. The outgoing handover Table 1 Transitions from state s = (d, b, v) to successor state t for the voice priority policy Successor state t
Condition
Rate
Event
(d, b, v + 1) (d, b, v − 1) (d + 1, b, v) (d − 1, b, v) (d, b + 1, v)
v0 d0 b
λv vµv (D − d)µR dµC 1 dµD 2
A voice call arrives A voice call completes A packet call starts A packet call terminates A short IP packet is generated
(d, β, v) (d, b − 1, v)
β = min(b + P, B) and b < B r = min(N − v, b) and b > 0
1 dµD 2 rcγ
A long IP packet is generated A radio block leaves the buffer
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flow is computed as λ(out) h
B D N = vµh π(d, b, v). v=1 d=0 b=0
The approach of using a fixed point procedure to compute incoming handover flows was widely used in the literature for the analysis of cellular systems, see for example, [2,3,6]. From the π(s)’s some interesting performance metrics can be computed. The offered radio block traffic O (which does not depend on the π(s)’s) is given by O = 21 (P + 1)µD
DµR , µC + µR
where the last term is the average number of active packet calls. Given O, the probability that a radio block is lost due to buffer overflow can be computed as N D B D N 1 Ld = (P − B + b)dµD π(d, b, v) + dµD π(d, B, v) , (2) 2O v=0 d=1 b=B−P+1 v=0 d=1 where the first sum refers to the arrival rate of long IP packets composed of P radio blocks, and the second sum refers to the arrival rate of short IP packets composed of one radio block only. With a different distribution of the IP packet size, a sum is necessary for each possible value of the number of radio blocks in which an IP packet can be segmented. The radio block throughput is X = O(1 − Ld ).
(3)
The average buffer occupancy in radio block is computed from E[b] =
D B N bπ(d, b, v)
(4)
v=0 d=0 b=1
and, by Little’s law, the average delay perceived by radio blocks is E[b] E[T ] = . X We can also evaluate the average buffer occupancy given that v voice calls are active: D B b=1 bπ(d, b, v) E[b|v] = d=0 . D B d=0 b=0 π(d, b, v)
(5)
(6)
The voice call blocking probability at the microcell is given by the probability that all channels are busy with voice connections: B D Pv = π(d, b, N). (7) d=0 b=0
Observe that, since we are considering the voice priority channel allocation policy, the presence of data traffic is transparent to voice users; thus, Pv can also be computed by simply applying the Erlang-B formula.
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The probability Pv represents also the probability that a voice call overflows to the macrocell. The average rate of voice call requests which are refused and overflow to the macrocell is fo = λv Pv .
(8)
4.2. Model of the cell cluster From the model of a cell we can develop a complete model to analyze the performance of clusters of cells. In our two-level hierarchical structure, macrocells are used only to accommodate the voice overflow traffic from microcells. We assume that the arrival process at the macrocell is Poisson with rate, δ = mfo , where m is the number of microcells in the cell cluster, and f0 the overflow traffic computed as in (8). It should be noted that overflow traffic is known to be much burstier that Poisson; however, the traffic that reaches the macrocell is the result of the superposition of a number of individual bursty overflow flows. It has been shown that the overall arrival process at the macrocell in this case can be well-approximated by a Poisson process even with a small number of cells [6]. Assuming that the user dwell time in the cell under consideration is a random variable with negative (M) exponential distribution with rate µ(M) /0 queue with service h , the macrocell can be modeled as a M/M/N (M) rate µ + µh . The steady-state probability π(i) that i channels are busy is (M) −1 N i ρj ρ , π(i) = π(0) and π(0) = (9) i! j! j=0 where ρ = δ/(µ + µ(M) h ). The voice call blocking probability at the macrocell, Pv(M) , is given by the Erlang-B formula, and it is equal to the probability π(N(M) ) that all channels are busy. A voice call is blocked and lost if both in the microcell and in the macrocell no channels are available; this happens with probability Lv = Pv Pv(M) .
(10)
4.3. R-reservation policy We describe in this section how the proposed model can be extended in order to describe the R-reservation channel allocation policy. As already mentioned, in a cell which adopts the R-reservation policy, R channels are reserved to data traffic, while the remaining N − R channels are shared between voice and data traffic, with priority to voice. The Markovian model introduced in Section 4.1 can be used also to describe the behavior of a cell adopting the R-reservation policy. The only difference is that under the R-reservation channel allocation policy, no more than N − R voice calls can be accepted. Therefore, under the R-reservation channel allocation policy, the state variable v ranges from 0 to N − R, and, correspondingly, the transition in the first row of Table 1 is possible only under the condition that v < N − R. Consider now the radio block service rate r, as defined in the last row of Table 1. When there are enough radio blocks in the buffer,
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since the maximum number of active voice calls is now N − R, the smallest value of the parameter r is equal to R. The minimum data service is thus guaranteed by R channels. The state space cardinality in this case reduces to (D + 1)(B + 1)(N − R + 1). As we will observe by means of numerical results in Section 5, the adoption of the R-reservation channel allocation policy implies an improvement of the QoS of the data transfer service. The cost of this improvement is paid in terms of a QoS deterioration of the telephony service. The voice call blocking probability in the microcell is in this case: Pv =
B D π(d, b, N − R)
(11)
d=0 b=0
which is larger than for the voice priority policy. 4.4. Dynamic reservation policy The dynamic reservation channel allocation policy infers the presence of data users activity and of potential data service QoS deterioration by means of the current buffer occupancy. When the buffer is underutilized, the voice priority policy is adopted. When buffer occupancy grows above a threshold, Th , the R-reservation policy is applied, instead. In the latter case, voice requests are accepted as long as no more than N −R channels are used for the voice service. Moreover, if the threshold is reached while more than N − R voice connections are already active, some voice calls which are active in the cell are forced to move to the macrocell by means of a forced handover procedure. The CTMC describing this system has the same state variable as in previous models. States with a number of active voice calls v larger than N − R and a buffer occupancy b larger than Th are impossible. Thus, the state space cardinality is now equal to (D + 1)[(B − Th )(N − R + 1) + (Th + 1)(N + 1)]. The rate of transitions between states are reported in Table 2. Observe that radio block generations, besides causing changes in the buffer occupancy, may also induce changes in the number of active voice calls, due to the threshold mechanism. Table 2 Transitions from state s = (d, b, v) to successor state t for the dynamic reservation policy Successor state t
Condition
Rate
Event
(d, b, v + 1)
λv
A voice call arrives
(d, b, v − 1) (d + 1, b, v) (d − 1, b, v) (d, b + 1, v)
(v < N ∧ b ≤ Th ) ∨ (v < N − R ∧ b > Th ) v>0 d0 (v ≤ N − R ∧ b < B) ∨ b < Th
vµv (D − d)µR dµC 1 dµD 2
A voice call completes A packet call starts A packet call terminates A short IP packet, no forced handovers
(d, b + 1, N − R)
b = Th ∧ v > N − R
A short IP packet, forced handovers
(d, β, v)
β = min(b + P, B) and v ≤ N − R ∨ b < Th − P + 1 β = min(b + P, B) and T h − P + 1 ≤ b ≤ Th ∧ v > N −R r = min(N − v, b)
1 dµD 2 1 dµD 2 1 dµD 2
A long IP packet, forced handovers
rcγ
A radio block leaves the buffer
(d, β, N − R) (d, b − 1, v)
A long IP packet, no forced handovers
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The performance perceived by telephony users is now measured in terms of blocking probability as well probability that a forced handover occurs. The voice blocking probability in the microcell is computed as Th D B π(d, b, N) + Pv = π(d, b, N − R) . (12) d=0
b=0
b=Th +1
The rate of forced handovers toward the macrocell is given by the arrival rate of the packets which make the radio block buffer occupancy grow above the threshold when the number of active voice calls is larger than N − R: Th N D 1 fh = dµD (v − N + R) π(d, Th , v) + π(d, b, v) (13) 2 d=1 v=N−R+1 b=T −P+1 h
and the probability of forced handover is Ph =
fh . λv (1 − Pv )
(14)
5. Numerical results In this section we present some numerical results to assess the relative merits of the different channel allocation policies. We first focus on the voice priority scheme performance at the cell level, discussing the interaction between voice and data traffic. Then, we evaluate the performance of the dynamic reservation policy. Finally, we compare the performance of the three resource management schemes described above: voice priority, R-reservation and dynamic reservation. For the derivation of numerical results we always use the traffic and system parameter values which are summarized in Table 3, unless otherwise specified. 5.1. Voice priority scheme Fig. 2 shows the voice call blocking probability Pv (dashed line) and the radio block loss probability Ld (solid lines) versus the voice traffic load, which is defined as λv /(µ+µh ). The radio block loss probability Ld is plotted for different values of the number of active sessions, D. Under the voice priority scheme, the voice call blocking probability is insensitive to data traffic; instead, the radio block loss probability increases with the number of data sources, since higher number of data sources translate into higher data traffic. In general, the results in Fig. 2 show that the radio block loss probability Ld can be rather high, unless the voice traffic load remains quite low (a radio block loss probability of about 1% is obtained when the cell loading factor is below 50%—less than three channels are used on the average, of the seven available in the cell). The average delay perceived by radio blocks, E[T] is presented in Fig. 3, for the same scenario of Fig. 2, for either 2 or 6 active data sessions. It can be observed that the delay suffered by radio blocks is quite large. This is due to the priority of voice traffic, and to the low bit rate of the radio channel. It thus appears that the QoS that can be offered to data users in a cell with the considered characteristics
M. Meo, M. Ajmone Marsan / Performance Evaluation 56 (2004) 73–92 Table 3 Parameters of the basic scenario Parameter
Value
No. of traffic channels in the cells, N No. of channels reserved to data, R No. of traffic channels in the macrocell, N(M) No. of microcells in a cluster, m 1/µ µh µ(M) h Buffer size, B No. of packet sessions, D Maximum number of radio blocks per packet, P NP 1/µD 1/µR c
7 1 14 19 180 s µ/2 /8 100 1, . . . , 6 16 25 0.5 s 41.2 s 0.95
Blocking and loss probability
1.0e-01
1.0e-02 voice data D=2 D=4 D=6 1.0e-03
2
2.5
3 3.5 Voice traffic load
4
Fig. 2. Voice priority. Voice blocking probability Pv and radio block loss probability Ld versus voice traffic load.
Average radio block delay [s]
1.0e+01
1.0e+00
D=2 D=6 1.0e-01 2
2.5
3
3.5
4
Voice traffic load
Fig. 3. Voice priority. Average radio block delay versus voice traffic load.
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Average buffer occupancy
1.0e+01
1.0e+00
D=2 D=6 1.0e-01
2
2.5
3 3.5 Voice traffic load
4
Fig. 4. Voice priority. Average radio block buffer occupancy versus voice traffic load.
is rather poor, even when the number of users is small, unless the voice traffic load is quite low. However, this behavior deserves further investigation, since the average bandwidth available to data (i.e., the bandwidth unused by voice) should be sufficient to satisfy the needs of a non-trivially small number of data users. By investigating further, we find a surprising result concerning the length of the queue of radio blocks. Indeed, even if the value of the radio block loss probability was observed to be rather large, the average radio block buffer occupancy is quite small, as can be noted from Fig. 4, again for 2 or 6 active data sessions. For all the considered values of voice traffic load, the average radio block buffer occupancy is always less than 10% (the radio block buffer size is 100, and the average queue length is always less than 10). This behavior means that the radio block buffer is almost always empty, but then something happens that fills up the buffer and causes the buffer to overflow. The responsibility for the buffer overflow is not in the burstiness of the data traffic; rather, it resides in the fact that voice has priority over data and in the different time scales of data and voice traffic. Indeed, the radio block service rate depends on the voice calls dynamics and, in particular, when all channels in the cell are busy with voice connections, no radio block can be transmitted over the radio channel: the data service is thus interrupted until at least one channel becomes available. During these intervals of service interruption, which are quite long compared to data traffic dynamics, the radio block buffer fills up, and a large number of radio blocks are lost. The fact that the radio block loss probability is dominated by the service interruption phenomenon is confirmed by Fig. 5, which shows the average buffer occupancy conditional on the number of active voice connections, versus the number of active voice connections, v, for different number of data traffic sources, D. The average buffer occupancy is quite small when at least one channel is available to serve data traffic (points with v < 7 in the figure), but becomes very close to the buffer size when all channels in the cell are used by voice connections (v = 7). Clearly, the radio block loss probability is dominated by the losses occurring during intervals with v = 7. Observe also that the average buffer occupancy conditional on seven active voice calls is so close to the buffer size that it varies only marginally with the number D of data traffic sources (this also explains why the data loss probability only marginally increases with the number of data sources, as shown in Fig. 2). These results clearly indicate that, in order to be able to provide data users with reasonable QoS guarantees, the adoption of a channel allocation scheme which gives priority to voice over data is not acceptable.
Average conditional buffer occupancy
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Fig. 5. Voice priority. Radio block buffer occupancy conditional on the number of active voice calls.
This observation motivated our definition of the different channel allocation policies that were described before, where some fraction of the cell resources is reserved for data services. Moreover, since the reservation of a fixed number of channels to data may affect the voice service QoS too negatively (even in periods in which the need for the allocation of resources to data services is not pressing), we devised the dynamic reservation scheme, that allocates resources to data only when the risk of QoS degradation becomes compelling. We thus expect the dynamic reservation scheme to be quite effective in improving the QoS provided to data traffic, while having just a mildly negative impact on voice. The impact of channel reservation on voice service will be assessed later. 5.2. Dynamic reservation scheme Fig. 6 reports the radio block loss probability versus the voice traffic load when the dynamic reservation scheme is adopted with threshold equal to 70 or 80 on a buffer whose capacity is equal to 100 radio blocks. Three different values of data traffic load are considered, corresponding to 2, 4 and 6 data traffic sources. Clearly, the radio block loss probability increases with voice traffic, and with data traffic as well. By
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Fig. 6. Dynamic reservation policy. Radio block loss probability Ld versus voice traffic load for different values of the threshold and of the number of data sources.
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Average buffer occupancy
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Fig. 7. Dynamic reservation policy. Average radio block buffer occupancy versus voice traffic load for different values of the threshold and of the number of data sources.
letting the threshold decrease from 80 to 70 we make the dynamic allocation to data traffic more prompt and we thus obtain a reduction of the loss probability. The average buffer occupancy is reported in Fig. 7 for the same scenarios as Fig. 6. The behavior of the average buffer occupancy is similar to that of the radio block loss probability: increases of voice or data traffic load cause increases of the buffer occupancy. Small values of the threshold correspond to reactive schemes which make a radio resource become available early as the buffer starts filling; thus, lower values of the threshold correspond to lower buffer occupancy. The average radio block delay is shown in Fig. 8. As expected, the average delay increases with voice traffic load. On the contrary, it slightly decreases with the number D of data sources. This behavior is due to the following reason. For larger values of D, the buffer fills and reaches the threshold faster; as soon as the threshold is reached, a channel becomes available to data traffic and radio blocks start to be served and removed from the buffer. A further performance parameter to be taken into account when discussing the dynamic reservation policy, is the probability that a voice call which is active in a microcell, is forced to move to a channel in the macrocell, in order to prevent data service interruption, when the buffer occupancy reaches the threshold Th . We call this event a forced handover. The probability Ph of a forced handover is plotted in Average radio block delay [s]
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Fig. 8. Dynamic reservation policy. Average radio block delay versus voice traffic load for different values of the threshold and of the number of data sources.
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Forced handover probability
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Fig. 9. Dynamic reservation policy. Probability that an active voice call undergoes forced handover Ph versus voice traffic load for different values of the threshold and of the number of data sources.
Fig. 9 for the dynamic reservation policy, again with Th equal to 70 or 80, and D equal to 2, 4 or 6. It is interesting to observe that Ph can be rather large, of the order of a few percentage points; this may be a drawback of the dynamic reservation policy. The availability of a tunable parameter, the threshold Th , which allows the cell performance to be tightly controlled, makes the dynamic reservation policy very attractive also from the network management point of view. In Figs. 10 and 11 we show how the threshold Th influences the radio block loss probability and the average radio block delay, respectively. Three values of the voice traffic load are considered: 2.4, 3.0 and 4.0 for 2 or 4 data sources. The availability of these results can provide the starting point for the possibly dynamic management of the cell resources through the threshold value. 5.3. Comparisons between different policies In this section we compare the three resource management policies considered in this paper: voice priority, R-reservation (with R = 1) and dynamic reservation. For all comparisons we consider D = 4 active data sessions. Fig. 12 reports the radio block loss probability. The highest curve refers to the voice priority scheme, the lowest curve refers to R-reservation. By comparing the results of these two schemes, we can conclude Radio block loss probability
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Fig. 10. Dynamic reservation. Radio block loss probability Ld versus threshold Th for different values of voice traffic load.
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Fig. 11. Dynamic reservation. Average radio block delay versus threshold Th for different values of voice traffic load.
that the reservation of channels for data services has a profound impact on the data loss probability, which improves drastically, dropping by about three orders of magnitude. Results for the dynamic channel reservation scheme vary between the two curves of the voice priority scheme and of the R-reservation scheme, depending on the value of the threshold Th . The dynamic reservation scheme avoids data service interruption by reserving a channel only when the buffer occupancy grows above Th , indicating that some radio blocks may soon be lost. Therefore, the dynamic reservation scheme is quite efficient in preventing data losses, and is capable of reducing the radio block loss probability of more than one order of magnitude with respect to voice priority. Similar conclusions can be drawn from another interesting QoS metric, which is the average radio block delay, shown in Fig. 13. Improvements of the average delay of roughly a factor 4 can be achieved by employing the dynamic reservation scheme instead of the voice priority policy. In order to further investigate the different behaviors of the three channel allocation policies, we show in Fig. 14 the average buffer occupancy conditional on the number of active voice calls, versus the number of active voice connections, v. Clearly, in the case of R-reservation policy no more than six voice connections can be active at the same time, so that no result exists for v = 7. The dynamic reservation policy succeeds in controlling the average radio block queue length, producing much smaller values than the voice priority scheme. This is the behavior behind the reduction in the radio block loss probability.
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Fig. 12. Comparison between different policies. Radio block loss probability Ld .
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Fig. 13. Comparison between different policies. Average radio block delay.
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Fig. 14. Comparison between different policies. Radio block buffer occupancy conditional on the number of active voice calls.
Voice call blocking probability
Of course, any improvement of the QoS obtained in data services must be paid by the voice service QoS, since the amount of cell channels that the two types of services share is fixed. It is thus interesting to quantify the voice service QoS reduction produced by the different channel allocation schemes. Fig. 15 shows the voice blocking probability Lv versus the voice traffic load. Notice that Lv accounts also for the 1.0e-01 dynamic Th=70 Th=80 1-res voice pr.
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Fig. 15. Comparison between different policies. Voice blocking probability Lv .
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presence of the macrocell radio channels, which serve voice connections which cannot be served in the microcells. Reserving one channel in microcells to data traffic makes the voice blocking probability increase remarkably (in some cases about two orders of magnitude). Again, the excellent performance of the dynamic reservation scheme can be observed from the graphs: dynamic reservation achieves intermediate performance between voice priority and R-reservation policies, and offers a very effective and flexible tradeoff between the needs to guarantee access to voice connections and to provide QoS to data traffic. From the numerical results that we have obtained, we can conclude that the dynamic reservation policy is a very interesting scheme for the effective provision of controlled QoS to both voice and data services.
6. Conclusions In this paper we have investigated channel allocation policies for GSM/GPRS cellular networks offering not only mobile telephony services, but also data services for the wireless access to the Internet. Three different alternatives were described, developing simple Markovian models for the assessment of their relative merits. Numerical results showed that the voice priority policy, that gives priority to voice in the access to radio channels, cannot provide acceptable performance to data services. The R-reservation policy, that statically reserves a fixed number of channels to data services, was shown to drastically improve their performance, but to exact a rather high toll in terms of the voice services QoS. This is specially annoying because this policy subtracts resources from voice users even when these are not needed for data, thus inducing an unnecessary performance degradation for voice services. Instead, the dynamic reservation policy, that dynamically allocates channels to data only when necessary, using the information about the queue length of GPRS data units within the base station, was shown to provide very effective performance tradeoffs for data and voice services, with the additional advantage of being easily managed through the setting of the threshold value that triggers the dynamic allocation of channels to data. A further advantage of the dynamic reservation scheme is the fact that it tries to allow a full exploitation of the system resources by voice traffic when no data traffic is present, but it gradually allocates resources to data, so as to guarantee the data services QoS. This may be an extremely attractive feature of the scheme in a scenario where wireless network operators generate most of their revenues with voice services, but are eager to carry data traffic with acceptable QoS, so as to be able to open a new market of mobile data services for the wireless access to the Internet.
Acknowledgements The authors would like to thank Cecilia Batetta for deriving some of the results presented in this paper. References [1] M. Ajmone Marsan, G. De Carolis, E. Leonardi, R. Lo Cigno, M. Meo, How many cells should be considered to accurately predict the performance of cellular networks?, in: Proceedings of the European Wireless’99 and Fourth ITG Mobile Communications, Munich, Germany, October 1999.
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[2] D. Hong, S. Rappaport, Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and non-prioritized handoff procedures, IEEE Trans. Vehicular Technol. VT-35 (3) (1986) 77–92. [3] K.K. Leung, W.A. Massey, W. Whitt, Traffic models for wireless communication networks, IEEE J. Select. Areas Commun. 12 (8) (1994) 1353–1364. [4] Y. Lin, Modeling techniques for large-scale PCS networks, IEEE Commun. Mag. 35 (2) (1997) 102–107. [5] L.R. Hu, S.S. Rappaport, Personal communication systems using multiple hierarchical cellular overlays, in: Proceedings of the IEEE ICUPC’94, San Diego, CA, September 1994. [6] M. Meo, M. Ajmone Marsan, Approximate analytical models for dual-band GSM networks design and planning, in: Proceedings of the Infocom 2000, Tel Aviv, Israel, March 2000. [7] Universal Mobile Telecommunications System (UMTS), Selection procedures for the choice of radio transmission technologies of the UMTS (UMTS 30.03 version 3.2.0), ETSI TR 101 112 V3.2.0 (1998-04). [8] M.H. Chiu, M.A. Bassiouni, Predictive schemes for handoff prioritization in cellular networks based on mobile positioning, IEEE J. Select. Areas Commun. 18 (3) (2000) 510–522. [9] S. Wu, K.Y. Wong, B. Li, A dynamic call admission policy with precision QoS guarantee using stochastic control for mobile wireless networks, IEEE/ACM Trans. Netw. 10 (2) (2002) 257–271. [10] R. Ramjee, R. Nagarajan, D. Towsley, On optimal call admission control in cellular networks, in: Proceedings of the Infocom’96, San Francisco, CA, USA, March 1996. [11] M. Rajaratnam, F. Takawira, Nonclassical traffic modeling and performance analysis of cellular mobile networks with and without channel reservation, IEEE Trans. Vehicular Technol. 49 (3) (2000) 817–834. [12] I.-S. Yoon, B.G. Lee, DDR: a distributed dynamic reservation scheme that supports mobility in wireless multimedia communications, IEEE J. Selected Areas Commun. 19 (11) (2001) 2243–2253. [13] B. Epstein, M. Schwartz, Reservation strategies for multi-media traffic in a wireless environment, in: Proceedings of the IEEE 45th Vehicular Technology Conference, vol. 1, 1995, pp. 165–169. [14] O. Yu, S. Khanvilkar, QoS provisioning over GPRS wireless mobile links, in: Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC 2002), vol. 1, September 2002, pp. 322–326. [15] A. Suriya, A. Charoenpanichkit, A. Thanasorravit, S. Aramvith, L. Wuttisittikulkij, New single-access channel reservation schemes for QoS constrained multimedia traffic, in: Proceedings of the IEEE 55th Vehicular Technology Conference (VTC Spring 2002), vol. 1, 2002, pp. 209–213. [16] L. Yin, B. Li, Z. Zhang, Y.-B. Lin, Performance analysis of a dual-threshold reservation (DTR) scheme for voice/data integrated mobile wireless networks, in: Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC 2000), vol. 1, pp. 258–262. [17] S.K. Das, R. Jayaram, N.K. Kakani, S.K. Sen, A call admission and control scheme for quality of service provisioning in next generation wireless networks, ACM/Baltzer Wireless Netw. 6 (1) (2000) 17–30. [18] P. Lin, Y.-B. Lin, Channel allocation for GPRS, IEEE Trans. Vehicular Technol. 50 (2) (2001) 375–387. [19] C. Lindemann, A. Thummler, Performance analysis of the general packet radio service, in: Proceedings of the 21st International Conference on Distributed Computing Systems, Phoenix, AZ, 2001, pp. 673–680. [20] M. Ajmone Marsan, M. Gribaudo, M. Meo, M. Sereno, On Petri net-based modeling paradigms for the performance analysis of wireless internet accesses, in: Proceedings of the Ninth International Workshop on Petri Nets and Performance Models, RWTH, Aachen, Germany, September 2001.
Michela Meo received the Dr.Ing. degree in electronic engineering in 1993, and the Ph.D. degree in electronic and telecommunication engineering in 1997, both from Politecnico di Torino, in Italy. Since then she has been working in the Telecommunication Networks Research Group of the Politecnico di Torino, where she is currently an assistant professor. Her research interests are in the field of performance evaluation of communication networks with a particular focus on wireless systems and end-to-end performance.
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Marco Ajmone Marsan is a full professor at the Electronics Department of Politecnico di Torino, in Italy, and the director of the Institute for Electronics, Information Engineering and Telecommunications of the National Research Council. He holds degrees in electronic engineering from Politecnico di Torino and University of California, Los Angeles. He has coauthored over 300 journal and conference papers in the areas of communications and computer science, as well as the two books “Performance Models of Multiprocessor Systems” published by the MIT Press, and “Modelling with Generalized Stochastic Petri Nets” published by John Wiley. He received the best paper award at the Third International Conference on Distributed Computing Systems in Miami, FL, in 1982. In 2002 he was awarded a “Honoris Causa” degree in Telecommunication Networks from the Budapest University of Technology and Economics. His current interests are in the fields of performance evaluation of communication networks and their protocols. He is a fellow of IEEE, and a corresponding member of the Academy of Sciences of Torino. He participates in a number of editorial boards of international journals, including the IEEE/ACM Transactions on Networking.
Resource management policies in GPRS systems夽 Michela Meo∗ , Marco Ajmone Marsan Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Abstract In this paper we consider the problem of resource management in GSM/GPRS cellular networks offering not only mobile telephony services, but also data services for the wireless access to the Internet. In particular, we investigate channel allocation policies that can provide a good tradeoff between the QoS guaranteed to voice and data services end users, considering three different alternatives, and developing analytical techniques for the assessment of their relative merits. The first channel allocation policy, voice priority, gives priority to voice in the access to radio channels; we show that this policy cannot provide acceptable performance to data services, since when all the channels are busy with voice connections, data services perceive long intervals of service interruption. The second channel allocation policy is called R-reservation; it statically reserves a fixed number of channels to data services, thus drastically improving their performance, but subtracting resources from voice users, even when these are not needed for data, thus inducing an unnecessary performance degradation for voice services. The third channel allocation policy is called dynamic reservation; as the name implies, it dynamically allocates channels to data when necessary, using the information about the queue length of GPRS data units within the base station. A threshold on the queue length is used in order to decide when channels must be allocated to data. Numerical results show that the dynamic reservation channel allocation policy can provide effective performance tradeoffs for data and voice services, with the additional advantage of being easily managed through the setting of the threshold value. © 2003 Elsevier B.V. All rights reserved. Keywords: GPRS system; Markovian model; Channel allocation
1. Introduction The successes of mobile telephony on one side, and Internet services on the other, are producing very high expectations for the commercial success of wireless Internet access services. Mobile telephony companies in Europe have made huge investments in this sector to acquire UMTS (Universal Mobile Telecommunications System) licenses, and are already offering data services over their existing GSM (Global System for Mobile Communications) networks, so as to start building the market, which will hopefully expand with the advent of UMTS and the proliferation of IEEE 802.11 Wireless LAN islands. 夽
This work was supported by the Center for Multimedia Radio Communications (CERCOM). Corresponding author. Tel.: +39-011-5644167; fax: +39-011-5644099. E-mail addresses: [email protected] (M. Meo), [email protected] (M. Ajmone Marsan). ∗
0166-5316/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.peva.2003.07.002
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The technology that is now becoming available to integrate packet data services into GSM networks is GPRS (Generalized Packet Radio Service). The fact that GPRS exploits the same resources used by mobile telephony raises a number of questions concerning the dimensioning and the management of the GSM/GPRS radio interface. In this paper we tackle this issue, and discuss three possible approaches to manage the radio interface in a GSM/GPRS cell, providing analytical models for their performance analysis, as well as numerical performance results that provide insight into the relative merits of the alternate approaches. The paper is organized as follows. In Section 2 we describe the characteristics of the GSM/GPRS cellular mobile communication network that we consider, together with the probabilistic assumptions that are needed to describe the system dynamics with Markovian models. In the same section we also describe the three channel allocation policies which will be analyzed and compared in the following sections. After a short discussion on related work in Section 3 we present the analytical models and their solutions in Section 4. Some numerical results are shown and discussed in Section 5. Section 6 concludes the paper.
2. System and modeling assumptions Dual-band GSM/GPRS networks exploit two separate frequency bands around 900 MHz and 1.8 GHz. Cells served by frequencies in the 900 MHz band are rather large (up to 35 km around the base station) and are normally called “macrocells,” whereas cells served by frequencies in the 1.8 GHz band are much smaller (typically with a diameter of less than 1 km), due to the much worse propagation characteristics of microwaves in the latter frequency range through the atmosphere. These cells are often called “microcells,” or simply cells. Radio coverage is thus obtained by a two-level hierarchical cellular structure. We focus on a particular area, covered by one macrocell and m cells, where the macrocells are essentially disjoint, and the macrocell overlaps with all cells. This structure is called a cell cluster. Within each cell or macrocell, one or more carrier frequencies are activated, and over each carrier a TDMA frame of Tf = 60/13 ms is defined, comprising eight slots of 15/26 ms each. A circuit (or channel) is defined by a slot position in the TDMA frame, and by a carrier frequency. Since some channels must be allocated for signaling, each carrier frequency can devote to the transmission of end user information from 6 to 8 channels, depending on the cell configuration; we will assume that the TDMA frame allocates seven slots to end users and one slot to signaling. In the model development, we assume that in the considered cell cluster the macrocell is equipped with N(M) user traffic channels, while each cell is equipped with N user traffic channels. We consider two services: telephony and data transfer. Telephony provisioning relies on the usual circuit-based GSM service; data packets are instead transferred according to the GPRS standard, using the same resources deployed for telephony. Based on the provider strategic decisions, different channel allocation policies can be adopted for the simultaneous delivery of telephony and data transfer services. In this paper we consider three different strategies, and we compare their performance. We focus on the telephone call blocking probability (where call blocking may result from the lack of channels to allocate either a new call request or a handover request) as the main QoS parameter for the telephony service. The main QoS parameters for the data transfer service are the data packet loss probability and average data packet transfer delay. The first channel allocation policy is the result of strategic decisions that acknowledge the primary role of the telephony service (telecommunications network operators today still generate most of their
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revenues through voice services). Telephone calls are set up as long as at least one channel is available in the cell of interest. As a consequence, data packets can be transmitted only over the channels which are not used by voice connections. This policy will be called voice priority. A different channel allocation policy is necessary when the telecommunications services provider desires to guarantee at least a minimum QoS level to the data service. In this case, a fixed number R of channels can be reserved to data transfers, while all remaining channels are shared by voice and data connections, with priority to voice. The improvement in the QoS provided to data is obtained at the cost of reducing the resources available for telephony, thus a performance degradation for voice is expected. This policy will be called R-reservation. A yet different channel allocation policy is necessary when the telecommunications service provider expects that the introduction of GPRS may involve a small number of users only, so that a static channel reservation may result in an inefficient use of radio resources, but still some QoS must be provided to data services users. In this scenario, it may happen that during long time intervals no data transfers are required. It is then convenient to dynamically (rather than statically) reserve channels on the basis of the actual data traffic load. This policy will be called dynamic reservation. The decision about when to start reserving channels to data users can exploit a threshold mechanism based on the occupancy of the transmission buffer which stores GPRS packets. In a hierarchical cellular structure, different policies may be employed at different levels of the hierarchy. For the sake of simplicity, we will consider the following scenario. Voice and data services coexist at the microcellular level only, where one of the policies mentioned above is adopted. Macrocell resources, instead, are employed exclusively for voice traffic, and, in particular, they collect the overflow traffic from the microcellular level. Clearly, the models that we describe in this paper can be easily extended to consider other strategies as well. The telecommunications system we consider supports user mobility. Users can roam from a cell to a neighboring cell during active voice calls: an active user (i.e., a user that has established a voice or data call) that roams from a cell to another, must execute a handover procedure transferring the call from the channel in the old cell to a channel in the new cell without interrupting the communication. If no channel is available in the new cell entered by the user, the system attempts to establish the connection employing a macrocell channel. If no channel is available in the macrocell either, the handover fails, and the call must be terminated (or dropped). Since the duration of a data transfer is typically much shorter than the time spent by a user in a cell, we neglect the possibility that a user requests a handover procedure while transferring data. We instead account for handovers of voice connections. As is normally done when modeling cellular telephony systems, we consider one cell at a time [1], and we neglect the impact of signaling (we neglect signaling delays and connection losses due to signaling, but we account for signaling channels). Moreover, in order to model the system, we introduce the assumptions discussed below. As customary in models of telephone systems, we assume that the sequence of new call requests follows a Poisson process with rate λ, and that the duration of calls is an exponentially distributed random variable with mean 1/µ. We also assume that incoming handover requests follow a Poisson process, whose rate is equal to λh (λh is derived by balancing the incoming and outgoing handover flows, as explained below). Thus, the voice call arrival process is Poisson with rate λ v = λ + λh .
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time
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Fig. 1. Model of GPRS traffic: a packet session.
The time spent by a user within a cell (which is normally called dwell time) is assumed to be exponentially distributed with mean 1/µh and 1/µ(M) h , respectively, for mobility within a cell and a macrocell. The call activity time within a cell (the channel holding time) is thus a random variable with negative exponential distribution with rate µv = µh + µ in the cell, and µ(M) = µ(M) + µ in the macrocell. v h Note that exponential assumptions are generally considered not to be critical in telephony models: telephone systems have been dimensioned using exponential assumptions for almost a century. More recently, these assumptions were used in modeling wireless systems [2–6]. GPRS was conceived for the transfer of packets over a GSM infrastructure, with a simplified allocation of resources over the wireless link, and an IP transport among additional elements of the wired GSM network. In order to cross the wireless link, IP packets are fragmented in radio blocks, that are transmitted in four slots in identical positions within consecutive GSM frames over the same carrier frequency. Depending on the length of the IP packet, the number of radio blocks necessary for the transfer may vary. The allocation of the radio link to radio block transmissions can either use dedicated resources for signaling, or (more usually) the same signaling resources that are available for telephony. In order to describe the GPRS traffic, we adopt the On–Off model of Internet traffic defined by the 3GPP (3rd Generation Partnership Project) in [7]; a sketch of the GPRS traffic model that we use is shown in Fig. 1. Active users within a cell execute a packet session, which is an alternating sequence of packet calls and reading times. According to [7], the number of packet calls within a packet session can be described by a geometrically distributed random variable; however, since we will study the system behavior for a fixed number D of concurrently active packet sessions, we will assume that packet sessions remain active for an indefinite amount of time. The reading time between packet calls is an exponentially distributed random variable with rate µR . Each packet call comprises a geometrically distributed number of packets with mean value NP ; the interarrival time between packets in a packet call is an exponentially distributed random variable with rate µD . According to [7], we shall assume 1/µR = 41.2, NP = 25 and 1/µD = 0.5, all times being expressed in seconds. The average packet call duration, 1/µC , is equal to the average packet interarrival time multiplied by the average number of packets generated during a packet call, so that µC = µD /NP . According to [7], the packet size in radio blocks can have a number of different distributions, some with heavy tail. In our model, for the sake of simplicity, the packet size is equal to either 1 or P radio blocks, with the same probability. Other discrete distributions could be easily introduced in our models in order to approximate heavy tailed distributions of the packet size. The transfer of radio blocks over the radio channel can either be successful, thus allowing the removal of the radio block from the buffer, or result in a failure due to noise, fading, or shadowing. In the latter case, radio block transmissions must be repeated. These events are modeled by a random choice: with probability c a radio block transfer is successful, and with probability 1 − c it fails.
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3. Related work Many papers in the literature propose and analyze channel reservation schemes. In the context of cellular networks, channel reservation is typically proposed in order to favor handover requests over new call requests in accessing the system resources, see for example, [8–12]. The rationale behind the idea of channel reservation for handovers is that the forced termination of an active call has a much worse impact on the QoS perceived by the user than the failure in a new connection set up. Some schemes account also for the introduction of traffic classes with different bandwidth requirements and QoS constraints, see for example, [13–16]. The possibility to dynamically degrade the service is considered in [17]. In [18], four channel allocation schemes are proposed for GPRS systems dealing with voice and data transmission requests, with the assumption that voice calls can be queued while waiting for a packet transmission to complete. A continuous-time Markovian model similar to the one proposed here for the R-reservation scheme is presented in [19]. While the idea of static and dynamic channel reservation was widely investigated in the literature, in this paper we propose a dynamic scheme based on a threshold mechanism on the data packet buffer occupancy. In order to evaluate and possibly compare the performance of the three considered schemes (the traditional voice priority, R-reservation and the proposed dynamic reservation) we develop a Markovian model of the system. Since the model explicitly accounts for the radio block buffer occupancy, it can be used to assess the QoS perceived by data service users. The model is flexible and simple enough to be easily adapted to describe the three considered schemes.
4. Analytical model In describing the analytical model, we first focus on the model of a single cell which adopts the voice priority channel allocation policy. We then describe how to derive, from the model of a cell, the behavior of the system which includes the hierarchical cell structure. Finally, we present the extensions to be introduced in the model in order to deal with the other considered channel allocation policies. 4.1. Model of a cell Each cell can be modeled by a queue with N servers, which represent the N available channels. Two classes of customers enter the queue. Customers in the first class represent voice connections. They arrive at the system according to a Poisson process with parameter λv and require a negative exponential service time with rate µv ; these users do not queue waiting for service: if no channel is available to set up the connection, i.e., if no server is free when the customer joins the queue, the request fails, and the customer is lost. The second class of customers represents GPRS radio blocks. The GPRS traffic representation in Fig. 1, is an On–Off traffic source. The time spent in state Off represents the reading time, while state On describes packet calls. In the latter state the GPRS user generates packets according to a Poisson process with rate µD . Packets can be short or long, with the same probability; a short packet is composed of one radio block, a long packet is segmented into P radio blocks. Radio blocks are queued waiting to be served in a transmission buffer whose capacity is equal to B radio blocks.
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A radio block is transmitted over the wireless link if a channel is available (i.e., it is not used by voice connections), hence if a server is idle. The radio block is removed from the buffer if the transmission is successful, with probability c. In the analytical model we assume that the transmission time of a radio block is a random variable with negative exponential distribution with mean value equal to four GSM frames, 1/γ = 4Tf . Of course, the radio block transmission time is constant and equal to 4Tf , rather than exponential. However, the impact of this assumption on the system performance was shown to be very limited, due to the variability introduced by the possible retransmissions. This phenomenon was studied in [20] by comparing the results obtained from a model which includes the exponential assumption for radio block transmission times against the results obtained from a discrete time model with constant radio block transmission times. The exponential assumption was observed to produce quite accurate results. Given the assumptions introduced above, we develop a continuous-time Markov chain (CTMC) model of the system, whose state is defined as s = (d, b, v), where 1. d is the number of active packet calls, d varies between 0 and the number of data sessions, D; 2. b is the number of radio blocks in the buffer, b varies between 0 and the buffer capacity, B; 3. v is the number of active voice calls, v varies between 0 and the number of channels in the cell, N. Let S be the state space of the CTMC model. The number of states in S is equal to (D + 1)(B + 1)(N + 1). Transitions from state s to all possible successor states are reported in Table 1 together with their rates and, possibly, with the condition under which the transitions exist; the last column indicates the type of event to which a transition refers. Changes of the state variable v are determined by the dynamics of voice connections. The state variable d increases when a GPRS packet call begins, and decreases when a packet call terminates. Whenever a packet is generated, the buffer occupancy b increases by one or P radio blocks, depending on the packet size. When no free positions are available in the buffer, some radio blocks are lost. Finally, transitions reported in the last row of the table refer to the removal of radio blocks from the buffer. A radio block is successfully transmitted with rate cγ. The factor r accounts for the number of radio blocks which can be transmitted during the same set of four frames; radio blocks are transmitted employing all the resources not used by voice connections: N − v channels are used if at least N − v radio blocks are in the buffer. Using standard techniques for the solution of Markov chains, we compute the steady-state probabilities of the CTMC. Let π(s) be the steady-state probability of state s (we will also use the notation π(d, b, v) for π(s)). The value of the arrival rate of incoming handover requests, λh , as in (1) is derived by balancing incoming and outgoing handover flows for voice users in a fixed point procedure. The outgoing handover Table 1 Transitions from state s = (d, b, v) to successor state t for the voice priority policy Successor state t
Condition
Rate
Event
(d, b, v + 1) (d, b, v − 1) (d + 1, b, v) (d − 1, b, v) (d, b + 1, v)
v
λv vµv (D − d)µR dµC 1 dµD 2
A voice call arrives A voice call completes A packet call starts A packet call terminates A short IP packet is generated
(d, β, v) (d, b − 1, v)
β = min(b + P, B) and b < B r = min(N − v, b) and b > 0
1 dµD 2 rcγ
A long IP packet is generated A radio block leaves the buffer
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flow is computed as λ(out) h
B D N = vµh π(d, b, v). v=1 d=0 b=0
The approach of using a fixed point procedure to compute incoming handover flows was widely used in the literature for the analysis of cellular systems, see for example, [2,3,6]. From the π(s)’s some interesting performance metrics can be computed. The offered radio block traffic O (which does not depend on the π(s)’s) is given by O = 21 (P + 1)µD
DµR , µC + µR
where the last term is the average number of active packet calls. Given O, the probability that a radio block is lost due to buffer overflow can be computed as N D B D N 1 Ld = (P − B + b)dµD π(d, b, v) + dµD π(d, B, v) , (2) 2O v=0 d=1 b=B−P+1 v=0 d=1 where the first sum refers to the arrival rate of long IP packets composed of P radio blocks, and the second sum refers to the arrival rate of short IP packets composed of one radio block only. With a different distribution of the IP packet size, a sum is necessary for each possible value of the number of radio blocks in which an IP packet can be segmented. The radio block throughput is X = O(1 − Ld ).
(3)
The average buffer occupancy in radio block is computed from E[b] =
D B N bπ(d, b, v)
(4)
v=0 d=0 b=1
and, by Little’s law, the average delay perceived by radio blocks is E[b] E[T ] = . X We can also evaluate the average buffer occupancy given that v voice calls are active: D B b=1 bπ(d, b, v) E[b|v] = d=0 . D B d=0 b=0 π(d, b, v)
(5)
(6)
The voice call blocking probability at the microcell is given by the probability that all channels are busy with voice connections: B D Pv = π(d, b, N). (7) d=0 b=0
Observe that, since we are considering the voice priority channel allocation policy, the presence of data traffic is transparent to voice users; thus, Pv can also be computed by simply applying the Erlang-B formula.
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The probability Pv represents also the probability that a voice call overflows to the macrocell. The average rate of voice call requests which are refused and overflow to the macrocell is fo = λv Pv .
(8)
4.2. Model of the cell cluster From the model of a cell we can develop a complete model to analyze the performance of clusters of cells. In our two-level hierarchical structure, macrocells are used only to accommodate the voice overflow traffic from microcells. We assume that the arrival process at the macrocell is Poisson with rate, δ = mfo , where m is the number of microcells in the cell cluster, and f0 the overflow traffic computed as in (8). It should be noted that overflow traffic is known to be much burstier that Poisson; however, the traffic that reaches the macrocell is the result of the superposition of a number of individual bursty overflow flows. It has been shown that the overall arrival process at the macrocell in this case can be well-approximated by a Poisson process even with a small number of cells [6]. Assuming that the user dwell time in the cell under consideration is a random variable with negative (M) exponential distribution with rate µ(M) /0 queue with service h , the macrocell can be modeled as a M/M/N (M) rate µ + µh . The steady-state probability π(i) that i channels are busy is (M) −1 N i ρj ρ , π(i) = π(0) and π(0) = (9) i! j! j=0 where ρ = δ/(µ + µ(M) h ). The voice call blocking probability at the macrocell, Pv(M) , is given by the Erlang-B formula, and it is equal to the probability π(N(M) ) that all channels are busy. A voice call is blocked and lost if both in the microcell and in the macrocell no channels are available; this happens with probability Lv = Pv Pv(M) .
(10)
4.3. R-reservation policy We describe in this section how the proposed model can be extended in order to describe the R-reservation channel allocation policy. As already mentioned, in a cell which adopts the R-reservation policy, R channels are reserved to data traffic, while the remaining N − R channels are shared between voice and data traffic, with priority to voice. The Markovian model introduced in Section 4.1 can be used also to describe the behavior of a cell adopting the R-reservation policy. The only difference is that under the R-reservation channel allocation policy, no more than N − R voice calls can be accepted. Therefore, under the R-reservation channel allocation policy, the state variable v ranges from 0 to N − R, and, correspondingly, the transition in the first row of Table 1 is possible only under the condition that v < N − R. Consider now the radio block service rate r, as defined in the last row of Table 1. When there are enough radio blocks in the buffer,
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since the maximum number of active voice calls is now N − R, the smallest value of the parameter r is equal to R. The minimum data service is thus guaranteed by R channels. The state space cardinality in this case reduces to (D + 1)(B + 1)(N − R + 1). As we will observe by means of numerical results in Section 5, the adoption of the R-reservation channel allocation policy implies an improvement of the QoS of the data transfer service. The cost of this improvement is paid in terms of a QoS deterioration of the telephony service. The voice call blocking probability in the microcell is in this case: Pv =
B D π(d, b, N − R)
(11)
d=0 b=0
which is larger than for the voice priority policy. 4.4. Dynamic reservation policy The dynamic reservation channel allocation policy infers the presence of data users activity and of potential data service QoS deterioration by means of the current buffer occupancy. When the buffer is underutilized, the voice priority policy is adopted. When buffer occupancy grows above a threshold, Th , the R-reservation policy is applied, instead. In the latter case, voice requests are accepted as long as no more than N −R channels are used for the voice service. Moreover, if the threshold is reached while more than N − R voice connections are already active, some voice calls which are active in the cell are forced to move to the macrocell by means of a forced handover procedure. The CTMC describing this system has the same state variable as in previous models. States with a number of active voice calls v larger than N − R and a buffer occupancy b larger than Th are impossible. Thus, the state space cardinality is now equal to (D + 1)[(B − Th )(N − R + 1) + (Th + 1)(N + 1)]. The rate of transitions between states are reported in Table 2. Observe that radio block generations, besides causing changes in the buffer occupancy, may also induce changes in the number of active voice calls, due to the threshold mechanism. Table 2 Transitions from state s = (d, b, v) to successor state t for the dynamic reservation policy Successor state t
Condition
Rate
Event
(d, b, v + 1)
λv
A voice call arrives
(d, b, v − 1) (d + 1, b, v) (d − 1, b, v) (d, b + 1, v)
(v < N ∧ b ≤ Th ) ∨ (v < N − R ∧ b > Th ) v>0 d
vµv (D − d)µR dµC 1 dµD 2
A voice call completes A packet call starts A packet call terminates A short IP packet, no forced handovers
(d, b + 1, N − R)
b = Th ∧ v > N − R
A short IP packet, forced handovers
(d, β, v)
β = min(b + P, B) and v ≤ N − R ∨ b < Th − P + 1 β = min(b + P, B) and T h − P + 1 ≤ b ≤ Th ∧ v > N −R r = min(N − v, b)
1 dµD 2 1 dµD 2 1 dµD 2
A long IP packet, forced handovers
rcγ
A radio block leaves the buffer
(d, β, N − R) (d, b − 1, v)
A long IP packet, no forced handovers
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The performance perceived by telephony users is now measured in terms of blocking probability as well probability that a forced handover occurs. The voice blocking probability in the microcell is computed as Th D B π(d, b, N) + Pv = π(d, b, N − R) . (12) d=0
b=0
b=Th +1
The rate of forced handovers toward the macrocell is given by the arrival rate of the packets which make the radio block buffer occupancy grow above the threshold when the number of active voice calls is larger than N − R: Th N D 1 fh = dµD (v − N + R) π(d, Th , v) + π(d, b, v) (13) 2 d=1 v=N−R+1 b=T −P+1 h
and the probability of forced handover is Ph =
fh . λv (1 − Pv )
(14)
5. Numerical results In this section we present some numerical results to assess the relative merits of the different channel allocation policies. We first focus on the voice priority scheme performance at the cell level, discussing the interaction between voice and data traffic. Then, we evaluate the performance of the dynamic reservation policy. Finally, we compare the performance of the three resource management schemes described above: voice priority, R-reservation and dynamic reservation. For the derivation of numerical results we always use the traffic and system parameter values which are summarized in Table 3, unless otherwise specified. 5.1. Voice priority scheme Fig. 2 shows the voice call blocking probability Pv (dashed line) and the radio block loss probability Ld (solid lines) versus the voice traffic load, which is defined as λv /(µ+µh ). The radio block loss probability Ld is plotted for different values of the number of active sessions, D. Under the voice priority scheme, the voice call blocking probability is insensitive to data traffic; instead, the radio block loss probability increases with the number of data sources, since higher number of data sources translate into higher data traffic. In general, the results in Fig. 2 show that the radio block loss probability Ld can be rather high, unless the voice traffic load remains quite low (a radio block loss probability of about 1% is obtained when the cell loading factor is below 50%—less than three channels are used on the average, of the seven available in the cell). The average delay perceived by radio blocks, E[T] is presented in Fig. 3, for the same scenario of Fig. 2, for either 2 or 6 active data sessions. It can be observed that the delay suffered by radio blocks is quite large. This is due to the priority of voice traffic, and to the low bit rate of the radio channel. It thus appears that the QoS that can be offered to data users in a cell with the considered characteristics
M. Meo, M. Ajmone Marsan / Performance Evaluation 56 (2004) 73–92 Table 3 Parameters of the basic scenario Parameter
Value
No. of traffic channels in the cells, N No. of channels reserved to data, R No. of traffic channels in the macrocell, N(M) No. of microcells in a cluster, m 1/µ µh µ(M) h Buffer size, B No. of packet sessions, D Maximum number of radio blocks per packet, P NP 1/µD 1/µR c
7 1 14 19 180 s µ/2 /8 100 1, . . . , 6 16 25 0.5 s 41.2 s 0.95
Blocking and loss probability
1.0e-01
1.0e-02 voice data D=2 D=4 D=6 1.0e-03
2
2.5
3 3.5 Voice traffic load
4
Fig. 2. Voice priority. Voice blocking probability Pv and radio block loss probability Ld versus voice traffic load.
Average radio block delay [s]
1.0e+01
1.0e+00
D=2 D=6 1.0e-01 2
2.5
3
3.5
4
Voice traffic load
Fig. 3. Voice priority. Average radio block delay versus voice traffic load.
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Average buffer occupancy
1.0e+01
1.0e+00
D=2 D=6 1.0e-01
2
2.5
3 3.5 Voice traffic load
4
Fig. 4. Voice priority. Average radio block buffer occupancy versus voice traffic load.
is rather poor, even when the number of users is small, unless the voice traffic load is quite low. However, this behavior deserves further investigation, since the average bandwidth available to data (i.e., the bandwidth unused by voice) should be sufficient to satisfy the needs of a non-trivially small number of data users. By investigating further, we find a surprising result concerning the length of the queue of radio blocks. Indeed, even if the value of the radio block loss probability was observed to be rather large, the average radio block buffer occupancy is quite small, as can be noted from Fig. 4, again for 2 or 6 active data sessions. For all the considered values of voice traffic load, the average radio block buffer occupancy is always less than 10% (the radio block buffer size is 100, and the average queue length is always less than 10). This behavior means that the radio block buffer is almost always empty, but then something happens that fills up the buffer and causes the buffer to overflow. The responsibility for the buffer overflow is not in the burstiness of the data traffic; rather, it resides in the fact that voice has priority over data and in the different time scales of data and voice traffic. Indeed, the radio block service rate depends on the voice calls dynamics and, in particular, when all channels in the cell are busy with voice connections, no radio block can be transmitted over the radio channel: the data service is thus interrupted until at least one channel becomes available. During these intervals of service interruption, which are quite long compared to data traffic dynamics, the radio block buffer fills up, and a large number of radio blocks are lost. The fact that the radio block loss probability is dominated by the service interruption phenomenon is confirmed by Fig. 5, which shows the average buffer occupancy conditional on the number of active voice connections, versus the number of active voice connections, v, for different number of data traffic sources, D. The average buffer occupancy is quite small when at least one channel is available to serve data traffic (points with v < 7 in the figure), but becomes very close to the buffer size when all channels in the cell are used by voice connections (v = 7). Clearly, the radio block loss probability is dominated by the losses occurring during intervals with v = 7. Observe also that the average buffer occupancy conditional on seven active voice calls is so close to the buffer size that it varies only marginally with the number D of data traffic sources (this also explains why the data loss probability only marginally increases with the number of data sources, as shown in Fig. 2). These results clearly indicate that, in order to be able to provide data users with reasonable QoS guarantees, the adoption of a channel allocation scheme which gives priority to voice over data is not acceptable.
Average conditional buffer occupancy
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1.0e+02 D=1 D=2 D=3 D=4 D=5 D=6
1.0e+01
1.0e+00
1.0e-01
0
1
2 3 4 5 6 Number of active voice calls
7
Fig. 5. Voice priority. Radio block buffer occupancy conditional on the number of active voice calls.
This observation motivated our definition of the different channel allocation policies that were described before, where some fraction of the cell resources is reserved for data services. Moreover, since the reservation of a fixed number of channels to data may affect the voice service QoS too negatively (even in periods in which the need for the allocation of resources to data services is not pressing), we devised the dynamic reservation scheme, that allocates resources to data only when the risk of QoS degradation becomes compelling. We thus expect the dynamic reservation scheme to be quite effective in improving the QoS provided to data traffic, while having just a mildly negative impact on voice. The impact of channel reservation on voice service will be assessed later. 5.2. Dynamic reservation scheme Fig. 6 reports the radio block loss probability versus the voice traffic load when the dynamic reservation scheme is adopted with threshold equal to 70 or 80 on a buffer whose capacity is equal to 100 radio blocks. Three different values of data traffic load are considered, corresponding to 2, 4 and 6 data traffic sources. Clearly, the radio block loss probability increases with voice traffic, and with data traffic as well. By
Radio block loss probability
1.0e-01 1.0e-02 1.0e-03 D=2 D=4 D=6 Th=80 Th=70
1.0e-04 1.0e-05
2
2.5
3
3.5 4 4.5 Voice traffic load
5
5.5
6
Fig. 6. Dynamic reservation policy. Radio block loss probability Ld versus voice traffic load for different values of the threshold and of the number of data sources.
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Average buffer occupancy
1.0e+02
1.0e+01
D=2 D=4 D=6 Th=80 Th=70
1.0e+00
1.0e-01
2
2.5
3
3.5 4 4.5 Voice traffic load
5
5.5
6
Fig. 7. Dynamic reservation policy. Average radio block buffer occupancy versus voice traffic load for different values of the threshold and of the number of data sources.
letting the threshold decrease from 80 to 70 we make the dynamic allocation to data traffic more prompt and we thus obtain a reduction of the loss probability. The average buffer occupancy is reported in Fig. 7 for the same scenarios as Fig. 6. The behavior of the average buffer occupancy is similar to that of the radio block loss probability: increases of voice or data traffic load cause increases of the buffer occupancy. Small values of the threshold correspond to reactive schemes which make a radio resource become available early as the buffer starts filling; thus, lower values of the threshold correspond to lower buffer occupancy. The average radio block delay is shown in Fig. 8. As expected, the average delay increases with voice traffic load. On the contrary, it slightly decreases with the number D of data sources. This behavior is due to the following reason. For larger values of D, the buffer fills and reaches the threshold faster; as soon as the threshold is reached, a channel becomes available to data traffic and radio blocks start to be served and removed from the buffer. A further performance parameter to be taken into account when discussing the dynamic reservation policy, is the probability that a voice call which is active in a microcell, is forced to move to a channel in the macrocell, in order to prevent data service interruption, when the buffer occupancy reaches the threshold Th . We call this event a forced handover. The probability Ph of a forced handover is plotted in Average radio block delay [s]
0.70 0.60 0.50 0.40 0.30
D=2 D=4 D=6 Th=80 Th=70
0.20 0.10 0.00
2
2.5
3
3.5 4 4.5 Voice traffic load
5
5.5
6
Fig. 8. Dynamic reservation policy. Average radio block delay versus voice traffic load for different values of the threshold and of the number of data sources.
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Forced handover probability
1.0e+00
1.0e-01
D=2 D=4 D=6 Th=80 Th=70
1.0e-02
1.0e-03
2
2.5
3
3.5 4 4.5 Voice traffic load
5
5.5
6
Fig. 9. Dynamic reservation policy. Probability that an active voice call undergoes forced handover Ph versus voice traffic load for different values of the threshold and of the number of data sources.
Fig. 9 for the dynamic reservation policy, again with Th equal to 70 or 80, and D equal to 2, 4 or 6. It is interesting to observe that Ph can be rather large, of the order of a few percentage points; this may be a drawback of the dynamic reservation policy. The availability of a tunable parameter, the threshold Th , which allows the cell performance to be tightly controlled, makes the dynamic reservation policy very attractive also from the network management point of view. In Figs. 10 and 11 we show how the threshold Th influences the radio block loss probability and the average radio block delay, respectively. Three values of the voice traffic load are considered: 2.4, 3.0 and 4.0 for 2 or 4 data sources. The availability of these results can provide the starting point for the possibly dynamic management of the cell resources through the threshold value. 5.3. Comparisons between different policies In this section we compare the three resource management policies considered in this paper: voice priority, R-reservation (with R = 1) and dynamic reservation. For all comparisons we consider D = 4 active data sessions. Fig. 12 reports the radio block loss probability. The highest curve refers to the voice priority scheme, the lowest curve refers to R-reservation. By comparing the results of these two schemes, we can conclude Radio block loss probability
1.0e-02
1.0e-03
1.0e-04
1.0e-05
D=4 D=2 voice load=4.0 voice load=3.0 voice load=2.4 30 35 40 45 50 55 60 65 70 75 80 Threshold
Fig. 10. Dynamic reservation. Radio block loss probability Ld versus threshold Th for different values of voice traffic load.
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Average radio block delay [s]
88
0.35 voice load=4.0 voice load=3.0 0.30 voice load=2.4 D=4 D=2 0.25 0.20 0.15 0.10 0.05 30
35
40
45
50 55 60 Threshold
65
70
75
80
Fig. 11. Dynamic reservation. Average radio block delay versus threshold Th for different values of voice traffic load.
that the reservation of channels for data services has a profound impact on the data loss probability, which improves drastically, dropping by about three orders of magnitude. Results for the dynamic channel reservation scheme vary between the two curves of the voice priority scheme and of the R-reservation scheme, depending on the value of the threshold Th . The dynamic reservation scheme avoids data service interruption by reserving a channel only when the buffer occupancy grows above Th , indicating that some radio blocks may soon be lost. Therefore, the dynamic reservation scheme is quite efficient in preventing data losses, and is capable of reducing the radio block loss probability of more than one order of magnitude with respect to voice priority. Similar conclusions can be drawn from another interesting QoS metric, which is the average radio block delay, shown in Fig. 13. Improvements of the average delay of roughly a factor 4 can be achieved by employing the dynamic reservation scheme instead of the voice priority policy. In order to further investigate the different behaviors of the three channel allocation policies, we show in Fig. 14 the average buffer occupancy conditional on the number of active voice calls, versus the number of active voice connections, v. Clearly, in the case of R-reservation policy no more than six voice connections can be active at the same time, so that no result exists for v = 7. The dynamic reservation policy succeeds in controlling the average radio block queue length, producing much smaller values than the voice priority scheme. This is the behavior behind the reduction in the radio block loss probability.
Radio block loss probability
1.0e+00 1.0e-01 1.0e-02 1.0e-03
dynamic Th=70 Th=80 voice pr. 1-res
1.0e-04 1.0e-05
2
2.5
3 3.5 4 Voice traffic load
4.5
5
Fig. 12. Comparison between different policies. Radio block loss probability Ld .
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Average radio block delay [s]
1.6 dynamic Th=70 Th=80 1-res voice pr.
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
2
2.5
3 3.5 4 Voice traffic load
4.5
5
Average conditional buffer occupancy
Fig. 13. Comparison between different policies. Average radio block delay.
1.0e+02 dynamic Th=70 Th=80 1-res voice pr.
1.0e+01
1.0e+00
1.0e-01
0
1
2 3 4 5 6 Number of active voice calls
7
Fig. 14. Comparison between different policies. Radio block buffer occupancy conditional on the number of active voice calls.
Voice call blocking probability
Of course, any improvement of the QoS obtained in data services must be paid by the voice service QoS, since the amount of cell channels that the two types of services share is fixed. It is thus interesting to quantify the voice service QoS reduction produced by the different channel allocation schemes. Fig. 15 shows the voice blocking probability Lv versus the voice traffic load. Notice that Lv accounts also for the 1.0e-01 dynamic Th=70 Th=80 1-res voice pr.
1.0e-02 1.0e-03 1.0e-04 1.0e-05 1.0e-06
2
2.5
3 3.5 4 Voice traffic load
4.5
5
Fig. 15. Comparison between different policies. Voice blocking probability Lv .
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presence of the macrocell radio channels, which serve voice connections which cannot be served in the microcells. Reserving one channel in microcells to data traffic makes the voice blocking probability increase remarkably (in some cases about two orders of magnitude). Again, the excellent performance of the dynamic reservation scheme can be observed from the graphs: dynamic reservation achieves intermediate performance between voice priority and R-reservation policies, and offers a very effective and flexible tradeoff between the needs to guarantee access to voice connections and to provide QoS to data traffic. From the numerical results that we have obtained, we can conclude that the dynamic reservation policy is a very interesting scheme for the effective provision of controlled QoS to both voice and data services.
6. Conclusions In this paper we have investigated channel allocation policies for GSM/GPRS cellular networks offering not only mobile telephony services, but also data services for the wireless access to the Internet. Three different alternatives were described, developing simple Markovian models for the assessment of their relative merits. Numerical results showed that the voice priority policy, that gives priority to voice in the access to radio channels, cannot provide acceptable performance to data services. The R-reservation policy, that statically reserves a fixed number of channels to data services, was shown to drastically improve their performance, but to exact a rather high toll in terms of the voice services QoS. This is specially annoying because this policy subtracts resources from voice users even when these are not needed for data, thus inducing an unnecessary performance degradation for voice services. Instead, the dynamic reservation policy, that dynamically allocates channels to data only when necessary, using the information about the queue length of GPRS data units within the base station, was shown to provide very effective performance tradeoffs for data and voice services, with the additional advantage of being easily managed through the setting of the threshold value that triggers the dynamic allocation of channels to data. A further advantage of the dynamic reservation scheme is the fact that it tries to allow a full exploitation of the system resources by voice traffic when no data traffic is present, but it gradually allocates resources to data, so as to guarantee the data services QoS. This may be an extremely attractive feature of the scheme in a scenario where wireless network operators generate most of their revenues with voice services, but are eager to carry data traffic with acceptable QoS, so as to be able to open a new market of mobile data services for the wireless access to the Internet.
Acknowledgements The authors would like to thank Cecilia Batetta for deriving some of the results presented in this paper. References [1] M. Ajmone Marsan, G. De Carolis, E. Leonardi, R. Lo Cigno, M. Meo, How many cells should be considered to accurately predict the performance of cellular networks?, in: Proceedings of the European Wireless’99 and Fourth ITG Mobile Communications, Munich, Germany, October 1999.
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Michela Meo received the Dr.Ing. degree in electronic engineering in 1993, and the Ph.D. degree in electronic and telecommunication engineering in 1997, both from Politecnico di Torino, in Italy. Since then she has been working in the Telecommunication Networks Research Group of the Politecnico di Torino, where she is currently an assistant professor. Her research interests are in the field of performance evaluation of communication networks with a particular focus on wireless systems and end-to-end performance.
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Marco Ajmone Marsan is a full professor at the Electronics Department of Politecnico di Torino, in Italy, and the director of the Institute for Electronics, Information Engineering and Telecommunications of the National Research Council. He holds degrees in electronic engineering from Politecnico di Torino and University of California, Los Angeles. He has coauthored over 300 journal and conference papers in the areas of communications and computer science, as well as the two books “Performance Models of Multiprocessor Systems” published by the MIT Press, and “Modelling with Generalized Stochastic Petri Nets” published by John Wiley. He received the best paper award at the Third International Conference on Distributed Computing Systems in Miami, FL, in 1982. In 2002 he was awarded a “Honoris Causa” degree in Telecommunication Networks from the Budapest University of Technology and Economics. His current interests are in the fields of performance evaluation of communication networks and their protocols. He is a fellow of IEEE, and a corresponding member of the Academy of Sciences of Torino. He participates in a number of editorial boards of international journals, including the IEEE/ACM Transactions on Networking.