- Email: [email protected]
Packet-based burst queue modeling at an edge in optical-burst switched networks
Computer Communications 29 (2006) 634–641 www.elsevier.com/locate/comcom
Packet-based burst queue modeling at an edge in optical-burst switched networks Sukyoung Lee* Graduate School of Information and Communications Sejong University, 98 Kunja-Dong, Kwangjin Ku, 143-747 Seoul, South Korea Received 19 April 2004; revised 24 April 2005; accepted 9 May 2005 Available online 13 June 2005
Abstract Optical burst switching is a promising solution for terabit transmission of IP data bursts over WDM networks as the next-generation Internet infrastructure. In this paper, we analyze burst queue with burst assembler at an edge in Optical Burst-Switched (OBS) networks. It is significant from the fact that most of processing and buffering are concentrated at the edge in OBS networks. Modeling the burst queue in terms of IP packets, we aim to investigate the waiting time in burst queue following burst assembler, the size of which influences the cost of constructing OBS networks. The proposed analytical model is verified through simulation. q 2005 Elsevier B.V. All rights reserved. Keywords: OBS; Burst queue; Burst assembly; IP packets
1. Introduction In order to realize such IP-over-WDM paradigms, optical switching function and its control protocols in optical routing nodes become indispensable between IP layer and underlying optical transport layer. Among various optical switching paradigms, optical burst switching has attracted more attention as a quite suitable network architecture for future Optical Internet backbones [1]. In an Optical BurstSwitched (OBS) network, an ingress OBS node assembles multiple IP packets into bursts and sends out a corresponding control packet for each data burst. This control packet is delivered out-of-band and leads the data burst by an offset time. The control packet reserves necessary resources all the way from the ingress node to the egress node. Then, the burst is transmitted without the need for any type of buffering at the intermediate nodes. This novel approach is expected to provide an infrastructure of the next-generation Internet against the exponential growth of the demands. The main question arising in OBS networks is how to carry IP traffic by means of a new network architecture * Present address: Dept. of Computer Science, Yonsei University, Seoul, Korea. Tel./fax: C82 2 3408 3963. E-mail address: [email protected].
0140-3664/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2005.05.005
adopting the OBS switching paradigm. One of the key problems in the application of burst switching in an optical domain is the aggregation of several IP packets in a single optical burst and hence, it is necessary to implement the assembly and disassembly functions from IP packets to the burst format and vice versa. In particular, once IP packets are aggregated into much larger bursts, they should wait in the burst queue [2] till the already assembled bursts are scheduled for transmission into the network core and then enough wavelength is reserved for themselves before transmission through the network. Even if there have been several works to investigate an edge in OBS networks [4–10], most of them have focused on how to assemble packets into a burst [4–8]. In [9], the performance of TCP traffic was studied under different burst assembly mechanisms. While the authors in [10] presented a queueing network model of an edge OBS node to study the performance of the edge node assuming an infinite server for the case there is no available outgoing channel, the burst assembly process at an edge was not considered seriously. Thus, in this paper, we focus on developing an analytical model of the burst queue with burst assembler in the light of IP packets rather than developing a burst assembly mechanism itself or only evaluating the performance of an edge OBS node. We investigate the waiting time as well as the expected number of IP packets in burst queue following burst assembler at an edge of OBS networks because most of processing and buffering are concentrated at the edge in an OBS network.
S. Lee / Computer Communications 29 (2006) 634–641
Further, most existing works in the literature [4,7–8] consider only burst assembly time for the processing delay at an edge while in addition to the burst assembly time, we take account of the waiting time in burst queue after the burst assembly is completed. Thus, our investigation of the average waiting time in burst queue and the average burst assembly time can be reflected into deciding when the control packet is transmitted to reduce end-toend delay as in [8]. This investigation could be also meaningful in the aspect that the size of burst queue would be decided on the basis of the expected number of IP packets in the burst queue and the tolerable delay limit of each traffic class. The remainder of the paper is organized as follows. Section 2 describes the overall queueing architecture at an OBS edge node while introducing a mechanism to reduce end-to-end delay. In Section 3, we develop an analytical model to calculate the waiting time in burst queue following burst assembler. Section 4 provides numerical results from simulation and analysis. Section 5 concludes the paper.
2. Overall queueing architecture at an OBS edge node 2.1. Burst generation from multiple traffic sources An edge OBS node is connected to a number of users or Label Switched Paths (LSPs) when OBS is utilizing GMPLS (Generalized MultiProtocol Label Switching) signaling [2,3] as can be seen in Fig. 1. That is, it receives bursts from users or LSPs. The functions zoomed in the edge OBS node in Fig. 1 are presented in Fig. 2. As shown in Fig. 2, a burst queue can be shared among several users or LSPs where the traffic arrives according to a burst arrival process at an edge node in OBS networks. If the traffic is composed of multiple classes, it is desirable to implement multiple burst queues with the same number of multiple burst assemblers, where incoming IP packets destined for the same destination node (or CoS: Class of Service) are sent to the same burst queue. That is, as soon as bursty IP traffic streams are assembled into bursts at burst assembler, these bursts are classified according to the destination (or priority of the traffic) [4].
635
Fig. 2. Overall queueing architecture at an edge.
Each incoming IP packet for a given burst needs to be stored in the burst assembler until the last packet of the burst arrives. As soon as the last packet arrives, all packets of the burst are transferred to the burst queue. Considering the burst arrival process to a given burst queue, the arrival process to the burst queue can be modelled as a superposition of N independent effective On/Off processes, each coming from N users or LSPs. We assume that the number of input ports of an edge node and the number of the users connected to the edge node are same. If we further assume that both On and Off periods are geometrically distributed with the same parameters a and b which denote the transition rates from Off to On and On to Off states, respectively, an Interrupted Bernoulli Process (IBP) can be used to model each burst assembler. We also assume that within the On state, at each time instant, there is an IP packet arrival with probability g from each active user/LSP and generated IP packets during an On period form a single burst. We base our system model on timer-based approach as burst assembly technique [5], whereby a predefined threshold is placed on the time it takes a new burst to be generated. The employment of timer-based approach will lead the edge optical burst switching node to having variable size bursts. For simplicity, we assume that the time should include an On period so that all the IP packets generated during the On period are supposed to be assembled into a burst. 2.2. End-to-end delay reduction
Fig. 1. Overall queueing architecture at an edge.
In our OBS edge node, the burst processing and the transmission of a control packet should be processed in parallel, the former of which consists of the burst assembly and the waiting in burst queue as can be seen in Fig. 2 and thereby minimize their impact on the total end-to-end burst delay. Let Ta and Tq be the burst assembly time and the waiting time in burst queue, respectively and let To denote the offset time. In [8], a burst assembly mechanism is
636
S. Lee / Computer Communications 29 (2006) 634–641
proposed for end-to-end delay reduction, in which a control packet is launched into the core network before burst assembly process is completed. However, in [8], only burst assembly time is considered for the processing delay at an edge while in addition to the burst assembly time, we take account of the waiting time in burst queue after the completion of the burst assembly. In case that Tq is not counted in for the processing delay at an edge and a control packet is sent into the core network during Ta, To can expire while bursts are waiting in the burst queue, resulting in dropping the bursts due to insufficient reservation time for the bursts. That is, when the bursts arrive at a core node, they find that the corresponding reservation time already began and will be over before the burst transmission is completed at the core node, leading to the burst dropping. Thus, we investigate the average waiting time in burst queue, T q by developing an analytical model. Further, in [8], the burst length should be known prior to the burst assembly completion, so that the burst length is estimated based on the fixed values of Ta and To. Thus, in this paper, the average burst assembly time, T a is also investigated based on On/Off traffic source model. In most existing works about OBS technology, as soon as each burst is at the head of the burst queue, it could not be transmitted into a network since it should usually wait for an offset time during which the control packet reserves the wavelength. Therefore, to reduce the delay which each burst experiences at an edge, the control packet generator in Fig. 2 has to transmit the control packet if the remaining waiting time of the burst in the burst queue with burst assembly is not less than the offset time. In Fig. 3, a simple mechanism is described to reduce the waiting time at an OBS edge node. In this mechanism, as in [8], a control packet is transmitted while the corresponding burst waits in burst queue as well as in burst assembler, that is before the burst is at the head of the burst queue. Accordingly, the offset time, To is included both in the burst assembly latency and in the waiting time in burst queue. In case that T a C T q is larger than To, the control packet should not be sent until the remaining waiting time at the edge becomes To unless an extra offset time is set for the burst. Even for the case that T a C T q is less than To, if the control packet is transmitted at the moment the first IP packet starts being assembled into a burst, the assembled burst only has to wait for To K T a K T q at the head of the burst queue, which is shorter than To. Similarly with the burst assembly mechanism in [8], we could see the reduction of waiting time at an edge OBS node in Fig. 4. However, unlike [8], our mechanism takes into account of the waiting time in the burst queue on the basis of multiple traffic sources/LSPs at an edge.
Fig. 3. The desired actions to reduce the waiting time at an edge OBS node.
3. Analytic model of edge node 3.1. Burst assembly If we denote pi as the steady-state probability that the burst assembler contains i IP packets under a single On/Off process, it is possible to model a Markov chain for each burst assembler as shown in Fig. 5 and the steady-state probability, pi is given by
pi Z
8 b > > ; > > a Cb > < a
for i Z 0
p; for i Z 1 b C gð1 K bÞ 0 > > > > gð1 K bÞ > : p ; for iR 2 b C gð1 K bÞ iK1
(1)
Assuming the event that the burst assembler is not empty, the conditional probability, Pi that the burst assembler contains i IP packets becomes Pi Z
pi ðiR 1Þ: 1 K p0
(2)
S. Lee / Computer Communications 29 (2006) 634–641
637
Fig. 4. The reduction of waiting time at an edge OBS node under existing and proposed mechanisms.
Thus, from the Eqs. (1) and (2), we get 8 b > > for i Z 1 < b C gð1 K bÞ ; iK1 Pi Z b b b > > : 1K 1K ; for iR 2 PiK1 Z b C gð1 K bÞ b C gð1 K bÞ b C gð1 K bÞ The above Eq. (3) is reduced to iK1 b b Pi Z 1K ; b C gð1 K bÞ b C gð1 K bÞ
for iR 1: (4)
Let Na and Ta denote the number of IP packets and the waiting time in burst assembler under the assumption that the burst assembler is not empty. Let N a and T a be the expected values of Na and Ta, respectively. From the Eq. (4) and the fact that memoryless property of pi leads Pi to having the geometric distribution, we have b C rð1 K bÞ : N a Z b
(5)
It is assumed that the processing time to generate a burst for each packet, tp is independent exponentially distributed random variable with mean 1/m. With substitution of b/(bCg(1Kb)) by p, the generating function for Na is GNa ðzÞ Z
p 1 K ð1 K pÞz
sinceP tp is independent exponentially distributed. Given that a Sa Z NkZ1 tk where tp becomes tk for kth packet, the mean of Sa is found by using conditional expectation: E½Sa Z E½E½Sa jNa Z E½Na E½tp Z E½Na E½tp ].
m m K jw
(8)
Therefore, we get FSa ðwÞ Z E½E½ejwSa jNa Z E½Ftp ðwÞNa Z E½zNa jzZFtp ðwÞ Z GNa ðFtp ðwÞÞ:
(9)
By substituting Eqs. (6) and (7) into the above Eq. (9), the characteristic function of Sa is evaluated as FSa ðwÞ Z
p 1 K mð1KpÞ mKjw
:
(6)
and the characteristic function for tp is derived as Ftp Z
(3)
(7) Fig. 5. State transition diagram for burst assembler.
(10)
638
S. Lee / Computer Communications 29 (2006) 634–641
Then, the probability density function of Sa is found by taking the inverse Fourier transform of the above Eq. (10): fSa ðxÞ Z pdðxÞ C ð1 K pÞpmeKpmx
xR 0:
(11)
From Eq. (11), we know that the total processing time to assemble IP packets into a burst is also exponentially distributed and under the assumption that the burst assembler is not empty, the mean is 1 b C gð1 K bÞ T a Z Z : pm bm
(12)
As mentioned above in the previous section, the aggregate arrival process to the burst queue consists of a superposition of N independent On/Off processes. We can describe the aggregate arrival process by a discrete-time batch Markovian arrival process (D-BMAP). Subsequently, the algorithm for computing the vector xi follows D-BMAP/D/1 model. However, it brings about the computational complexity in getting xi to compute the transition probability that the number of On sources changes from i to j generating a total of k packets in D-BMAP/D/1 model [11]. In advance of computing the approximation of xi, the traffic density can be defined as N a N : T
3.2. Burst queue modeling
rZ
In OBS networks, it is known that a burst in burst queue is transmitted to an out port after an offset time when offset-based wavelength reservation scheme is being run on the network [1]. The data bursts in a burst queue are assumed to be drained virtually in terms of IP packet. Thus, the burst queue is investigated using a discrete-time system where one time slot is equivalent to the duration an IP packet consisting of one burst, is transmitted on a wavelength. If we assume that the packets are not bound to arrive back-to-back, inter-arrival times of successive packets are i.i.d. (independent and identically distributed) [10]. That is, the length of a burst which consists of the packets during the On period is uncorrelated to the interarrival time. Often we think in terms of activity cycle, bK1 which has units of the average number of seconds per an On duration, is the active cycle while aK1 means the idle cycle. Then, overall one cycle T becomes aK1CbK1. The probability of such a traffic source being in the On state, pon is given by bK1/T. Then, we get the probability that a single source transits from On state to Off state in a time slot as followings
Let l denote 1=N a . Substituting Eq. (15) into (14), taking N/N and lr[1, we obtain the approximation of Eq. (14) 8 Klr e z1 K lr; i Z 0 > > > > < Klr iZ1 (16) Gi z lre zlr; > > i > ðlrÞ > : eKlr z0; otherwise i!
pt Z P½Transition_to_OffjBeing_in_On Z pon b:
(13)
Let Gi denote the probability that i out of N active sources transit from On state to Off state in a time slot. Then, Gi can be expressed as
(15)
where the first-order approximation can be applied. From Eq. (16), we get the probability, bi that i IP packets arrive to form a burst transiting from an On state to an Off state. This is expressed in the form of ( G0 Z 1 K lr; i Z0 bi Z (17) G1 Pi Z l2 rð1 K lÞiK1 ; iR 1 where bi also follows a geometric distribution. Fig. 6 depicts the state transition diagram of the burst queue which works on the basis of one time slot. According to the transition rules defined in this Figure, a system of difference equations may be derived for the approximation of xi, x~i as follows: x~ 0 ð1Kb0 ÞZ x~ 1 b0 x~ 1 ð1Kb1 ÞZ x~ 2 b0 C x~ 0 b1 x~ i ð1Kb1 ÞZ x~ iC1 b0 C x~ 0 bi C
Gi Z bði; N; pt Þ
(14)
where b(i; n, p) represents the binomial distribution with all n sources. Let x be the probability distribution of burst queue. We define xi as the steady-state probability that the burst queue contains i packets under a total of N On/Off sources from users/LSPs. Let xi denote the probability vector with N components, xi,n(1%n%N) which is the probability that the burst queue contains i packets and n sources are at On state.
iK1 X
(18) x~ i biKnC1 ; for iO1
nZ1
Fig. 6. State transition diagram of burst queue.
S. Lee / Computer Communications 29 (2006) 634–641
639
As usual, we solve the above equilibrium Eq. (18) using the method of z-transform, thus we have ð1Kb1 Þ
N X
x~ n zn
nZ2
Z
N N N X nK1 X X b0 X bn zn C x~ nC1 znC1 C x~ 0 x~ i bnKiC1 zn z nZ2 nZ2 nZ2 iZ1
(19) From the Eq. (19), z-transform of x~ i , X(z) is derived as follows: XðzÞZ x~ 0
zGðzÞKGðzÞ ; zKGðzÞ
(20)
where G(z), the z-transform of bi is z : GðzÞZ1KlrCl2 r 1Kð1KlÞz
(21)
To eliminate x~ 0 , X(1)Z1 is applied, that yields x~ 0 Z1Kr. We now make use of Eq. (21), 1 dn XðzÞ
x~ 0 Z1Kr and x~ n Z n! dzn zZ0
Fig. 7. Average waiting time (ms) in burst queue with burst assembly when lZ 1=N a Z 0:1 and 0.05.
the IP packets from the sources/LSPs to wait in burst queue even after being assembled into a burst.
to obtain x~ n . Thus, we have x~ n Z
4. Performance evaluation
lrð1KrÞð1KlÞnK1 : ð1KlrÞn
(22)
(24)
To assess the accuracy of our model, we compare our analytical results with those obtained by means of simulations. In our simulation, the burst sources were individually simulated with the On/Off model as explained in the Burst Assembly section. Simulation experiments are performed with varying traffic load, where there are 10 hops between ingress and egress nodes and the capacity of each link is 10 Gbps. The average packet length is set to 100 Kbyte. In order to capture the burstiness of data at the edge nodes, the traffic from a user to the edge node is
This analytic model of burst queue, in combination with carriers’ QoS mechanisms, could be used to allow the carriers to offer customized levels of burst assembly latency and waiting time in burst queue, which will have a significant impact on data burst’s end-to-end delay. Specifically, the analytic model in Eqs. (12) and (24) can be reflected in determining when the control packet is sent into an OBS network, to reduce the burst assembly latency and the waiting time in burst queue, resulting in reducing the end-to-end delay. Specially, while in [8], the burst assembly time and offset time were fixed, on the basis of which the burst length was simply estimated from traffic measurement, we analyzed the mean waiting time at an edge, which does not include only burst assembly latency but also waiting time in burst queue when multiple traffic sources are multiplexed into the edge node. The situation where multiple traffic sources/LSPs are multiplexed into an edge node is more realistic, leading
Fig. 8. Average waiting time (ms) in burst queue with burst assembly when lZ 1=N a Z 0:01 and 0.005.
Finally, the expected number of IP packets in the burst queue under N users/LSPs is derived as E½nZ
N X nZ0
n~xn Z
N X
n~xn Z
nZ1
rð1KlrÞ : lð1KrÞ
(23)
From Eq. (23), the mean waiting time in burst queue, T q becomes E½n rð1KlrÞ Z 2 : T q Z l l ð1KrÞ
640
S. Lee / Computer Communications 29 (2006) 634–641
Table 1 The difference of the analytical result compared with simulation results r
lZ0.1
lZ0.05
lZ0.01
NZ10
NZ50
NZ10
NZ50
NZ10
NZ50
NZ10
NZ50
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.73!10K2 1.76!10K2 1.83!10K2 2.02!10K2 2.03!10K2 2.32!10K2 8.01!10K2 1.13!10K1 1.42!10K1
7.93!10K3 9.41!10K3 1.54!10K2 1.57!10K2 1.94!10K2 2.14!10K2 2.90!10K2 3.07!10K2 6.46!10K2
1.28!10K2 1.26!10K2 1.77!10K2 2.84!10K2 3.41!10K2 3.77!10K2 7.58!10K2 1.18!10K1 1.29!10K1
1.23!10K2 1.27!10K2 1.72!10K2 1.74!10K2 1.92!10K2 1.96!10K2 2.08!10K2 2.78!10K2 3.79!10K2
1.17!10K2 1.25!10K2 1.93!10K2 3.04!10K2 2.87!10K2 4.30!10K2 6.62!10K2 7.68!10K2 8.76!10K2
8.98!10K3 9.24!10K3 1.14!10K2 1.48!10K2 1.80!10K2 1.97!10K2 2.06!10K2 1.90!10K2 3.39!10K2
1.65!10K2 1.61!10K2 1.83!10K2 1.79!10K2 2.03!10K2 2.79!10K2 3.19!10K2 4.40!10K2 7.68!10K2
9.22!10K3 1.29!10K2 1.24!10K2 1.60!10K2 1.67!10K2 2.06!10K2 2.07!10K2 2.63!10K2 3.01!10K2
generated by Poisson packet arrivals from 10 and 50 independent traffic sources that are either transmitting packets during the On period or is idle during the Off period. The On and the Off periods are assumed to be exponentially distributed with mean of 1 s. For each simulation, depending on the offered load, between two million and one hundred million packets were simulated. Figs. 7 and 8 plot the average waiting time in burst queue with burst assembly versus the traffic density for the simulation with different number of sources such as users or LSPs: NZ10, NZ50 and the analytical model. As can be easily expected, the burst buffering in any OBS network strongly depends on the traffic statistics of arriving packets [12]. In other words, as the mean arrival rate increases, so does the average waiting time. From the graphs in Figs. 7 and 8, we observe that the error increases as the r increases, that is, the traffic density increases. There may be some concern that the analytical model may not work very well if there are just a few sources under the assumption that N/N. But this concern falls off in the bar for both simulation experiments with NZ10 and NZ50. As can be seen in Table 1, the maximum error in difference between the analytical and simulation results is 1.42!10K1 when there are 10 sources and the traffic density is 0.9. Even if the traffic density increases, the error does not increase as much as that in the case of NZ10 does. The maximum does not exceed 7!10K2 when NZ50. Especially, at very high loads the analytical model performs better than that at low loads. But we know that the difference is further reduced as N increases. We expect the analytical result to track the simulation result more closely as the traffic arrivals increase, because lr[1 is assumed in our analytical model. From the Table 1, as the burst arrival increases, we also see good agreement between the analytical and the simulation results. Accordingly, from this analytical model, Internet Service Providers (ISPs) expect how tolerable delay limit could be provided for each service class in an OBS network, according to such network status as number of users or LSPs, link density, CoS, and etc. We now investigate the end-to-end delay under the simple mode of the existing OBS signaling scheme
lZ0.005
where control packet is sent when the burst is at the head of burst queue and those under the scheme of [8] and the proposed scheme which start resource reservation during Ta and TaCTq, respectively (called Ta Resource Reservation (RR) and TaCTqRR, respectively). The delay of a data burst is defined as the average delay of all the packets. Fig. 9 shows the delay reduction by TaRR and TaCTqRR over the simple mode under the traffic load of 0.5 as the burst assembly time, Ta varies from 1 ms up to 100 ms when To is set to 1, 5 and 10 ms. Both the TaRR and TaCTqRR schemes show the same performance improvement in terms of the delay reduction only if the resource reservation is successful, since control packet is sent at the time of TaKTo and TaCTbKTo, respectively, for the two schemes. However, in the TaRR, because Tb is not considered, in the case that bursts must wait in the burst queue, To expires while the bursts are still waiting in the burst queue, leading to insufficient resource reservation time for the bursts. The drop rate resulting from the insufficient resource reservation time is shown in Fig. 10(a) and (b) for NZ10 and 50, respectively. As we expected in Section 2.2, we observe that the drop rate experienced by TaRR is much higher than
Fig. 9. Average reduced delay rate for different values of To.
S. Lee / Computer Communications 29 (2006) 634–641
641
into the core network while the burst waits in the burst queue. As our future research, we are extending this model to be implemented with offset time and priorities based on end-toend delay that would be closely related to the waiting time in the burst queue as well as the burst assembly latency.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) through OIRC project. And also the author would like to thank Lae Young Kim for her help in performing the simulations.
Fig. 10. Average packet drop rate for different values of when NZ10 and 50.
the other schemes due to the unsuccessful resource reservation. In particular, as the overall offered load becomes higher, the drop rate difference between TaRR and the other schemes increases because the waiting time in the burst queue increases while the control packet is sent at the time of TaKTo under the TaRR scheme. It is also noted from Fig. 10 that compared to the simple mode, TaCTbRR scheme maintains its average drop rate lower while achieving better performance in terms of end-to-end delay.
5. Conclusion OBS is a desirable approach to support real-time multimedia traffic in the Internet, which is bursty and requires low latency. It is especially economic and efficient for providing high-end users or applications with sessions having a high bit-rate, low latency and short duration upon their requests. However it is possible that the processing at an edge would be a bottleneck to those applications. Therefore, in this paper, we investigated the burst queue with burst assembler at an edge in OBS networks in the light of IP packets from multiple traffic sources/LSPs. We observed that the developed analytical model of waiting time at an OBS edge node, performs as well as the simulations in all load conditions when there are large number of sources. The simulation results indicated that as the packet arrivals increase, the analytical model approximates more to the simulation results, while it lightens the computation overhead. We also noted that it is possible to reduce the end-to-end delay by sending the control packet
References [1] T. Battestilli, H. Perros, An introduction to optical burst switching, IEEE Communications Magazine 41 (8) (2003) s10–s15. [2] H.M. Chaskar, S. Verma, R. Ravikanth, Robust transport of IP traffic over WDM using optical burst switching, Optical Networks Magazine 3 (4) (2002). [3] S. Ovadia, C. Maciocco, M. Paniccia, Photonic burst switching (PBS) architecture for hop and span constrained optical networks, IEEE Communications Magazine 41 (11) (2003) s24–s32. [4] S.Y. Oh, M. Kang, A burst assembly algorithm in optical burst switching networks, Optical Fiber Communication Conference 2002, 2002. [5] V. Vokkarane, K. Haridoss, J. Jue, Threshold-based burst assembly policies for QoS support in optical burst-switched networks, Proceedings, SPIE Optical Networking and Communication Conference 2002, vol. 4874, 2002 pp. 125–136. [6] V. Vokkarane, J. Jue, Prioritized burst segmentation and composite burst assembly techniques for QoS support in optical burst-switched networks, IEEE JSAC-High-Performance Optical/Electronic Switches/Routers for High-Speed Internet 21 (7) (2003) 1198–1209. [7] K. Long, R.S. Tucker, C. Wang, A new framework and burst assembly for IP DiffServ over optical burst switching networks, IEEE Proceedings of Globecom’03, San Francisco, USA, 2002 pp. 3159–3164. [8] T. Hashiguchi, X. Wang, H. Morikawa, T. Aoyama, Burst assembly mechanism with delay reduction for OBS networks, Proceedings of Conference on the Optical Internet(COIN 2003), Melbourne, Australia, 2003 pp. 664–666. [9] X. Ca, J. Li, Y. Chen, C. Qiao, Assembling TCP/IP packets in optical burst switched networks, IEEE Proceedings of GLOBECOM’02 3 (2002) 2808–2812. [10] L. XU, H.G. Perros, G.N. Rouskas, A queueing network model of an edge optical burst switching node, IEEE Proceedings of INFOCOM’03, 2003. [11] I. Widjaja, M.F. Neuts, J-M. Li, Conditional overflow probability and profile curve for ATM congestion detection, IEEE Proceedings of INFOCOM’96, 1996. [12] M. Dueser, P. Bayvel, Performance of a dynamically wavelengthrouted optical burst switched network, IEEE Photonics Technology Letters 14 (2) (2002) 239–241.
Packet-based burst queue modeling at an edge in optical-burst switched networks Sukyoung Lee* Graduate School of Information and Communications Sejong University, 98 Kunja-Dong, Kwangjin Ku, 143-747 Seoul, South Korea Received 19 April 2004; revised 24 April 2005; accepted 9 May 2005 Available online 13 June 2005
Abstract Optical burst switching is a promising solution for terabit transmission of IP data bursts over WDM networks as the next-generation Internet infrastructure. In this paper, we analyze burst queue with burst assembler at an edge in Optical Burst-Switched (OBS) networks. It is significant from the fact that most of processing and buffering are concentrated at the edge in OBS networks. Modeling the burst queue in terms of IP packets, we aim to investigate the waiting time in burst queue following burst assembler, the size of which influences the cost of constructing OBS networks. The proposed analytical model is verified through simulation. q 2005 Elsevier B.V. All rights reserved. Keywords: OBS; Burst queue; Burst assembly; IP packets
1. Introduction In order to realize such IP-over-WDM paradigms, optical switching function and its control protocols in optical routing nodes become indispensable between IP layer and underlying optical transport layer. Among various optical switching paradigms, optical burst switching has attracted more attention as a quite suitable network architecture for future Optical Internet backbones [1]. In an Optical BurstSwitched (OBS) network, an ingress OBS node assembles multiple IP packets into bursts and sends out a corresponding control packet for each data burst. This control packet is delivered out-of-band and leads the data burst by an offset time. The control packet reserves necessary resources all the way from the ingress node to the egress node. Then, the burst is transmitted without the need for any type of buffering at the intermediate nodes. This novel approach is expected to provide an infrastructure of the next-generation Internet against the exponential growth of the demands. The main question arising in OBS networks is how to carry IP traffic by means of a new network architecture * Present address: Dept. of Computer Science, Yonsei University, Seoul, Korea. Tel./fax: C82 2 3408 3963. E-mail address: [email protected].
0140-3664/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2005.05.005
adopting the OBS switching paradigm. One of the key problems in the application of burst switching in an optical domain is the aggregation of several IP packets in a single optical burst and hence, it is necessary to implement the assembly and disassembly functions from IP packets to the burst format and vice versa. In particular, once IP packets are aggregated into much larger bursts, they should wait in the burst queue [2] till the already assembled bursts are scheduled for transmission into the network core and then enough wavelength is reserved for themselves before transmission through the network. Even if there have been several works to investigate an edge in OBS networks [4–10], most of them have focused on how to assemble packets into a burst [4–8]. In [9], the performance of TCP traffic was studied under different burst assembly mechanisms. While the authors in [10] presented a queueing network model of an edge OBS node to study the performance of the edge node assuming an infinite server for the case there is no available outgoing channel, the burst assembly process at an edge was not considered seriously. Thus, in this paper, we focus on developing an analytical model of the burst queue with burst assembler in the light of IP packets rather than developing a burst assembly mechanism itself or only evaluating the performance of an edge OBS node. We investigate the waiting time as well as the expected number of IP packets in burst queue following burst assembler at an edge of OBS networks because most of processing and buffering are concentrated at the edge in an OBS network.
S. Lee / Computer Communications 29 (2006) 634–641
Further, most existing works in the literature [4,7–8] consider only burst assembly time for the processing delay at an edge while in addition to the burst assembly time, we take account of the waiting time in burst queue after the burst assembly is completed. Thus, our investigation of the average waiting time in burst queue and the average burst assembly time can be reflected into deciding when the control packet is transmitted to reduce end-toend delay as in [8]. This investigation could be also meaningful in the aspect that the size of burst queue would be decided on the basis of the expected number of IP packets in the burst queue and the tolerable delay limit of each traffic class. The remainder of the paper is organized as follows. Section 2 describes the overall queueing architecture at an OBS edge node while introducing a mechanism to reduce end-to-end delay. In Section 3, we develop an analytical model to calculate the waiting time in burst queue following burst assembler. Section 4 provides numerical results from simulation and analysis. Section 5 concludes the paper.
2. Overall queueing architecture at an OBS edge node 2.1. Burst generation from multiple traffic sources An edge OBS node is connected to a number of users or Label Switched Paths (LSPs) when OBS is utilizing GMPLS (Generalized MultiProtocol Label Switching) signaling [2,3] as can be seen in Fig. 1. That is, it receives bursts from users or LSPs. The functions zoomed in the edge OBS node in Fig. 1 are presented in Fig. 2. As shown in Fig. 2, a burst queue can be shared among several users or LSPs where the traffic arrives according to a burst arrival process at an edge node in OBS networks. If the traffic is composed of multiple classes, it is desirable to implement multiple burst queues with the same number of multiple burst assemblers, where incoming IP packets destined for the same destination node (or CoS: Class of Service) are sent to the same burst queue. That is, as soon as bursty IP traffic streams are assembled into bursts at burst assembler, these bursts are classified according to the destination (or priority of the traffic) [4].
635
Fig. 2. Overall queueing architecture at an edge.
Each incoming IP packet for a given burst needs to be stored in the burst assembler until the last packet of the burst arrives. As soon as the last packet arrives, all packets of the burst are transferred to the burst queue. Considering the burst arrival process to a given burst queue, the arrival process to the burst queue can be modelled as a superposition of N independent effective On/Off processes, each coming from N users or LSPs. We assume that the number of input ports of an edge node and the number of the users connected to the edge node are same. If we further assume that both On and Off periods are geometrically distributed with the same parameters a and b which denote the transition rates from Off to On and On to Off states, respectively, an Interrupted Bernoulli Process (IBP) can be used to model each burst assembler. We also assume that within the On state, at each time instant, there is an IP packet arrival with probability g from each active user/LSP and generated IP packets during an On period form a single burst. We base our system model on timer-based approach as burst assembly technique [5], whereby a predefined threshold is placed on the time it takes a new burst to be generated. The employment of timer-based approach will lead the edge optical burst switching node to having variable size bursts. For simplicity, we assume that the time should include an On period so that all the IP packets generated during the On period are supposed to be assembled into a burst. 2.2. End-to-end delay reduction
Fig. 1. Overall queueing architecture at an edge.
In our OBS edge node, the burst processing and the transmission of a control packet should be processed in parallel, the former of which consists of the burst assembly and the waiting in burst queue as can be seen in Fig. 2 and thereby minimize their impact on the total end-to-end burst delay. Let Ta and Tq be the burst assembly time and the waiting time in burst queue, respectively and let To denote the offset time. In [8], a burst assembly mechanism is
636
S. Lee / Computer Communications 29 (2006) 634–641
proposed for end-to-end delay reduction, in which a control packet is launched into the core network before burst assembly process is completed. However, in [8], only burst assembly time is considered for the processing delay at an edge while in addition to the burst assembly time, we take account of the waiting time in burst queue after the completion of the burst assembly. In case that Tq is not counted in for the processing delay at an edge and a control packet is sent into the core network during Ta, To can expire while bursts are waiting in the burst queue, resulting in dropping the bursts due to insufficient reservation time for the bursts. That is, when the bursts arrive at a core node, they find that the corresponding reservation time already began and will be over before the burst transmission is completed at the core node, leading to the burst dropping. Thus, we investigate the average waiting time in burst queue, T q by developing an analytical model. Further, in [8], the burst length should be known prior to the burst assembly completion, so that the burst length is estimated based on the fixed values of Ta and To. Thus, in this paper, the average burst assembly time, T a is also investigated based on On/Off traffic source model. In most existing works about OBS technology, as soon as each burst is at the head of the burst queue, it could not be transmitted into a network since it should usually wait for an offset time during which the control packet reserves the wavelength. Therefore, to reduce the delay which each burst experiences at an edge, the control packet generator in Fig. 2 has to transmit the control packet if the remaining waiting time of the burst in the burst queue with burst assembly is not less than the offset time. In Fig. 3, a simple mechanism is described to reduce the waiting time at an OBS edge node. In this mechanism, as in [8], a control packet is transmitted while the corresponding burst waits in burst queue as well as in burst assembler, that is before the burst is at the head of the burst queue. Accordingly, the offset time, To is included both in the burst assembly latency and in the waiting time in burst queue. In case that T a C T q is larger than To, the control packet should not be sent until the remaining waiting time at the edge becomes To unless an extra offset time is set for the burst. Even for the case that T a C T q is less than To, if the control packet is transmitted at the moment the first IP packet starts being assembled into a burst, the assembled burst only has to wait for To K T a K T q at the head of the burst queue, which is shorter than To. Similarly with the burst assembly mechanism in [8], we could see the reduction of waiting time at an edge OBS node in Fig. 4. However, unlike [8], our mechanism takes into account of the waiting time in the burst queue on the basis of multiple traffic sources/LSPs at an edge.
Fig. 3. The desired actions to reduce the waiting time at an edge OBS node.
3. Analytic model of edge node 3.1. Burst assembly If we denote pi as the steady-state probability that the burst assembler contains i IP packets under a single On/Off process, it is possible to model a Markov chain for each burst assembler as shown in Fig. 5 and the steady-state probability, pi is given by
pi Z
8 b > > ; > > a Cb > < a
for i Z 0
p; for i Z 1 b C gð1 K bÞ 0 > > > > gð1 K bÞ > : p ; for iR 2 b C gð1 K bÞ iK1
(1)
Assuming the event that the burst assembler is not empty, the conditional probability, Pi that the burst assembler contains i IP packets becomes Pi Z
pi ðiR 1Þ: 1 K p0
(2)
S. Lee / Computer Communications 29 (2006) 634–641
637
Fig. 4. The reduction of waiting time at an edge OBS node under existing and proposed mechanisms.
Thus, from the Eqs. (1) and (2), we get 8 b > > for i Z 1 < b C gð1 K bÞ ; iK1 Pi Z b b b > > : 1K 1K ; for iR 2 PiK1 Z b C gð1 K bÞ b C gð1 K bÞ b C gð1 K bÞ The above Eq. (3) is reduced to iK1 b b Pi Z 1K ; b C gð1 K bÞ b C gð1 K bÞ
for iR 1: (4)
Let Na and Ta denote the number of IP packets and the waiting time in burst assembler under the assumption that the burst assembler is not empty. Let N a and T a be the expected values of Na and Ta, respectively. From the Eq. (4) and the fact that memoryless property of pi leads Pi to having the geometric distribution, we have b C rð1 K bÞ : N a Z b
(5)
It is assumed that the processing time to generate a burst for each packet, tp is independent exponentially distributed random variable with mean 1/m. With substitution of b/(bCg(1Kb)) by p, the generating function for Na is GNa ðzÞ Z
p 1 K ð1 K pÞz
sinceP tp is independent exponentially distributed. Given that a Sa Z NkZ1 tk where tp becomes tk for kth packet, the mean of Sa is found by using conditional expectation: E½Sa Z E½E½Sa jNa Z E½Na E½tp Z E½Na E½tp ].
m m K jw
(8)
Therefore, we get FSa ðwÞ Z E½E½ejwSa jNa Z E½Ftp ðwÞNa Z E½zNa jzZFtp ðwÞ Z GNa ðFtp ðwÞÞ:
(9)
By substituting Eqs. (6) and (7) into the above Eq. (9), the characteristic function of Sa is evaluated as FSa ðwÞ Z
p 1 K mð1KpÞ mKjw
:
(6)
and the characteristic function for tp is derived as Ftp Z
(3)
(7) Fig. 5. State transition diagram for burst assembler.
(10)
638
S. Lee / Computer Communications 29 (2006) 634–641
Then, the probability density function of Sa is found by taking the inverse Fourier transform of the above Eq. (10): fSa ðxÞ Z pdðxÞ C ð1 K pÞpmeKpmx
xR 0:
(11)
From Eq. (11), we know that the total processing time to assemble IP packets into a burst is also exponentially distributed and under the assumption that the burst assembler is not empty, the mean is 1 b C gð1 K bÞ T a Z Z : pm bm
(12)
As mentioned above in the previous section, the aggregate arrival process to the burst queue consists of a superposition of N independent On/Off processes. We can describe the aggregate arrival process by a discrete-time batch Markovian arrival process (D-BMAP). Subsequently, the algorithm for computing the vector xi follows D-BMAP/D/1 model. However, it brings about the computational complexity in getting xi to compute the transition probability that the number of On sources changes from i to j generating a total of k packets in D-BMAP/D/1 model [11]. In advance of computing the approximation of xi, the traffic density can be defined as N a N : T
3.2. Burst queue modeling
rZ
In OBS networks, it is known that a burst in burst queue is transmitted to an out port after an offset time when offset-based wavelength reservation scheme is being run on the network [1]. The data bursts in a burst queue are assumed to be drained virtually in terms of IP packet. Thus, the burst queue is investigated using a discrete-time system where one time slot is equivalent to the duration an IP packet consisting of one burst, is transmitted on a wavelength. If we assume that the packets are not bound to arrive back-to-back, inter-arrival times of successive packets are i.i.d. (independent and identically distributed) [10]. That is, the length of a burst which consists of the packets during the On period is uncorrelated to the interarrival time. Often we think in terms of activity cycle, bK1 which has units of the average number of seconds per an On duration, is the active cycle while aK1 means the idle cycle. Then, overall one cycle T becomes aK1CbK1. The probability of such a traffic source being in the On state, pon is given by bK1/T. Then, we get the probability that a single source transits from On state to Off state in a time slot as followings
Let l denote 1=N a . Substituting Eq. (15) into (14), taking N/N and lr[1, we obtain the approximation of Eq. (14) 8 Klr e z1 K lr; i Z 0 > > > > < Klr iZ1 (16) Gi z lre zlr; > > i > ðlrÞ > : eKlr z0; otherwise i!
pt Z P½Transition_to_OffjBeing_in_On Z pon b:
(13)
Let Gi denote the probability that i out of N active sources transit from On state to Off state in a time slot. Then, Gi can be expressed as
(15)
where the first-order approximation can be applied. From Eq. (16), we get the probability, bi that i IP packets arrive to form a burst transiting from an On state to an Off state. This is expressed in the form of ( G0 Z 1 K lr; i Z0 bi Z (17) G1 Pi Z l2 rð1 K lÞiK1 ; iR 1 where bi also follows a geometric distribution. Fig. 6 depicts the state transition diagram of the burst queue which works on the basis of one time slot. According to the transition rules defined in this Figure, a system of difference equations may be derived for the approximation of xi, x~i as follows: x~ 0 ð1Kb0 ÞZ x~ 1 b0 x~ 1 ð1Kb1 ÞZ x~ 2 b0 C x~ 0 b1 x~ i ð1Kb1 ÞZ x~ iC1 b0 C x~ 0 bi C
Gi Z bði; N; pt Þ
(14)
where b(i; n, p) represents the binomial distribution with all n sources. Let x be the probability distribution of burst queue. We define xi as the steady-state probability that the burst queue contains i packets under a total of N On/Off sources from users/LSPs. Let xi denote the probability vector with N components, xi,n(1%n%N) which is the probability that the burst queue contains i packets and n sources are at On state.
iK1 X
(18) x~ i biKnC1 ; for iO1
nZ1
Fig. 6. State transition diagram of burst queue.
S. Lee / Computer Communications 29 (2006) 634–641
639
As usual, we solve the above equilibrium Eq. (18) using the method of z-transform, thus we have ð1Kb1 Þ
N X
x~ n zn
nZ2
Z
N N N X nK1 X X b0 X bn zn C x~ nC1 znC1 C x~ 0 x~ i bnKiC1 zn z nZ2 nZ2 nZ2 iZ1
(19) From the Eq. (19), z-transform of x~ i , X(z) is derived as follows: XðzÞZ x~ 0
zGðzÞKGðzÞ ; zKGðzÞ
(20)
where G(z), the z-transform of bi is z : GðzÞZ1KlrCl2 r 1Kð1KlÞz
(21)
To eliminate x~ 0 , X(1)Z1 is applied, that yields x~ 0 Z1Kr. We now make use of Eq. (21), 1 dn XðzÞ
x~ 0 Z1Kr and x~ n Z n! dzn zZ0
Fig. 7. Average waiting time (ms) in burst queue with burst assembly when lZ 1=N a Z 0:1 and 0.05.
the IP packets from the sources/LSPs to wait in burst queue even after being assembled into a burst.
to obtain x~ n . Thus, we have x~ n Z
4. Performance evaluation
lrð1KrÞð1KlÞnK1 : ð1KlrÞn
(22)
(24)
To assess the accuracy of our model, we compare our analytical results with those obtained by means of simulations. In our simulation, the burst sources were individually simulated with the On/Off model as explained in the Burst Assembly section. Simulation experiments are performed with varying traffic load, where there are 10 hops between ingress and egress nodes and the capacity of each link is 10 Gbps. The average packet length is set to 100 Kbyte. In order to capture the burstiness of data at the edge nodes, the traffic from a user to the edge node is
This analytic model of burst queue, in combination with carriers’ QoS mechanisms, could be used to allow the carriers to offer customized levels of burst assembly latency and waiting time in burst queue, which will have a significant impact on data burst’s end-to-end delay. Specifically, the analytic model in Eqs. (12) and (24) can be reflected in determining when the control packet is sent into an OBS network, to reduce the burst assembly latency and the waiting time in burst queue, resulting in reducing the end-to-end delay. Specially, while in [8], the burst assembly time and offset time were fixed, on the basis of which the burst length was simply estimated from traffic measurement, we analyzed the mean waiting time at an edge, which does not include only burst assembly latency but also waiting time in burst queue when multiple traffic sources are multiplexed into the edge node. The situation where multiple traffic sources/LSPs are multiplexed into an edge node is more realistic, leading
Fig. 8. Average waiting time (ms) in burst queue with burst assembly when lZ 1=N a Z 0:01 and 0.005.
Finally, the expected number of IP packets in the burst queue under N users/LSPs is derived as E½nZ
N X nZ0
n~xn Z
N X
n~xn Z
nZ1
rð1KlrÞ : lð1KrÞ
(23)
From Eq. (23), the mean waiting time in burst queue, T q becomes E½n rð1KlrÞ Z 2 : T q Z l l ð1KrÞ
640
S. Lee / Computer Communications 29 (2006) 634–641
Table 1 The difference of the analytical result compared with simulation results r
lZ0.1
lZ0.05
lZ0.01
NZ10
NZ50
NZ10
NZ50
NZ10
NZ50
NZ10
NZ50
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.73!10K2 1.76!10K2 1.83!10K2 2.02!10K2 2.03!10K2 2.32!10K2 8.01!10K2 1.13!10K1 1.42!10K1
7.93!10K3 9.41!10K3 1.54!10K2 1.57!10K2 1.94!10K2 2.14!10K2 2.90!10K2 3.07!10K2 6.46!10K2
1.28!10K2 1.26!10K2 1.77!10K2 2.84!10K2 3.41!10K2 3.77!10K2 7.58!10K2 1.18!10K1 1.29!10K1
1.23!10K2 1.27!10K2 1.72!10K2 1.74!10K2 1.92!10K2 1.96!10K2 2.08!10K2 2.78!10K2 3.79!10K2
1.17!10K2 1.25!10K2 1.93!10K2 3.04!10K2 2.87!10K2 4.30!10K2 6.62!10K2 7.68!10K2 8.76!10K2
8.98!10K3 9.24!10K3 1.14!10K2 1.48!10K2 1.80!10K2 1.97!10K2 2.06!10K2 1.90!10K2 3.39!10K2
1.65!10K2 1.61!10K2 1.83!10K2 1.79!10K2 2.03!10K2 2.79!10K2 3.19!10K2 4.40!10K2 7.68!10K2
9.22!10K3 1.29!10K2 1.24!10K2 1.60!10K2 1.67!10K2 2.06!10K2 2.07!10K2 2.63!10K2 3.01!10K2
generated by Poisson packet arrivals from 10 and 50 independent traffic sources that are either transmitting packets during the On period or is idle during the Off period. The On and the Off periods are assumed to be exponentially distributed with mean of 1 s. For each simulation, depending on the offered load, between two million and one hundred million packets were simulated. Figs. 7 and 8 plot the average waiting time in burst queue with burst assembly versus the traffic density for the simulation with different number of sources such as users or LSPs: NZ10, NZ50 and the analytical model. As can be easily expected, the burst buffering in any OBS network strongly depends on the traffic statistics of arriving packets [12]. In other words, as the mean arrival rate increases, so does the average waiting time. From the graphs in Figs. 7 and 8, we observe that the error increases as the r increases, that is, the traffic density increases. There may be some concern that the analytical model may not work very well if there are just a few sources under the assumption that N/N. But this concern falls off in the bar for both simulation experiments with NZ10 and NZ50. As can be seen in Table 1, the maximum error in difference between the analytical and simulation results is 1.42!10K1 when there are 10 sources and the traffic density is 0.9. Even if the traffic density increases, the error does not increase as much as that in the case of NZ10 does. The maximum does not exceed 7!10K2 when NZ50. Especially, at very high loads the analytical model performs better than that at low loads. But we know that the difference is further reduced as N increases. We expect the analytical result to track the simulation result more closely as the traffic arrivals increase, because lr[1 is assumed in our analytical model. From the Table 1, as the burst arrival increases, we also see good agreement between the analytical and the simulation results. Accordingly, from this analytical model, Internet Service Providers (ISPs) expect how tolerable delay limit could be provided for each service class in an OBS network, according to such network status as number of users or LSPs, link density, CoS, and etc. We now investigate the end-to-end delay under the simple mode of the existing OBS signaling scheme
lZ0.005
where control packet is sent when the burst is at the head of burst queue and those under the scheme of [8] and the proposed scheme which start resource reservation during Ta and TaCTq, respectively (called Ta Resource Reservation (RR) and TaCTqRR, respectively). The delay of a data burst is defined as the average delay of all the packets. Fig. 9 shows the delay reduction by TaRR and TaCTqRR over the simple mode under the traffic load of 0.5 as the burst assembly time, Ta varies from 1 ms up to 100 ms when To is set to 1, 5 and 10 ms. Both the TaRR and TaCTqRR schemes show the same performance improvement in terms of the delay reduction only if the resource reservation is successful, since control packet is sent at the time of TaKTo and TaCTbKTo, respectively, for the two schemes. However, in the TaRR, because Tb is not considered, in the case that bursts must wait in the burst queue, To expires while the bursts are still waiting in the burst queue, leading to insufficient resource reservation time for the bursts. The drop rate resulting from the insufficient resource reservation time is shown in Fig. 10(a) and (b) for NZ10 and 50, respectively. As we expected in Section 2.2, we observe that the drop rate experienced by TaRR is much higher than
Fig. 9. Average reduced delay rate for different values of To.
S. Lee / Computer Communications 29 (2006) 634–641
641
into the core network while the burst waits in the burst queue. As our future research, we are extending this model to be implemented with offset time and priorities based on end-toend delay that would be closely related to the waiting time in the burst queue as well as the burst assembly latency.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) through OIRC project. And also the author would like to thank Lae Young Kim for her help in performing the simulations.
Fig. 10. Average packet drop rate for different values of when NZ10 and 50.
the other schemes due to the unsuccessful resource reservation. In particular, as the overall offered load becomes higher, the drop rate difference between TaRR and the other schemes increases because the waiting time in the burst queue increases while the control packet is sent at the time of TaKTo under the TaRR scheme. It is also noted from Fig. 10 that compared to the simple mode, TaCTbRR scheme maintains its average drop rate lower while achieving better performance in terms of end-to-end delay.
5. Conclusion OBS is a desirable approach to support real-time multimedia traffic in the Internet, which is bursty and requires low latency. It is especially economic and efficient for providing high-end users or applications with sessions having a high bit-rate, low latency and short duration upon their requests. However it is possible that the processing at an edge would be a bottleneck to those applications. Therefore, in this paper, we investigated the burst queue with burst assembler at an edge in OBS networks in the light of IP packets from multiple traffic sources/LSPs. We observed that the developed analytical model of waiting time at an OBS edge node, performs as well as the simulations in all load conditions when there are large number of sources. The simulation results indicated that as the packet arrivals increase, the analytical model approximates more to the simulation results, while it lightens the computation overhead. We also noted that it is possible to reduce the end-to-end delay by sending the control packet
References [1] T. Battestilli, H. Perros, An introduction to optical burst switching, IEEE Communications Magazine 41 (8) (2003) s10–s15. [2] H.M. Chaskar, S. Verma, R. Ravikanth, Robust transport of IP traffic over WDM using optical burst switching, Optical Networks Magazine 3 (4) (2002). [3] S. Ovadia, C. Maciocco, M. Paniccia, Photonic burst switching (PBS) architecture for hop and span constrained optical networks, IEEE Communications Magazine 41 (11) (2003) s24–s32. [4] S.Y. Oh, M. Kang, A burst assembly algorithm in optical burst switching networks, Optical Fiber Communication Conference 2002, 2002. [5] V. Vokkarane, K. Haridoss, J. Jue, Threshold-based burst assembly policies for QoS support in optical burst-switched networks, Proceedings, SPIE Optical Networking and Communication Conference 2002, vol. 4874, 2002 pp. 125–136. [6] V. Vokkarane, J. Jue, Prioritized burst segmentation and composite burst assembly techniques for QoS support in optical burst-switched networks, IEEE JSAC-High-Performance Optical/Electronic Switches/Routers for High-Speed Internet 21 (7) (2003) 1198–1209. [7] K. Long, R.S. Tucker, C. Wang, A new framework and burst assembly for IP DiffServ over optical burst switching networks, IEEE Proceedings of Globecom’03, San Francisco, USA, 2002 pp. 3159–3164. [8] T. Hashiguchi, X. Wang, H. Morikawa, T. Aoyama, Burst assembly mechanism with delay reduction for OBS networks, Proceedings of Conference on the Optical Internet(COIN 2003), Melbourne, Australia, 2003 pp. 664–666. [9] X. Ca, J. Li, Y. Chen, C. Qiao, Assembling TCP/IP packets in optical burst switched networks, IEEE Proceedings of GLOBECOM’02 3 (2002) 2808–2812. [10] L. XU, H.G. Perros, G.N. Rouskas, A queueing network model of an edge optical burst switching node, IEEE Proceedings of INFOCOM’03, 2003. [11] I. Widjaja, M.F. Neuts, J-M. Li, Conditional overflow probability and profile curve for ATM congestion detection, IEEE Proceedings of INFOCOM’96, 1996. [12] M. Dueser, P. Bayvel, Performance of a dynamically wavelengthrouted optical burst switched network, IEEE Photonics Technology Letters 14 (2) (2002) 239–241.