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data networks
Computer Communications 25 (2002) 1653±1664
www.elsevier.com/locate/comcom
Joint call admission control/congestion control for wireless integrated voice/data networks Shun-Ping Chung*, Chin-Lien Chiu Department of Electrical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei, Taiwan, ROC Received 11 October 2001; revised 19 December 2001; accepted 29 January 2002
Abstract We consider wireless communication systems supporting both voice and data services, where not only call admission control (CAC) is used to maintain quality of service (QoS) at the call level, but also congestion control is used to guarantee QoS at the packet level. The CAC adopted is a simple threshold scheme, i.e. the number of voice terminals in use cannot exceed a threshold. The congestion control used is a modi®ed version of dynamic time division multiple access with priority-based request packet transmission scheme (D-TDMA/PRPTS), where to avoid excessive delay due to mini-slot contention, voice request packet is dropped if it cannot succeed in the originating frame. For comparison, two scenarios involving only the voice traf®c are considered: dynamic and static. In dynamic scenarios, the number of ongoing voice calls may vary over time, whereas that in static scenarios, it is ®xed. With appropriate Markovian models, the voice packet loss probability, voice call blocking probability and channel utilization of voice traf®c are derived, and the analytical results are veri®ed with the simulation results. For integrated voice/data traf®c, due to the mathematical complexity, only computer simulation is used to evaluate the effect of proposed CAC and congestion control on the performance measures of both voice and data traf®c. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Call admission control; Congestion control; Call blocking probability; Packet loss probability; Channel utilization
1. Introduction Future wireless personal communication networks are expected to provide users a way to communicate with anyone in any place at any point of time. The information transmitted may include voice, video, and data [1]. Different kinds of information have different transmission characteristics and quality of service (QoS) requirements. Generally speaking, real-time voice and video are delay-sensitive but loss-insensitive. In other words, if the delay of one voice packet exceeds a threshold, that packet is of no use and can be dropped. Non-real-time data is delay-insensitive but losssensitive. It is also worth noting that a call may have QoS requirements at different time levels. For example, the call blocking probability at the connection level, and the packet dropping probability and packet average delay at the packet level. All QoS requirements have to be satis®ed. Therefore, how to design an ef®cient media access control to guarantee QoS is an important topic for wireless personal communication systems. More speci®cally, CAC is needed to guarantee * Corresponding author. Tel.: 1886-2273-76703; fax: 1886-227376699. E-mail address: [email protected] (S.-P. Chung).
the QoS at the connection level, while the congestion control is enforced to satisfy the QoS at the packet level. Many media access control schemes for wireless systems with integrated voice and data have been proposed, e.g. circuit-switched time division multiple access [5,6], packet reservation multiple access (PRMA) [7±9], idle signal multiple access for integrated services (I-ISMA) [10], and dynamic TDMA (D-TDMA) [2±4,11±17]. Speci®cally, DTDMA is based on a frame structure, where a frame consists of mini-slots, voice slots, and data slots. The voice slots and data slots are used for voice and data transmission and the mini-slots are used to transmit the request packets, where the request packets contain information needed for the slot reservation. D-TDMA uses slotted ALOHA (S-ALOHA) as the request packet transmission scheme [18]. It is shown in Ref. [19] that a conversational speech can be segmented into talkspurt and silence periods, and the activity factor is less than 50%. Therefore, for using the channel ef®ciently, speech activity detector (SAD) is widely used in the wireline communication system. Gang et al. [18] proposed DTDMA with data steal into voice technique (D-TDMA/ DSV), where voice terminals are allocated channels only when they are in the talkspurt period. When they are in the silence period, the channel is released to others. They
0140-3664/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0140-366 4(02)00050-6
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need to contend a voice slot to transmit the packet by transmitting a request packet in the mini-slots if they enter into the talkspurt period again. Jeong et al. [20] noticed that collisions between the voice request packets and the data request packets cause the packet dropping and thus limit throughput. Therefore, D-TDMA with priority-based request packet transmission scheme (D-TDMA/PRPTS) is proposed in Ref. [20] to give the voice request packets priority over the data request packets. The voice request packets are transmitted preferentially, and the data request packets can be transmitted only after waiting for a certain time limit. This can avoid collision between the voice request packet and the data request packet, and thus reduce the packet dropping probability and enhance the voice capacity. One common drawback of the above schemes is that they do not consider CAC and congestion control at the same time. The congestion control used is Modi®ed DTDMA/PRPTS, with the modi®cation that, to avoid excessive delay due to mini-slot contention, voice request packet is dropped if it cannot succeed in the frame at which it originates. The CAC adopted in this paper is a simple threshold scheme, i.e. the number of voice terminals in use cannot exceed a threshold. The performance measures of interest are the voice packet dropping probability, voice call blocking probability, data average delay, and channel utilization. Due to the increasing demand of capacity and thus the popularity of microcells, the number of ongoing calls in a cell may vary signi®cantly in a short time interval. To explore the time-varying nature of cell occupancy and the interaction of CAC and congestion control, two scenarios are studied: dynamic and static. In dynamic scenarios, the number of ongoing voice calls may vary over time, whereas that in the static scenarios is ®xed. For dynamic and static scenarios involving voice traf®c only, appropriate Markovian models are formulated, analytical results for voice call blocking probability, voice packet dropping probability and channel utilization for voice traf®c are derived, and the analytical results are veri®ed with the simulation results. Last but not the least, for integrated voice/data traf®c, computer simulation is used to evaluate the associated performance measures due to the mathematical complexity. The rest of this paper is organized as follows. In Section 2, we describe the system model. In Section 3, appropriate Markovian models are formulated to derive performance measures of interest for both dynamic and static scenarios involving voice traf®c only. In Section 4, analytical results are veri®ed with simulation results for both dynamic and static scenarios involving voice traf®c only. We also present the simulation results of integrated voice and data traf®c. Some conclusions are drawn in Section 5. 2. System model In this section, the system model in question is described in detail. In the studied wireless system, the service area is
composed of the cells. Every cell includes a base station and many mobile terminals. Every mobile terminal communicates to the base station with a pair of uplink and downlink channels. It uses the frequency division duplex mode. A channel is divided into a series of periodic frames in time. Each frame is subdivided into many slots. Each frame includes three kinds of slots: mini-slots, voice slots, and data slots. The mini-slots are used to transmit connection request packets and reservation request packets. The voice slots are used to transmit the voice packets and the data slots to transmit the data packets. We consider homogeneous system, i.e. all cells are statistically identical. Thus, we can focus on any one particular cell. 2.1. Call level model In the call level model, there are many mobile terminals. Each mobile terminal can generate voice call and data call. The number of ongoing calls may vary due to call completions or mobility, i.e. leaving the cell in question. For simplicity, the effect of mobility is neglected. For comparison purposes, we consider two scenarios: dynamic and static. Dynamic scenarios imply that the number of ongoing voice calls could vary, whereas that for static scenarios is ®xed. It is noted that the number of ongoing data calls is always assumed to be constant. The traf®c model for the dynamic scenarios is described as follows. When a terminal wants to make a voice call, it needs to transmit a connection request to base station via the uplink channel. The base station decides whether to accept this request with CAC. The base station uses the downlink channel to notify the mobile terminal what the decision is. If the request is refused, the call is rejected and cleared. If the request is accepted, the mobile terminal can continue and transmit a reservation request to reserve slots for packet transmission. The voice call arrival process is assumed to be Poisson with an average arrival rate l , and average interarrival time It 1=l: The service time distribution of voice calls is exponentially distributed with mean m . When a voice call is complete, the corresponding voice terminal is referred to as ®nished. 2.2. Call admission control In order to study how the system performance is affected by CAC, a simple threshold CAC is used for the dynamic scenarios. Speci®cally, a voice connection request is accepted if the number of voice connections is less than the voice threshold Vt : Since the number of data connections is ®xed, there is no CAC for data connections. Obviously, the voice threshold has a signi®cant effect on the system performance. When the threshold value increases, the voice blocking probability decreases but packet dropping probability and packet delay of voice and data traf®c becomes worse. Apparently, an appropriate tradeoff is needed.
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2.3. Packet level model We assume that for both voice and data traf®c, the packet level models alternate between the busy state and idle state. The duration of busy (talkspurt) state and the idle (silence) state for voice traf®c is geometrically distributed with mean Tt 1=av and Ts 1=bv ; respectively. The voice traf®c is considered as real time traf®c. If the voice packets cannot transmit successfully within a threshold, they are dropped. For the data traf®c, the duration of busy state and idle state is also geometrically distributed with mean 1=ad and 1=bd ; respectively. The data traf®c is considered as non-real time traf®c. The data packets are never dropped and are queued until they can be transmitted. A voice terminal can be in one of the following three states: silent, contending, and reserved. We assume that all voice terminals begin with the silent state when they start a connection. In the silent state, a voice terminal waits for the arrival of a talkspurt. Upon arrival of a talkspurt, the voice terminal enters the contending state, and transmits a voice request packet with the probability Pv : A voice terminal in the contending state contends with the other voice terminals in the same state to transmit a voice request packet. If there are two or more request packets transmitted in a mini-slot, they collide, and all the collided request packets fail. In other words, a voice request packet transmission is successful only if it is the only one transmitted in the mini-slot in question. All unsuccessful voice terminals continue to contend in the successive mini-slots of the originating frame. If at the end of the originating frame any voice terminal in the contending state is still unsuccessful, that voice terminal returns to the silent state and the associated voice packet is dropped. After a voice terminal wins a mini-slot, it waits for an available voice slot assigned by system to enter the reserved state. A voice terminal in the reserved state uses its reserved voice slot in every frame until its talkspurt terminates. After the last voice packet of the talkspurt is transmitted, the voice terminal returns to the silent state. The state transition diagram is shown in Fig. 1, where the talkspurt to silence transition probability is Pts ; the silence to talkspurt transition probability is Pst ; and the transition probability from contending state to reserved state is P Tf Pts 1 2 exp 2 1 Tt T Pst 1 2 exp 2 f Ts
2
where Tt Ts is the mean duration in the talkspurt (silent) state, and Tf is the frame duration. 2.4. Congestion control We assume that the channel impairments, e.g. noise and interference, do not lead to the packet transmission fail-
Fig. 1. State transition diagram of a voice terminal.
ures, and the only reason of transmission failures is packet collision, and the capture effect is not taken into account, that is, all the collided packets fail. The congestion control we adopted is a modi®ed version of D-TDMA/PRPTS [20]. Fig. 2 shows the associated frame structure. As can be seen, there are three kinds of slots in each frame: mini-slots, voice slots, and data slots. There are Ms mini-slots, Vs voice slots, and Ds data slots per frame, with the number of normal slots Ns Vs 1 Ds : When a terminal wants to send a voice or data packet, ®rstly, it needs to send a request packet via the mini-slots. If more than one request packet is transmitted in the same mini-slot, all those request packets fail. All unsuccessful data terminals retry to send the request packet in the successive mini-slots until it succeeds. For all unsuccessful voice terminals, to avoid unduly long delay and thus low throughput, only a retry in successive mini-slots of the originating frame is allowed. In other words, if one voice request packet cannot transmit successfully after retrying in all the mini-slots of the originating frame, that voice packet is dropped. Upon receipt of the request packet, the base station tries to assign a free slot to the associated terminal. If there are no free slots, the base station refuses the request packet. After a terminal reserves the slot successfully, it can start to transmit the data. The terminal uses the slot until it ®nishes transmitting, and then the slot is released. More importantly, as in the DTDMA/PRPTS, the voice request packets are given priority over the data request packets to reduce the voice packet dropping probability at the expense of fewer mini-slots. Basically, the transmissions of voice request packets begin right at the beginning boundary of a mini-slot. In contrast, data request packets can be transmitted in a mini-slot only after con®rming that there are no voice request packet transmissions in the mini-slot in question. The con®rmation is based on a signaling message from the base station. Obviously, the size of mini-slots with the aforesaid priority scheme is larger than that of mini-slots without that priority scheme.
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3. Mathematical analysis In this section, we formulate appropriate Markovian models to derive the voice call blocking probability, packet dropping probability, and channel utilization for voice traf®c under both dynamic and static scenarios. 3.1. Dynamic scenarios The steady state probability distribution of voice terminals when the number of voice terminals may vary over time is derived in this section. Let random variables Vi ; Ci ; and Ri represent the number of active voice terminals, that of voice terminals in the contending state, that of voice terminals in the reserved state, respectively, at the beginning of the ith frame. Obviously, {Vi ; Ci ; Ri ; i 1; 2; ¼} constitutes a discrete time Markov chain. Let P u; c; r represent the steady state probability when there are u voice terminals in the system, and among those voice terminals, c voice terminals are in the contending state and r voice terminals in the reserved state. Let P u; c; ruv; `; m be the one-step transition probability. First, let us focus on P u; c; ruv; c; r which is the conditional probability that the number of active voice terminals changes from v to u, with the other parameters remaining ®xed. Since the frame time is much less than the average call interarrival time and average call service time, we assume that no more than one arrival or departure can occur within one frame time. Let Pa i represent the probability that one voice call arrives within one frame time when there are i voice calls in progress. Let Pd i represent the probability that one voice call departs within one frame time when there are i voice calls in progress. It is easy to show that ( 1 2 e2lTf 0 # i # Vt 2 1 Pa i 3 0 i Vt ! i Pd i 1 2 e2mTf e2 i21mTf 0 # i # Vt 4 i21 Therefore,
Fig. 2. The associated frame structure.
where the random variable Si denotes the number of voice terminals which contend successfully during the ith frame, and Ms is the number of mini-slots in each frame. Speci®cally, n must not be less than the increment of the number of voice terminals in the reserved state, and must not be greater than the original number of voice terminals in the contending state and the number of mini-slots per frame. In Eq. (6), P v; c; ruv; `; m is expressed as the summation of the products of two conditional probabilities, with the additional condition being the number of terminals that win the contention during the current frame. ! m1n P{v; c; ruv; `; m; Si n} Pts m1n2r 1 m1n2r 2 Pts r Pc where Pc
c X v2`2m t0
P v; c; ruv; `; m P{Vi11 v; Ci11 c; Ri11 ruVi v; Ci `; Ri m}
min `;M X s nmax r 2 m;0
P{v; c; ruv; `; m; Si n}P{Si nuv; `; m}
6
c2t
! Ptst 1 2 Pst v2`2m2t
Pts`2n2c2t 1 2 Pts c2t
In Eq. (7), P{v; c; ruv; `; m; Si n} is expressed as the product of the probability that m 1 n 2 r out of m 1 n terminals in the reserved state return to the silent state and the probability that t out of v 2 ` 2 m terminals in the
8 P{Vi11 j; Ci11 c; Ri11 ruVi i; Ci c; Ri r} > > > > > > > Pa i; < P j; c; rui; c; r Pd i; > > > > 1 2 Pa i 2 Pd i; > > > : 0; It is noted that Pa Vt 0 and Pd 0 0: Second, the conditional probability P v; c; ruv; `; m is computed as follows
`2n
t !
7
j i 1 1; 0 # i # Vt j i 2 1; 0 # i # Vt
5
j i; 0 # i # Vt otherwise
silent state enter the contending state and c 2 t out of ` 2 n terminals in the contending state remain in the contending state for 0 # t # c: In Eq. (6), P{Si nuv; `; m} is the probability that n out of ` contending terminals win the contention during the current frame. It is independent of m but dependent on Ms : Thus, we can replace P{Si nuv; `; m} with P{Si nu`; Ms }: Speci®cally, P{nu`; ms } is the probability that n out of ` contending terminals win the
S.-P. Chung, C.-L. Chiu / Computer Communications 25 (2002) 1653±1664
contention during ms mini-slots. We can obtain this probability recursively as in Ref. [21]: 8 < `Pv 1 2 Pv `21 ; `.0 8 Csucc ` : 0; otherwise where Csucc ` denotes the probability that a voice request packet is transmitted successfully in a mini-slot when there are ` voice terminals in the contending state, and Pv is the transmission probability of request packets. P{0u`; ms } 1 2 Csucc `ms ( P{nu`; ms }
9
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Obviously, the steady state equations are
p u; c; r
Vt X v vX 2` X
P u; c; ruv; `; mp v; `; m
14
v0 `0 m0 Vt X u uX 2c X
p u; c; r 1
15
u0 c0 r0
Let P p i; j; k denote the steady state probability vector in lexicographic order. We compute P via an iterative algorithm with the initial distribution P 0 ;
Csucc `P{n 2 1u` 2 1; ms 2 1} 1 1 2 Csucc `P{nu`; ms 2 1}; 0 # n # min `; ms ; ` . 0; Ms $ ms . 0 0;
otherwise
10 Then, the derivation of P u; c; ruv; `; m is shown. There are two cases: Case 1: u v 2 1 ( P u; c; ruv; `; m
P u; c; ruv; c; rV; for c 1 r # u 0;
otherwise
11
P n11 P n P;
n$0
16
where P is the associated one-step transition probability matrix. When the following criterion is satis®ed, the iteration is stopped. upi11 u; c; r 2 pi u; c; ru # e
V V1 1 V2 1 V3 V 1 P v; c; ruv; `; m
and let
0 # u # Vt ; 0 # c # u; 0 # r # u 2 c v2c2r ; v
V 2 P v; c 1 1; ruv; `; m
c11 ; v
V 3 P v; c; r 1 1uv; `; m
r11 ; v
17
where e is a very small value, and in all the cases studied we choose e 10210 : The probability distribution derived in the last iteration is used as the associated steady state probability distribution. 3.2. Static scenarios In this section, we derive the steady state probability distribution of voice terminals when the number of voice terminals is ®xed, i.e. there are no call arrivals and departures. Similar to Ref. [20], the associated probability distribution can be found as follows:
where V 1 is the probability that the system state changes from v; `; m to v; c; r and one of silent v 2 c 2 r terminals is ®nished, V 2 is the probability that the system state changes from v; `; m to v; c 1 1; r and one of c 1 1 contending terminals is ®nished, and V 3 is the probability that the system state changes from v; `; m to
P v; c; ruv; `; m P{Vi11 v; Ci11 c; Ri11 ruVi v; Ci `;
v; c; r 1 1
Ri m}
and one of r 1 1 reserved terminals is ®nished. Case 2: u $ v: Since we assume that all voice terminals begin with the silent state when they start a connection, it is obvious that P u; c; ruv; `; m P u; c; ruv; c; rP v; c; ruv; `; m
i!1
nmax r 2 m;0
13
P{v; c; ruv; `; m; Si n}P{Si nuv; `; m}
where v is a constant, and P{v; c; ruv; `; m; Si n}
12
After all the one-step transition probabilities P u; c; ruv; `; m are found, we use them to derive P u; c; r as follows. Let
p u; c; r lim P{Vi u; Ci c; Ri r}
min `;M X s
Pc
c X v2`2m t0
`2n c2t
t !
18 m1n
!
m1n2r
P m1n2r 1 2 Pts r Pc ts
19
! Ptst 1 2 Pst v2`2m2t
Pts`2n2c2t 1 2 Pts c2t
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Table 1 System parameters Variable
Symbol
Value
Arrival rate of voice terminal Service rate of voice terminal (s) Mean talkspurt duration (s) Mean silent duration (s) Arrival rate of data messages (msg/s/user) Average length of data messages (bits) Channel rate (kbits/s) Speech coding rate (kbits/s) Frame length (ms) Normal (voice or data) slot length (ms) Mini-slot length (ms) Voice packet delay threshold (ms) Number of mini-slots/frame Maximum number of voice slots/frame Number of normal slots/frame
l m 1=av 1=bv ad 1=bd Rc Rv Tf
Variable 180 1.0 1.3 0.1 1000 450 32 16.6 1.23 0.13 32 12 8 12
Vd Ms Vs. Ns
and ( P{nu`; ms }
32 ms, which is slightly less than two frame times. In other words, if one voice request packet is not transmitted successfully after retrying in all the mini-slots of the originating frame, that voice packet is dropped. Thus, the voice packet dropping probability can be found as Pdrop
Vt X u uX 2c X
min c;M X s
u0 c0 r0
n0
c 2 n 1 max 0; n 1 r
2 Vs P nuc; Ms P u; c; r=Pn
27
with Pn
Vt X u uX 2c X u0 c0 r0
P u; c; r £ u £ PT and PT
Tt Tt 1 Ts
where Vs is the maximum number of voice slots per frame, Ms is the number of mini-slots per frame, and PT is the steady state probability of voice terminal in the talkspurt state. More speci®cally, c 2 n is the number of voice term-
Csucc `P{n 2 1u` 2 1; ms 2 1} 1 1 2 Csucc `P{nu`; ms 2 1}; 0 # n # min `; ms ; ` . 0; Ms $ ms . 0 0;
otherwise
20 P{0u`; ms } 1 2 Csucc `ms Csucc `
p v; c; r
8 < `Pv 1 2 Pv `21 ; :
0;
v vX 2` X
21 `.0 otherwise
P v; c; ruv; `; mp v; `; m
22
23
`0 m0 v vX 2c X
p v; c; r 1
24
c0 r0 i11
up
i
v; c; r 2 p v; c; ru # e;
0 # c # v; 0 # r # v 2 c
25
3.3. Performance measures After deriving the steady state probability distribution P u; c; r; we use it to compute the voice call blocking probability, voice packet dropping probability and channel utilization for voice traf®c. When a new voice call arrives, if there are Vt active voice terminals in the system, the new voice call is refused. Thus, the voice call blocking probability is given by Pblock
Vt VX t 2c X c0 r0
P Vt ; c; r
26
When a voice packet is delayed beyond a threshold, the voice packet is dropped. The delay threshold is set to
inals that do not contend successfully in the c contending users. n 1 r 2 Vs represents the number of voice terminals which contend successfully but there are no voice slots available. Finally, we compute the channel utilization for voice traf®cs as follows: Cu
Vt X u uX 2c X
min c;M X s
u0 c0 r0
n0
min n 1 r; Vs P nuc; Ms
£ P u; c; r=Ns
28
where Ns is the number of normal slots per frame. To elaborate, the term min c; Nm re¯ects the fact that the number of voice terminals which contend successfully cannot exceed the number of contending voice terminals and the number of mini-slots per frame. The term min n 1 r; Vs implies that the number of voice terminals in the reserved state cannot be greater than the maximum number of voice slots per frame. 4. Simulation results and analysis In this section, the results from analysis and simulation for the proposed call admission control/congestion control in wireless integrated voice/data networks are presented. For simplicity, we consider homogeneous cellular systems. Thus we concentrate on one single cell. The effect of mobility is neglected. The aforesaid frame structure is adopted. We consider two scenarios: dynamic and static. Dynamic scenarios imply that the number of ongoing voice calls could vary, whereas that for static scenarios is ®xed. It is
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Fig. 3. Simulation vs. analytical results with Vt 12.
noted that the number of ongoing data calls is always assumed to be constant. The voice call arrival process is assumed to be Poisson, and the service time distribution of voice calls is exponentially distributed. For every ongoing voice call, it can be modeled as a two-state Markov
chain at the packet level. The duration of busy (talkspurt) state and idle (silence) state for voice traf®c is geometrically distributed. During a talkspurt, one voice packet is generated by one voice terminal in every frame. If the voice packets cannot transmit successfully within a threshold,
Fig. 4. Simulation vs. analytical results with Vt 14.
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Fig. 5. Effects of voice threshold and Pv with It 20.
they are dropped. As to data traf®c, each data terminal generates data messages according to a Poisson process, and the length of each message is geometrically distributed. Each time a data user generates one new data message, it
must contend again for the data slots by sending a data request. Once it wins the contention, it starts transmitting if there are data slots available, or it is queued, until all packets within that message are sent successfully. The
Fig. 6. Effects of number of voice slots and Pv with It 20 and Vt 14.
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Fig. 7. Effects of Pv with Vt 18.
data packets are never dropped and are queued until they can be transmitted. No new arrivals are generated by a terminal with an ongoing talkspurt (or data message) until that ongoing talkspurt (or data message) is ®nished or dropped due to excessive delay. The parameters used are summarized in Table 1. The simulation program is written in C. The simulation runs over 108 frames for dynamic scenarios and over 3 £ 106 frames for static scenarios. 4.1. Voice traf®c First, simulation results are shown to verify the analytical results of voice traf®c. Figs. 3 and 4 show various simulation and analytical performance measures versus Pv under both dynamic and static scenarios for different values of Vt with It 24: It is noted that in static scenarios the number of ongoing voice calls is ®xed and set to be Vt : As can be seen, for both dynamic and static scenarios, the simulation results are in very good agreement with the analytical results. Thus, for clarity, we show analytical results only from now on. Furthermore, dynamic scenarios achieve lower voice packet loss probability than static scenarios at the expense of lower channel utilization. The low channel utilization is in part due to the fact that not all slots are available to voice calls, i.e. Vs # Ns : It is also noted that low channel utilization is bene®cial to low-priority data calls. In addition, although changing Pv does not affect the voice blocking probability, it does affect packet loss probability. Further, as Vt changes from 12 to 14, the packet loss probability exceeds the target value 1022 under the static scenarios, whereas under the dynamic scenarios the packet loss probability always meets the target value at the expense of non-zero voice blocking probability (,0.1). Next, Fig. 5 shows various performance measures versus voice threshold
for different values of Pv with It 20: As the voice threshold increases, the voice blocking probability decreases, while the packet dropping probability and channel utilization increase. The effect of Pv is not signi®cant. Fig. 6 shows various performance measures versus number of voice slots per frame for different values of Pv with It 20 and Vt 14: When the number of voice slots increases, the packet dropping probability decreases, and the changes of voice blocking probability and channel utilization are insigni®cant, even with different Pv : The packet loss probability with Pv 0:5 is much lower than that with Pv 0:1 or 0.9, especially when the number of voice slots becomes larger. 4.2. Integrated voice/data traf®c Simulation results of integrated voice/data traf®c under dynamic scenarios are presented next. The performance measures of interest include voice packet dropping probability, voice call blocking probability, data average delay and channel utilization. As is widely accepted, 1% of packet dropping probability and voice blocking probability is tolerable. We use this target value to determine the optimal values of Pv ; Pd ; voice call arrival rate, and voice threshold. 4.3. Determine the optimal Pv and Pd First of all, Fig. 7 shows the various performance measures versus Pv with Vt 18; It 19; Nv 8; Nd 56; and Pd 0:03: Obviously, the Pv does not affect the voice blocking probability because it does not affect the call arrival rate and call service time of voice terminal. It is also observed that without appropriate selection of Pv ; the voice packet dropping probability may exceed the target
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Fig. 8. Effects of Pd with It 20.
value. With smaller values of Pv ; voice packets contend less likely, and this results in larger delay and thus larger packet loss. On the other hand, with larger values of Pv ; voice packets contend more likely, and this results in more collisions and larger access delay and thus larger packet loss. It is noted that the data average delay and channel utilization ®rst remain almost constant and then decrease as Pv increases. According to the results of our studied cases, the optimal Pv appears to be around 0.6. Fig. 8 shows the various performance measures versus Pd with It 20; Vt 24; Nv 8; Nd 56; and Pv 0:6: Apparently, as Pd increases, the
data average delay ®rst increases and then decreases, whereas the voice packet dropping probability, voice call blocking probability, and channel utilization remains relatively constant. Similarly, data packets contend less likely with smaller values of Pd ; and data packets result in more collisions with larger values of Pv ; and thus larger packet loss. It is also noted that as voice packets have higher priority than data packets, Pd has no effect on voice packet loss probability. According to the results of all our studied cases, the optimal Pd appears to be around 0.03.
Fig. 9. Effects of interarrival time of voice calls.
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Fig. 10. Effects of voice threshold.
4.4. Interaction between CAC and congestion control factors Fig. 9 shows the various performance measures versus the interarrival time of voice calls for different values of Pv with Vt 20; Nd 56; and Pd 0:03: The voice blocking probability, voice packet dropping probability, data message transmission delay get better and the channel utilization gets worse as the interarrival time of voice calls increases. Fig. 10 shows the various performance measures versus the voice threshold with It 19; Nd 56; Pv 0:6; and Pd
0:03: Obviously, when the voice threshold increases, the voice blocking probability decreases but the voice packet dropping probability, data average delay and channel utilization increases. These results show that there exists a tradeoff between voice arrival rate and voice threshold. When the arrival rate increase, the voice blocking probability increases. If we want to reduce the voice blocking probability, we need to add the voice threshold. However, when the voice threshold increases, the voice packet dropping probability gets worse. With the target voice packet dropping probability and voice blocking probability being 1%, and
Fig. 11. Effects of number of voice slots.
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the interarrival time is 19 s, it is found that the maximum voice threshold is 24, and the associated channel utilization is about 80%. Fig. 11 shows the various performance measures versus the maximum number of voice slots per frame with It 12; Vt 24; Nd 56; Pv 0:6; and Pd 0:03: Obviously, the voice packet dropping probability decreases and the data average delay increases as that number increases. Lastly, it can also be shown that with Nd 56; Pv 0:6; and Pd 0:03; if the number of voice slots is 12, the maximum voice threshold is 26 provided that the call interarrival time is 11 s, and the associated channel utilization is about 87%. It is noted that this channel utilization corresponds to the maximum channel bandwidth available for the voice and data packets since about 11±12% of channel resource is devoted to the mini-slots. 5. Conclusion We consider wireless communication systems supporting both voice and data services, where call admission control (CAC) is used to guarantee QoS at the connection level and congestion control to guarantee QoS at the cell level. We study the effect of voice interarrival time and voice threshold on voice packet loss probability, voice call blocking probability, data packet average delay, and channel utilization. With appropriate Markovian models, the voice packet loss probability, voice blocking probability and channel utilization of voice traf®cs are derived for both dynamic and static scenarios, and the analytical results are shown to be in good agreement with the simulation results. It is shown that voice call blocking probability can be traded off for packet loss probability and channel utilization. In addition, for integrated voice/data traf®c, computer simulation is used to evaluate the effect of proposed CAC and congestion control on the performance measures of both voice and data traf®cs. With the computer simulation results it is found that the optimal Pv is about 0.6 and the optimal Pd is about 0.03. When the number of voice slots is 12, given that the call interarrival time is 11 s, the maximum voice threshold is 26, and the associated channel utilization is about 87%, which corresponds to the maximum channel bandwidth available for the voice and data packets. References [1] D.C. Cox, Wireless network access for personal communications, IEEE Commun. Mag. 30 (12) (1992) 96±115.
[2] E. Ayanoglu, K.Y. Eng, M.J. Karol, Wireless ATM: limits, challenges, and proposals, IEEE Personal Commun. 3 (4) (1996) 18±34. [3] D. Raychaudhuri, Wireless ATM networks: architecture, system design and prototyping, IEEE Personal Commun. 34 (1996) 42±49. [4] D. Raychaudhuri, L.J. French, R.J. Siracusa, R. Yuan, P. Narasimhan, C. Johnston, WATMnet: a prototype wireless ATM system for multimedia personal communication, ICC'96 1 (1996) 469±477. [5] D. Weissman, A.H. Levesque, R.A. Dean, Interoperable wireless data, IEEE Commun. Mag. 31 (2) (1993) 68±77. [6] J.E. Wieselthier, A. Ephremides, Performance analysis of ®xed- and movable-boundary channel-access schemes for integrated voice/data wireless networks, INFOCOM'93 3 (1993) 1204±1213. [7] S. Nanda, D.J. Goodman, U. Timor, Performance of PRMA: a packet voice protocol for cellular systems, IEEE Trans. Veh. Tech. 40 (1991) 585±598. [8] W.C. Wong, D.J. Goodman, A packet reservation multiple access protocol for integrated speech and data transmission, IEE Proc. 139 (1992) 585±598. [9] P. Naras, R.D. Yates, A new protocol for the integration of voice and data over PRMA, IEEE JSAC 14 (4) (1996). [10] G. Wu, K. Mukumoto, A. Fukuda, An integrated voice and data transmission system with idle signal multiple access-static analysis, IEICE Trans. Commun. E76-B (11) (1993) 1398±1407. [11] N.D. Wilson, R. Ganesh, K. Josesph, D. Raychaudhuri, Packet CDMA versus dynamic TDMA for multiple access in an integrated voice/data PCN, IEEE JSAC 11 (6) (1993) 870±884. [12] B.C. Kim, C.K. Un, Capacity of wireless dynamic TDMA and media access control for packetized voice/data integration, Wireless Personal Commun. (1995) 313±319. [13] J.G. Gruber, N. Le, Performance requirements for integrated voice/ data networks, IEEE JSAC 1 (6) (1983) 981±1005. [14] K. Zhang, K. Pahlavan, An integrated voice/data system for mobile indoor radio networks, IEEE Trans. Veh. Tech. 39 (1) (1990) 75±82. [15] J.-F. Frigon, H.C.B. Chan, V.C.M. Leung, Data and voice integration in DR-TDMA for wireless ATM networks, ICC'99 (1999) 1696± 1700. [16] H. Liu, L. Dittmann, U. Glieise, P. Danielsen, Multiple access protocol for supporting multimedia services in wireless ATM networks, IEEE Veh. Tech. Conf. 2 (2) (1999) 1146±1150. [17] O. Kubbar, H.T. Mouftah, Multiple access control protocols for wireless ATM: problems de®nition and design objectives, IEEE Commun. Mag. 35 (11) (1997) 93±99. [18] G. Wu, K. Mukumoto, A. Fukuda, M. Mizuno, A dynamic TDMA wireless integrated voice/data system with data steal into voice (DSV) technique, IEICE Trans. Commun. E78-B (8) (1995) 1125±1135. [19] P.T. Brady, A technique for investigating on±off patterns of speech, BSTJ 44 (1) (1965) 1±22. [20] E. Jeong, L. Jacob, S. Maeng, Dynamic TDMA with priority-based request packet transmission scheme for integrated multimedia traf®cs, IEICE Trans. Commun. E82-B (12) (1999) 2136±2144. [21] S. Jangi, L. Merakos, Performance analysis of reservation random access protocols for wireless access networks, IEEE Trans. Commun. 42 (2) (1994) 1223±1234.
www.elsevier.com/locate/comcom
Joint call admission control/congestion control for wireless integrated voice/data networks Shun-Ping Chung*, Chin-Lien Chiu Department of Electrical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei, Taiwan, ROC Received 11 October 2001; revised 19 December 2001; accepted 29 January 2002
Abstract We consider wireless communication systems supporting both voice and data services, where not only call admission control (CAC) is used to maintain quality of service (QoS) at the call level, but also congestion control is used to guarantee QoS at the packet level. The CAC adopted is a simple threshold scheme, i.e. the number of voice terminals in use cannot exceed a threshold. The congestion control used is a modi®ed version of dynamic time division multiple access with priority-based request packet transmission scheme (D-TDMA/PRPTS), where to avoid excessive delay due to mini-slot contention, voice request packet is dropped if it cannot succeed in the originating frame. For comparison, two scenarios involving only the voice traf®c are considered: dynamic and static. In dynamic scenarios, the number of ongoing voice calls may vary over time, whereas that in static scenarios, it is ®xed. With appropriate Markovian models, the voice packet loss probability, voice call blocking probability and channel utilization of voice traf®c are derived, and the analytical results are veri®ed with the simulation results. For integrated voice/data traf®c, due to the mathematical complexity, only computer simulation is used to evaluate the effect of proposed CAC and congestion control on the performance measures of both voice and data traf®c. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Call admission control; Congestion control; Call blocking probability; Packet loss probability; Channel utilization
1. Introduction Future wireless personal communication networks are expected to provide users a way to communicate with anyone in any place at any point of time. The information transmitted may include voice, video, and data [1]. Different kinds of information have different transmission characteristics and quality of service (QoS) requirements. Generally speaking, real-time voice and video are delay-sensitive but loss-insensitive. In other words, if the delay of one voice packet exceeds a threshold, that packet is of no use and can be dropped. Non-real-time data is delay-insensitive but losssensitive. It is also worth noting that a call may have QoS requirements at different time levels. For example, the call blocking probability at the connection level, and the packet dropping probability and packet average delay at the packet level. All QoS requirements have to be satis®ed. Therefore, how to design an ef®cient media access control to guarantee QoS is an important topic for wireless personal communication systems. More speci®cally, CAC is needed to guarantee * Corresponding author. Tel.: 1886-2273-76703; fax: 1886-227376699. E-mail address: [email protected] (S.-P. Chung).
the QoS at the connection level, while the congestion control is enforced to satisfy the QoS at the packet level. Many media access control schemes for wireless systems with integrated voice and data have been proposed, e.g. circuit-switched time division multiple access [5,6], packet reservation multiple access (PRMA) [7±9], idle signal multiple access for integrated services (I-ISMA) [10], and dynamic TDMA (D-TDMA) [2±4,11±17]. Speci®cally, DTDMA is based on a frame structure, where a frame consists of mini-slots, voice slots, and data slots. The voice slots and data slots are used for voice and data transmission and the mini-slots are used to transmit the request packets, where the request packets contain information needed for the slot reservation. D-TDMA uses slotted ALOHA (S-ALOHA) as the request packet transmission scheme [18]. It is shown in Ref. [19] that a conversational speech can be segmented into talkspurt and silence periods, and the activity factor is less than 50%. Therefore, for using the channel ef®ciently, speech activity detector (SAD) is widely used in the wireline communication system. Gang et al. [18] proposed DTDMA with data steal into voice technique (D-TDMA/ DSV), where voice terminals are allocated channels only when they are in the talkspurt period. When they are in the silence period, the channel is released to others. They
0140-3664/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0140-366 4(02)00050-6
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need to contend a voice slot to transmit the packet by transmitting a request packet in the mini-slots if they enter into the talkspurt period again. Jeong et al. [20] noticed that collisions between the voice request packets and the data request packets cause the packet dropping and thus limit throughput. Therefore, D-TDMA with priority-based request packet transmission scheme (D-TDMA/PRPTS) is proposed in Ref. [20] to give the voice request packets priority over the data request packets. The voice request packets are transmitted preferentially, and the data request packets can be transmitted only after waiting for a certain time limit. This can avoid collision between the voice request packet and the data request packet, and thus reduce the packet dropping probability and enhance the voice capacity. One common drawback of the above schemes is that they do not consider CAC and congestion control at the same time. The congestion control used is Modi®ed DTDMA/PRPTS, with the modi®cation that, to avoid excessive delay due to mini-slot contention, voice request packet is dropped if it cannot succeed in the frame at which it originates. The CAC adopted in this paper is a simple threshold scheme, i.e. the number of voice terminals in use cannot exceed a threshold. The performance measures of interest are the voice packet dropping probability, voice call blocking probability, data average delay, and channel utilization. Due to the increasing demand of capacity and thus the popularity of microcells, the number of ongoing calls in a cell may vary signi®cantly in a short time interval. To explore the time-varying nature of cell occupancy and the interaction of CAC and congestion control, two scenarios are studied: dynamic and static. In dynamic scenarios, the number of ongoing voice calls may vary over time, whereas that in the static scenarios is ®xed. For dynamic and static scenarios involving voice traf®c only, appropriate Markovian models are formulated, analytical results for voice call blocking probability, voice packet dropping probability and channel utilization for voice traf®c are derived, and the analytical results are veri®ed with the simulation results. Last but not the least, for integrated voice/data traf®c, computer simulation is used to evaluate the associated performance measures due to the mathematical complexity. The rest of this paper is organized as follows. In Section 2, we describe the system model. In Section 3, appropriate Markovian models are formulated to derive performance measures of interest for both dynamic and static scenarios involving voice traf®c only. In Section 4, analytical results are veri®ed with simulation results for both dynamic and static scenarios involving voice traf®c only. We also present the simulation results of integrated voice and data traf®c. Some conclusions are drawn in Section 5. 2. System model In this section, the system model in question is described in detail. In the studied wireless system, the service area is
composed of the cells. Every cell includes a base station and many mobile terminals. Every mobile terminal communicates to the base station with a pair of uplink and downlink channels. It uses the frequency division duplex mode. A channel is divided into a series of periodic frames in time. Each frame is subdivided into many slots. Each frame includes three kinds of slots: mini-slots, voice slots, and data slots. The mini-slots are used to transmit connection request packets and reservation request packets. The voice slots are used to transmit the voice packets and the data slots to transmit the data packets. We consider homogeneous system, i.e. all cells are statistically identical. Thus, we can focus on any one particular cell. 2.1. Call level model In the call level model, there are many mobile terminals. Each mobile terminal can generate voice call and data call. The number of ongoing calls may vary due to call completions or mobility, i.e. leaving the cell in question. For simplicity, the effect of mobility is neglected. For comparison purposes, we consider two scenarios: dynamic and static. Dynamic scenarios imply that the number of ongoing voice calls could vary, whereas that for static scenarios is ®xed. It is noted that the number of ongoing data calls is always assumed to be constant. The traf®c model for the dynamic scenarios is described as follows. When a terminal wants to make a voice call, it needs to transmit a connection request to base station via the uplink channel. The base station decides whether to accept this request with CAC. The base station uses the downlink channel to notify the mobile terminal what the decision is. If the request is refused, the call is rejected and cleared. If the request is accepted, the mobile terminal can continue and transmit a reservation request to reserve slots for packet transmission. The voice call arrival process is assumed to be Poisson with an average arrival rate l , and average interarrival time It 1=l: The service time distribution of voice calls is exponentially distributed with mean m . When a voice call is complete, the corresponding voice terminal is referred to as ®nished. 2.2. Call admission control In order to study how the system performance is affected by CAC, a simple threshold CAC is used for the dynamic scenarios. Speci®cally, a voice connection request is accepted if the number of voice connections is less than the voice threshold Vt : Since the number of data connections is ®xed, there is no CAC for data connections. Obviously, the voice threshold has a signi®cant effect on the system performance. When the threshold value increases, the voice blocking probability decreases but packet dropping probability and packet delay of voice and data traf®c becomes worse. Apparently, an appropriate tradeoff is needed.
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2.3. Packet level model We assume that for both voice and data traf®c, the packet level models alternate between the busy state and idle state. The duration of busy (talkspurt) state and the idle (silence) state for voice traf®c is geometrically distributed with mean Tt 1=av and Ts 1=bv ; respectively. The voice traf®c is considered as real time traf®c. If the voice packets cannot transmit successfully within a threshold, they are dropped. For the data traf®c, the duration of busy state and idle state is also geometrically distributed with mean 1=ad and 1=bd ; respectively. The data traf®c is considered as non-real time traf®c. The data packets are never dropped and are queued until they can be transmitted. A voice terminal can be in one of the following three states: silent, contending, and reserved. We assume that all voice terminals begin with the silent state when they start a connection. In the silent state, a voice terminal waits for the arrival of a talkspurt. Upon arrival of a talkspurt, the voice terminal enters the contending state, and transmits a voice request packet with the probability Pv : A voice terminal in the contending state contends with the other voice terminals in the same state to transmit a voice request packet. If there are two or more request packets transmitted in a mini-slot, they collide, and all the collided request packets fail. In other words, a voice request packet transmission is successful only if it is the only one transmitted in the mini-slot in question. All unsuccessful voice terminals continue to contend in the successive mini-slots of the originating frame. If at the end of the originating frame any voice terminal in the contending state is still unsuccessful, that voice terminal returns to the silent state and the associated voice packet is dropped. After a voice terminal wins a mini-slot, it waits for an available voice slot assigned by system to enter the reserved state. A voice terminal in the reserved state uses its reserved voice slot in every frame until its talkspurt terminates. After the last voice packet of the talkspurt is transmitted, the voice terminal returns to the silent state. The state transition diagram is shown in Fig. 1, where the talkspurt to silence transition probability is Pts ; the silence to talkspurt transition probability is Pst ; and the transition probability from contending state to reserved state is P Tf Pts 1 2 exp 2 1 Tt T Pst 1 2 exp 2 f Ts
2
where Tt Ts is the mean duration in the talkspurt (silent) state, and Tf is the frame duration. 2.4. Congestion control We assume that the channel impairments, e.g. noise and interference, do not lead to the packet transmission fail-
Fig. 1. State transition diagram of a voice terminal.
ures, and the only reason of transmission failures is packet collision, and the capture effect is not taken into account, that is, all the collided packets fail. The congestion control we adopted is a modi®ed version of D-TDMA/PRPTS [20]. Fig. 2 shows the associated frame structure. As can be seen, there are three kinds of slots in each frame: mini-slots, voice slots, and data slots. There are Ms mini-slots, Vs voice slots, and Ds data slots per frame, with the number of normal slots Ns Vs 1 Ds : When a terminal wants to send a voice or data packet, ®rstly, it needs to send a request packet via the mini-slots. If more than one request packet is transmitted in the same mini-slot, all those request packets fail. All unsuccessful data terminals retry to send the request packet in the successive mini-slots until it succeeds. For all unsuccessful voice terminals, to avoid unduly long delay and thus low throughput, only a retry in successive mini-slots of the originating frame is allowed. In other words, if one voice request packet cannot transmit successfully after retrying in all the mini-slots of the originating frame, that voice packet is dropped. Upon receipt of the request packet, the base station tries to assign a free slot to the associated terminal. If there are no free slots, the base station refuses the request packet. After a terminal reserves the slot successfully, it can start to transmit the data. The terminal uses the slot until it ®nishes transmitting, and then the slot is released. More importantly, as in the DTDMA/PRPTS, the voice request packets are given priority over the data request packets to reduce the voice packet dropping probability at the expense of fewer mini-slots. Basically, the transmissions of voice request packets begin right at the beginning boundary of a mini-slot. In contrast, data request packets can be transmitted in a mini-slot only after con®rming that there are no voice request packet transmissions in the mini-slot in question. The con®rmation is based on a signaling message from the base station. Obviously, the size of mini-slots with the aforesaid priority scheme is larger than that of mini-slots without that priority scheme.
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3. Mathematical analysis In this section, we formulate appropriate Markovian models to derive the voice call blocking probability, packet dropping probability, and channel utilization for voice traf®c under both dynamic and static scenarios. 3.1. Dynamic scenarios The steady state probability distribution of voice terminals when the number of voice terminals may vary over time is derived in this section. Let random variables Vi ; Ci ; and Ri represent the number of active voice terminals, that of voice terminals in the contending state, that of voice terminals in the reserved state, respectively, at the beginning of the ith frame. Obviously, {Vi ; Ci ; Ri ; i 1; 2; ¼} constitutes a discrete time Markov chain. Let P u; c; r represent the steady state probability when there are u voice terminals in the system, and among those voice terminals, c voice terminals are in the contending state and r voice terminals in the reserved state. Let P u; c; ruv; `; m be the one-step transition probability. First, let us focus on P u; c; ruv; c; r which is the conditional probability that the number of active voice terminals changes from v to u, with the other parameters remaining ®xed. Since the frame time is much less than the average call interarrival time and average call service time, we assume that no more than one arrival or departure can occur within one frame time. Let Pa i represent the probability that one voice call arrives within one frame time when there are i voice calls in progress. Let Pd i represent the probability that one voice call departs within one frame time when there are i voice calls in progress. It is easy to show that ( 1 2 e2lTf 0 # i # Vt 2 1 Pa i 3 0 i Vt ! i Pd i 1 2 e2mTf e2 i21mTf 0 # i # Vt 4 i21 Therefore,
Fig. 2. The associated frame structure.
where the random variable Si denotes the number of voice terminals which contend successfully during the ith frame, and Ms is the number of mini-slots in each frame. Speci®cally, n must not be less than the increment of the number of voice terminals in the reserved state, and must not be greater than the original number of voice terminals in the contending state and the number of mini-slots per frame. In Eq. (6), P v; c; ruv; `; m is expressed as the summation of the products of two conditional probabilities, with the additional condition being the number of terminals that win the contention during the current frame. ! m1n P{v; c; ruv; `; m; Si n} Pts m1n2r 1 m1n2r 2 Pts r Pc where Pc
c X v2`2m t0
P v; c; ruv; `; m P{Vi11 v; Ci11 c; Ri11 ruVi v; Ci `; Ri m}
min `;M X s nmax r 2 m;0
P{v; c; ruv; `; m; Si n}P{Si nuv; `; m}
6
c2t
! Ptst 1 2 Pst v2`2m2t
Pts`2n2c2t 1 2 Pts c2t
In Eq. (7), P{v; c; ruv; `; m; Si n} is expressed as the product of the probability that m 1 n 2 r out of m 1 n terminals in the reserved state return to the silent state and the probability that t out of v 2 ` 2 m terminals in the
8 P{Vi11 j; Ci11 c; Ri11 ruVi i; Ci c; Ri r} > > > > > > > Pa i; < P j; c; rui; c; r Pd i; > > > > 1 2 Pa i 2 Pd i; > > > : 0; It is noted that Pa Vt 0 and Pd 0 0: Second, the conditional probability P v; c; ruv; `; m is computed as follows
`2n
t !
7
j i 1 1; 0 # i # Vt j i 2 1; 0 # i # Vt
5
j i; 0 # i # Vt otherwise
silent state enter the contending state and c 2 t out of ` 2 n terminals in the contending state remain in the contending state for 0 # t # c: In Eq. (6), P{Si nuv; `; m} is the probability that n out of ` contending terminals win the contention during the current frame. It is independent of m but dependent on Ms : Thus, we can replace P{Si nuv; `; m} with P{Si nu`; Ms }: Speci®cally, P{nu`; ms } is the probability that n out of ` contending terminals win the
S.-P. Chung, C.-L. Chiu / Computer Communications 25 (2002) 1653±1664
contention during ms mini-slots. We can obtain this probability recursively as in Ref. [21]: 8 < `Pv 1 2 Pv `21 ; `.0 8 Csucc ` : 0; otherwise where Csucc ` denotes the probability that a voice request packet is transmitted successfully in a mini-slot when there are ` voice terminals in the contending state, and Pv is the transmission probability of request packets. P{0u`; ms } 1 2 Csucc `ms ( P{nu`; ms }
9
1657
Obviously, the steady state equations are
p u; c; r
Vt X v vX 2` X
P u; c; ruv; `; mp v; `; m
14
v0 `0 m0 Vt X u uX 2c X
p u; c; r 1
15
u0 c0 r0
Let P p i; j; k denote the steady state probability vector in lexicographic order. We compute P via an iterative algorithm with the initial distribution P 0 ;
Csucc `P{n 2 1u` 2 1; ms 2 1} 1 1 2 Csucc `P{nu`; ms 2 1}; 0 # n # min `; ms ; ` . 0; Ms $ ms . 0 0;
otherwise
10 Then, the derivation of P u; c; ruv; `; m is shown. There are two cases: Case 1: u v 2 1 ( P u; c; ruv; `; m
P u; c; ruv; c; rV; for c 1 r # u 0;
otherwise
11
P n11 P n P;
n$0
16
where P is the associated one-step transition probability matrix. When the following criterion is satis®ed, the iteration is stopped. upi11 u; c; r 2 pi u; c; ru # e
V V1 1 V2 1 V3 V 1 P v; c; ruv; `; m
and let
0 # u # Vt ; 0 # c # u; 0 # r # u 2 c v2c2r ; v
V 2 P v; c 1 1; ruv; `; m
c11 ; v
V 3 P v; c; r 1 1uv; `; m
r11 ; v
17
where e is a very small value, and in all the cases studied we choose e 10210 : The probability distribution derived in the last iteration is used as the associated steady state probability distribution. 3.2. Static scenarios In this section, we derive the steady state probability distribution of voice terminals when the number of voice terminals is ®xed, i.e. there are no call arrivals and departures. Similar to Ref. [20], the associated probability distribution can be found as follows:
where V 1 is the probability that the system state changes from v; `; m to v; c; r and one of silent v 2 c 2 r terminals is ®nished, V 2 is the probability that the system state changes from v; `; m to v; c 1 1; r and one of c 1 1 contending terminals is ®nished, and V 3 is the probability that the system state changes from v; `; m to
P v; c; ruv; `; m P{Vi11 v; Ci11 c; Ri11 ruVi v; Ci `;
v; c; r 1 1
Ri m}
and one of r 1 1 reserved terminals is ®nished. Case 2: u $ v: Since we assume that all voice terminals begin with the silent state when they start a connection, it is obvious that P u; c; ruv; `; m P u; c; ruv; c; rP v; c; ruv; `; m
i!1
nmax r 2 m;0
13
P{v; c; ruv; `; m; Si n}P{Si nuv; `; m}
where v is a constant, and P{v; c; ruv; `; m; Si n}
12
After all the one-step transition probabilities P u; c; ruv; `; m are found, we use them to derive P u; c; r as follows. Let
p u; c; r lim P{Vi u; Ci c; Ri r}
min `;M X s
Pc
c X v2`2m t0
`2n c2t
t !
18 m1n
!
m1n2r
P m1n2r 1 2 Pts r Pc ts
19
! Ptst 1 2 Pst v2`2m2t
Pts`2n2c2t 1 2 Pts c2t
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Table 1 System parameters Variable
Symbol
Value
Arrival rate of voice terminal Service rate of voice terminal (s) Mean talkspurt duration (s) Mean silent duration (s) Arrival rate of data messages (msg/s/user) Average length of data messages (bits) Channel rate (kbits/s) Speech coding rate (kbits/s) Frame length (ms) Normal (voice or data) slot length (ms) Mini-slot length (ms) Voice packet delay threshold (ms) Number of mini-slots/frame Maximum number of voice slots/frame Number of normal slots/frame
l m 1=av 1=bv ad 1=bd Rc Rv Tf
Variable 180 1.0 1.3 0.1 1000 450 32 16.6 1.23 0.13 32 12 8 12
Vd Ms Vs. Ns
and ( P{nu`; ms }
32 ms, which is slightly less than two frame times. In other words, if one voice request packet is not transmitted successfully after retrying in all the mini-slots of the originating frame, that voice packet is dropped. Thus, the voice packet dropping probability can be found as Pdrop
Vt X u uX 2c X
min c;M X s
u0 c0 r0
n0
c 2 n 1 max 0; n 1 r
2 Vs P nuc; Ms P u; c; r=Pn
27
with Pn
Vt X u uX 2c X u0 c0 r0
P u; c; r £ u £ PT and PT
Tt Tt 1 Ts
where Vs is the maximum number of voice slots per frame, Ms is the number of mini-slots per frame, and PT is the steady state probability of voice terminal in the talkspurt state. More speci®cally, c 2 n is the number of voice term-
Csucc `P{n 2 1u` 2 1; ms 2 1} 1 1 2 Csucc `P{nu`; ms 2 1}; 0 # n # min `; ms ; ` . 0; Ms $ ms . 0 0;
otherwise
20 P{0u`; ms } 1 2 Csucc `ms Csucc `
p v; c; r
8 < `Pv 1 2 Pv `21 ; :
0;
v vX 2` X
21 `.0 otherwise
P v; c; ruv; `; mp v; `; m
22
23
`0 m0 v vX 2c X
p v; c; r 1
24
c0 r0 i11
up
i
v; c; r 2 p v; c; ru # e;
0 # c # v; 0 # r # v 2 c
25
3.3. Performance measures After deriving the steady state probability distribution P u; c; r; we use it to compute the voice call blocking probability, voice packet dropping probability and channel utilization for voice traf®c. When a new voice call arrives, if there are Vt active voice terminals in the system, the new voice call is refused. Thus, the voice call blocking probability is given by Pblock
Vt VX t 2c X c0 r0
P Vt ; c; r
26
When a voice packet is delayed beyond a threshold, the voice packet is dropped. The delay threshold is set to
inals that do not contend successfully in the c contending users. n 1 r 2 Vs represents the number of voice terminals which contend successfully but there are no voice slots available. Finally, we compute the channel utilization for voice traf®cs as follows: Cu
Vt X u uX 2c X
min c;M X s
u0 c0 r0
n0
min n 1 r; Vs P nuc; Ms
£ P u; c; r=Ns
28
where Ns is the number of normal slots per frame. To elaborate, the term min c; Nm re¯ects the fact that the number of voice terminals which contend successfully cannot exceed the number of contending voice terminals and the number of mini-slots per frame. The term min n 1 r; Vs implies that the number of voice terminals in the reserved state cannot be greater than the maximum number of voice slots per frame. 4. Simulation results and analysis In this section, the results from analysis and simulation for the proposed call admission control/congestion control in wireless integrated voice/data networks are presented. For simplicity, we consider homogeneous cellular systems. Thus we concentrate on one single cell. The effect of mobility is neglected. The aforesaid frame structure is adopted. We consider two scenarios: dynamic and static. Dynamic scenarios imply that the number of ongoing voice calls could vary, whereas that for static scenarios is ®xed. It is
S.-P. Chung, C.-L. Chiu / Computer Communications 25 (2002) 1653±1664
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Fig. 3. Simulation vs. analytical results with Vt 12.
noted that the number of ongoing data calls is always assumed to be constant. The voice call arrival process is assumed to be Poisson, and the service time distribution of voice calls is exponentially distributed. For every ongoing voice call, it can be modeled as a two-state Markov
chain at the packet level. The duration of busy (talkspurt) state and idle (silence) state for voice traf®c is geometrically distributed. During a talkspurt, one voice packet is generated by one voice terminal in every frame. If the voice packets cannot transmit successfully within a threshold,
Fig. 4. Simulation vs. analytical results with Vt 14.
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Fig. 5. Effects of voice threshold and Pv with It 20.
they are dropped. As to data traf®c, each data terminal generates data messages according to a Poisson process, and the length of each message is geometrically distributed. Each time a data user generates one new data message, it
must contend again for the data slots by sending a data request. Once it wins the contention, it starts transmitting if there are data slots available, or it is queued, until all packets within that message are sent successfully. The
Fig. 6. Effects of number of voice slots and Pv with It 20 and Vt 14.
S.-P. Chung, C.-L. Chiu / Computer Communications 25 (2002) 1653±1664
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Fig. 7. Effects of Pv with Vt 18.
data packets are never dropped and are queued until they can be transmitted. No new arrivals are generated by a terminal with an ongoing talkspurt (or data message) until that ongoing talkspurt (or data message) is ®nished or dropped due to excessive delay. The parameters used are summarized in Table 1. The simulation program is written in C. The simulation runs over 108 frames for dynamic scenarios and over 3 £ 106 frames for static scenarios. 4.1. Voice traf®c First, simulation results are shown to verify the analytical results of voice traf®c. Figs. 3 and 4 show various simulation and analytical performance measures versus Pv under both dynamic and static scenarios for different values of Vt with It 24: It is noted that in static scenarios the number of ongoing voice calls is ®xed and set to be Vt : As can be seen, for both dynamic and static scenarios, the simulation results are in very good agreement with the analytical results. Thus, for clarity, we show analytical results only from now on. Furthermore, dynamic scenarios achieve lower voice packet loss probability than static scenarios at the expense of lower channel utilization. The low channel utilization is in part due to the fact that not all slots are available to voice calls, i.e. Vs # Ns : It is also noted that low channel utilization is bene®cial to low-priority data calls. In addition, although changing Pv does not affect the voice blocking probability, it does affect packet loss probability. Further, as Vt changes from 12 to 14, the packet loss probability exceeds the target value 1022 under the static scenarios, whereas under the dynamic scenarios the packet loss probability always meets the target value at the expense of non-zero voice blocking probability (,0.1). Next, Fig. 5 shows various performance measures versus voice threshold
for different values of Pv with It 20: As the voice threshold increases, the voice blocking probability decreases, while the packet dropping probability and channel utilization increase. The effect of Pv is not signi®cant. Fig. 6 shows various performance measures versus number of voice slots per frame for different values of Pv with It 20 and Vt 14: When the number of voice slots increases, the packet dropping probability decreases, and the changes of voice blocking probability and channel utilization are insigni®cant, even with different Pv : The packet loss probability with Pv 0:5 is much lower than that with Pv 0:1 or 0.9, especially when the number of voice slots becomes larger. 4.2. Integrated voice/data traf®c Simulation results of integrated voice/data traf®c under dynamic scenarios are presented next. The performance measures of interest include voice packet dropping probability, voice call blocking probability, data average delay and channel utilization. As is widely accepted, 1% of packet dropping probability and voice blocking probability is tolerable. We use this target value to determine the optimal values of Pv ; Pd ; voice call arrival rate, and voice threshold. 4.3. Determine the optimal Pv and Pd First of all, Fig. 7 shows the various performance measures versus Pv with Vt 18; It 19; Nv 8; Nd 56; and Pd 0:03: Obviously, the Pv does not affect the voice blocking probability because it does not affect the call arrival rate and call service time of voice terminal. It is also observed that without appropriate selection of Pv ; the voice packet dropping probability may exceed the target
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Fig. 8. Effects of Pd with It 20.
value. With smaller values of Pv ; voice packets contend less likely, and this results in larger delay and thus larger packet loss. On the other hand, with larger values of Pv ; voice packets contend more likely, and this results in more collisions and larger access delay and thus larger packet loss. It is noted that the data average delay and channel utilization ®rst remain almost constant and then decrease as Pv increases. According to the results of our studied cases, the optimal Pv appears to be around 0.6. Fig. 8 shows the various performance measures versus Pd with It 20; Vt 24; Nv 8; Nd 56; and Pv 0:6: Apparently, as Pd increases, the
data average delay ®rst increases and then decreases, whereas the voice packet dropping probability, voice call blocking probability, and channel utilization remains relatively constant. Similarly, data packets contend less likely with smaller values of Pd ; and data packets result in more collisions with larger values of Pv ; and thus larger packet loss. It is also noted that as voice packets have higher priority than data packets, Pd has no effect on voice packet loss probability. According to the results of all our studied cases, the optimal Pd appears to be around 0.03.
Fig. 9. Effects of interarrival time of voice calls.
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Fig. 10. Effects of voice threshold.
4.4. Interaction between CAC and congestion control factors Fig. 9 shows the various performance measures versus the interarrival time of voice calls for different values of Pv with Vt 20; Nd 56; and Pd 0:03: The voice blocking probability, voice packet dropping probability, data message transmission delay get better and the channel utilization gets worse as the interarrival time of voice calls increases. Fig. 10 shows the various performance measures versus the voice threshold with It 19; Nd 56; Pv 0:6; and Pd
0:03: Obviously, when the voice threshold increases, the voice blocking probability decreases but the voice packet dropping probability, data average delay and channel utilization increases. These results show that there exists a tradeoff between voice arrival rate and voice threshold. When the arrival rate increase, the voice blocking probability increases. If we want to reduce the voice blocking probability, we need to add the voice threshold. However, when the voice threshold increases, the voice packet dropping probability gets worse. With the target voice packet dropping probability and voice blocking probability being 1%, and
Fig. 11. Effects of number of voice slots.
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the interarrival time is 19 s, it is found that the maximum voice threshold is 24, and the associated channel utilization is about 80%. Fig. 11 shows the various performance measures versus the maximum number of voice slots per frame with It 12; Vt 24; Nd 56; Pv 0:6; and Pd 0:03: Obviously, the voice packet dropping probability decreases and the data average delay increases as that number increases. Lastly, it can also be shown that with Nd 56; Pv 0:6; and Pd 0:03; if the number of voice slots is 12, the maximum voice threshold is 26 provided that the call interarrival time is 11 s, and the associated channel utilization is about 87%. It is noted that this channel utilization corresponds to the maximum channel bandwidth available for the voice and data packets since about 11±12% of channel resource is devoted to the mini-slots. 5. Conclusion We consider wireless communication systems supporting both voice and data services, where call admission control (CAC) is used to guarantee QoS at the connection level and congestion control to guarantee QoS at the cell level. We study the effect of voice interarrival time and voice threshold on voice packet loss probability, voice call blocking probability, data packet average delay, and channel utilization. With appropriate Markovian models, the voice packet loss probability, voice blocking probability and channel utilization of voice traf®cs are derived for both dynamic and static scenarios, and the analytical results are shown to be in good agreement with the simulation results. It is shown that voice call blocking probability can be traded off for packet loss probability and channel utilization. In addition, for integrated voice/data traf®c, computer simulation is used to evaluate the effect of proposed CAC and congestion control on the performance measures of both voice and data traf®cs. With the computer simulation results it is found that the optimal Pv is about 0.6 and the optimal Pd is about 0.03. When the number of voice slots is 12, given that the call interarrival time is 11 s, the maximum voice threshold is 26, and the associated channel utilization is about 87%, which corresponds to the maximum channel bandwidth available for the voice and data packets. References [1] D.C. Cox, Wireless network access for personal communications, IEEE Commun. Mag. 30 (12) (1992) 96±115.
[2] E. Ayanoglu, K.Y. Eng, M.J. Karol, Wireless ATM: limits, challenges, and proposals, IEEE Personal Commun. 3 (4) (1996) 18±34. [3] D. Raychaudhuri, Wireless ATM networks: architecture, system design and prototyping, IEEE Personal Commun. 34 (1996) 42±49. [4] D. Raychaudhuri, L.J. French, R.J. Siracusa, R. Yuan, P. Narasimhan, C. Johnston, WATMnet: a prototype wireless ATM system for multimedia personal communication, ICC'96 1 (1996) 469±477. [5] D. Weissman, A.H. Levesque, R.A. Dean, Interoperable wireless data, IEEE Commun. Mag. 31 (2) (1993) 68±77. [6] J.E. Wieselthier, A. Ephremides, Performance analysis of ®xed- and movable-boundary channel-access schemes for integrated voice/data wireless networks, INFOCOM'93 3 (1993) 1204±1213. [7] S. Nanda, D.J. Goodman, U. Timor, Performance of PRMA: a packet voice protocol for cellular systems, IEEE Trans. Veh. Tech. 40 (1991) 585±598. [8] W.C. Wong, D.J. Goodman, A packet reservation multiple access protocol for integrated speech and data transmission, IEE Proc. 139 (1992) 585±598. [9] P. Naras, R.D. Yates, A new protocol for the integration of voice and data over PRMA, IEEE JSAC 14 (4) (1996). [10] G. Wu, K. Mukumoto, A. Fukuda, An integrated voice and data transmission system with idle signal multiple access-static analysis, IEICE Trans. Commun. E76-B (11) (1993) 1398±1407. [11] N.D. Wilson, R. Ganesh, K. Josesph, D. Raychaudhuri, Packet CDMA versus dynamic TDMA for multiple access in an integrated voice/data PCN, IEEE JSAC 11 (6) (1993) 870±884. [12] B.C. Kim, C.K. Un, Capacity of wireless dynamic TDMA and media access control for packetized voice/data integration, Wireless Personal Commun. (1995) 313±319. [13] J.G. Gruber, N. Le, Performance requirements for integrated voice/ data networks, IEEE JSAC 1 (6) (1983) 981±1005. [14] K. Zhang, K. Pahlavan, An integrated voice/data system for mobile indoor radio networks, IEEE Trans. Veh. Tech. 39 (1) (1990) 75±82. [15] J.-F. Frigon, H.C.B. Chan, V.C.M. Leung, Data and voice integration in DR-TDMA for wireless ATM networks, ICC'99 (1999) 1696± 1700. [16] H. Liu, L. Dittmann, U. Glieise, P. Danielsen, Multiple access protocol for supporting multimedia services in wireless ATM networks, IEEE Veh. Tech. Conf. 2 (2) (1999) 1146±1150. [17] O. Kubbar, H.T. Mouftah, Multiple access control protocols for wireless ATM: problems de®nition and design objectives, IEEE Commun. Mag. 35 (11) (1997) 93±99. [18] G. Wu, K. Mukumoto, A. Fukuda, M. Mizuno, A dynamic TDMA wireless integrated voice/data system with data steal into voice (DSV) technique, IEICE Trans. Commun. E78-B (8) (1995) 1125±1135. [19] P.T. Brady, A technique for investigating on±off patterns of speech, BSTJ 44 (1) (1965) 1±22. [20] E. Jeong, L. Jacob, S. Maeng, Dynamic TDMA with priority-based request packet transmission scheme for integrated multimedia traf®cs, IEICE Trans. Commun. E82-B (12) (1999) 2136±2144. [21] S. Jangi, L. Merakos, Performance analysis of reservation random access protocols for wireless access networks, IEEE Trans. Commun. 42 (2) (1994) 1223±1234.