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Pre-print QoS Behavior of Optical Burst Switching under Multimedia Traffic: an Analytical Approach Aresh Dadlani, Ahmad Khonsari 1,2 1 University of Tehran, ECE Department North Karegar Ave., Tehran, Iran 2 IPM School of Computer Science Niavaran Sq., Tehran, Iran [email protected], [email protected]

Abstract Recent studies in modern telecommunication networks have convincingly revealed that IP traffic exhibits a perceptible self-similar behavior over a wide range of time scales. Adapting the traditional Poisson model can therefore lead to erroneous conclusions regarding network performance dynamics. On the other hand, with growing demand for greater bandwidth, several optical paradigms have been proposed as substitutes for the next-generation Internet backbone. Among all these approaches, Optical Burst Switching (OBS) has been widely recognized as a suitable alternative to Optical Packet Switching (OPS) due to its support for bursty traffic and high bandwidth granularity. Thus, devising suitable buffers so as to accurately capture the fractal behavior of multimedia traffic in such optical core switches has become a major scientific endeavor. For the first time, in this paper, we propose an analytical model with Quality of Service (QoS) provision at a complete OBS network level. We then study the performance of the presented model in terms of blocking probability. Using this model, we also study the impact of burst aggregation time on the total loss probability and validate its correctness through simulation results.

1. Introduction As demonstrated through various research experiments, traffic in contemporary packet networks such as corporate LANs, variable-bit-rate (VBR) video over ATM, CCSN/SS7 and other communication systems appears to be self-similar in nature (scale-invariant burstiness) with long-range dependence (LRD) [1-3]. This means that traffic traces of such networks show similar statistical patterns over different time scales and look the same over a long

Mohammadreza Aghajani, Ali Rajabi IPM School of Computer Science Niavaran Sq., Tehran, Iran [email protected], [email protected]

range of time interval. Therefore, properties of models based on self-similar traffic are quite different from those based on short-range dependent (SRD) processes such as the traditional Poisson process [2]. In addition, several switching paradigms such as optical circuit switching (OCS) [4], optical packet switching (OPS) [5] and optical burst switching (OBS) [6] have been proposed in the literature to satisfy the ever-growing surge of bandwidth demand due to increase in the myriad of realtime and multimedia applications over the Internet. However, among all the proposed paradigms, OBS seems to be the preferred option for providing quality of service (QoS) at the optical layer and in presence of bursty traffic [7]. With the failure of modeling the behavior of the actual LAN traffic with traditional processes, the need for equipping high-speed optical networks with suitable storage systems for long-range dependent input processes has gained growing importance. One such storage-level model with self-similar input has been investigated in [8]. In the literature, several queuing models for optical networks have been reported [9-11]. However, to the best of our knowledge, none of these models have been scrutinized under multimedia traffic at network-level. In fact, they have all been modeled using traditional Poisson-based processes. In this paper, we propose a novel analytical model based on the storage-level model reported in [8] using self-similar traffic model for an entire OBS network. We then analyze the performance of the proposed model in terms of blocking probability and justify its appropriateness through results obtained from simulation experiments. The rest of the paper is organized as follows. In Section 2, we briefly introduce the framework of an OBS network. In Section 3, we specify the assumptions made in our proposed model followed by a step-by-step analysis of the model at three different levels of abstraction in Section 4. In Section 5, we study the performance of the proposed model

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Optical Burst Switching Network E1

C1

E3

C3

packets

LAN/ WAN 1

LAN/ WAN 3

packets

E2

burst C2

C4

LAN/ WAN 2

Router + Burst Disassembler Router + Burst Assembler Ingress Node

Switching Fabric + Switching Control Unit + Routing & Signaling Processors

Egress Node

Core Node

Figure 1. A graphical representation of an OBS network comprising of three edge nodes (E1 , E2 and E3 ) and four core nodes (C1 , C2 , C3 , and C4 ).

in terms of loss probability. Finally, we summarize our contributions and future works in Section 6.

2. The OBS framework Nodes in an OBS network (OBSN) are mainly of two types: edge and core nodes [12]. An edge node is further classified into ingress and egress nodes. An ingress node consists of a router and a burst assembler, while an egress node is made up of a router and a burst disassembler. An OBS core node is composed of a switching fabric and a control unit. In terms of functionality, the ingress node is responsible for collecting the incoming packets from the outside electronic world and aggregating them into bursts according to their destination addresses. Prior to the burst transmission, the OBS edge node creates and sends a control packet towards the destination of the corresponding burst. In general, all OBS designs include an offset time between the transmission of a control packet and its corresponding burst. This offset time allows the control packet to reserve the required resources along the path before the burst arrival. In OBSNs, the two fundamental resources available for reservation in the optical domain are wavelengths and fiber delay lines (FDLs or optical buffers). When a control packet reaches a core node, it is routed to the next core node based upon the resource availability. If, at any time instant, no free resource is available, the burst is dropped. However, in presence of wavelength converters (WCs) and variable FDLs, the burst loss can be reduced to a great extent. When a burst reaches an egress edge, it is disassembled back into packets before being transmitted into the electronic world. As shown in Figure 1, for a burst traveling from edge 2 (E2 )

to edge 3 (E3 ) via core nodes C2 and C3 , E2 and E3 act as the ingress and egress nodes, respectively. Some of the most common burst assembly algorithms can be classified into timer-based, threshold-based, and mixed timer/threshold-based algorithms. In the timer-based approach, a timer is set at the beginning of every new assembly cycle, determining the transmission time of the burst into the core network [13]. After a fixed amount of time, all the packets that arrived during that time period are assembled into a burst. In the threshold-based approach, a threshold is specified to determine the generation and transmission time of a burst into the optical network [14]. The incoming packets are stored in the prioritized queues in the ingress node, until the threshold condition is satisfied. Once the threshold is reached, a burst is created and sent into the optical core. The timeout value for the timer-based schemes should be set carefully. If the value is chosen to be too large, the packet delay at the edge might become intolerable. On the other hand, if the value is too small, too many small-sized bursts will be generated, resulting in control overhead. While timer-based schemes might result in undesirable burst lengths, threshold-based assembly algorithms do not guarantee on the packet assembly delay. A mixed timer/threshold-based algorithm may perform better, especially with self-similar traffic, but may experience higher operational complexity [15, 16]. A signaling protocol is the procedure through which a control packet reserves resources for the corresponding data burst by guiding it through a routing path. In an optical network, there are one-way and two-way reservations signaling protocols. In one-way reservation [6], a control packet reserves resources along the path for the corresponding data burst without any acknowledgement from the destination

Pre-print a function that returns the node having l connected to

node. On the contrary, in a two-way reservation [17], a control packet collects link and topology information instead of reserving resources for the data burst. The acknowledgement packet from the destination node to the source node reserves resources for the corresponding data burst while traversing along the reverse path. Since one-way reservation protocols are more flexible, have lower latency, and are more efficient as compared to two-way reservation protocols, they are mainly adopted in OBSNs.

3. Assumptions and notations Before introducing our model, we highlight the assumptions and notations to be used hereafter in this paper. • In our model, the OBSN comprises of j ingress and k egress nodes, such that each egress node is reachable from all ingress nodes. We define the set of ingress nodes as I = {I1 , I2 , . . . , Ij } and the set of egress nodes as E = {E1 , E2 , . . . , Ek }. Hence forward, the terms ingress and egress are used interchangeably as source and destination, respectively. • The Breadth First Search (BFS) algorithm is used to determine the shortest path between every source and destination. If more than one such path exists, one is chosen at random. • Each ingress switch is connected to just one core switch via a single link with a capacity of w wavelengths. • Ingress switch Iq (1 ≤ q ≤ j) generates traffic in accordance with a LRD process having mean input rate of mq . • The destination of a burst generated by an ingress node is uniformly distributed over the total number of destinations, i.e. k. • D physical FDLs (each of length L) are assigned to each optical link. Therefore, the total number of virtual FDLs is Dw. • For any arbitrary link l, let λl and δl denote, respectively, the burst arrival and departure rates of l. Further, let P bl denote the blocking probability of l, i.e. the probability that a burst intending to pass the link does not succeed and is dropped due to resource unavailability (all wavelengths and FDLs are busy serving other bursts). • Each link connects one of the output interfaces of a node to an input interface of another node. We define head(l) as a function that returns the node having l connected to one of its output interfaces and tail(l) as

one of its input interfaces. Further, let P be a path between some source and destination including l as one of its links. We define precP (l) as a function that returns the preceding link of l on P , or null if l is the first link on P . Also, last(P ) is defined as a function that returns the final link on P connected to an egress node. • Let Pl = {P1 , P2 , . . . , Pj , . . . , PQ } be the set of all paths, each containing l as one of its links. Also, let Pl l λP l and δl be the burst arrival and departure rates of l on path Pj , respectively. • The blocking probability of a link connecting an ingress node to a core node is taken to be zero. In other words, P bl = 0 if head(l) ∈ I. • Finally, we define P b as the network blocking probability, i.e. the probability that an arbitrary burst is dropped somewhere on its path from source to destination.

4. The analytical model In this section, we present our analytical model in three steps. First, we introduce the model for a single ingress node with self-similar traffic model. Then, we present a model for a single core node followed by a model for the entire OBSN.

4.1. The model of an ingress node In this sub-section, we present the analytical model for an ingress node under LRD input traffic. As illustrated in Figure 2, an ingress node connects the outside electronic world to the inner optical core network. Packets arriving at such a node are aggregated into optical bursts before being sent into the core network. Due to

Electronic Network

Optical Network Ingress node

A(t)

Figure 2. A single ingress node with selfsimilar input traffic A(t).

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the LRD nature of self-similar traffic, we adapt the timecontinuous process reported in [8] to model the traffic in our proposed model. That is, √ (1) A(t) = mt + am · Z(t),

where m is the mean input rate, a is a variance coefficient (a > 0), and Z(t) is the standard fractional Brownian motion (FBM) with self-similarity parameter H (also known as Hurst parameter). As given in [8], Z(t) is characterized by the following properties:

Core

B1(t) B2(t)

l1 l2

l’1 l’2

C1(t) C2(t)

Bx(t)

lx

l’y

Cy(t)

w wavelengths

Figure 3. A single core node with x input links and y output links. Each link has a capacity of w wavelengths. The traffic into link li (1 ≤ i ≤ x) and out of link lj0 (1 ≤ j ≤ y) is denoted by Bi (t) and Cj (t), respectively.

P1 : Z(t) has stationary increments. P2 : Z(t) = 0 and E[Z(t)] = 0 for all t. P3 : E[Z(t)]2 = |t|2H for all t. P4 : Z(t) has continuous paths. P5 : Z(t) is Gaussian, i.e. its finite-dimensional distributions are multivariate Gaussian distributions. Based on the above definition, we assume that the traffic entering an ingress node is of the form A(t). Packets entering the ingress node are aggregated into bursts and sent into the optical core after constant time intervals, say ∆T . Thus, the length of the ith burst (Li ) generated in the ingress node depends on the amount of traffic entering that node between time intervals (i − 1)∆T and i∆T . Therefore, we have: Li = A(i∆T ) − A((i − 1)∆T ).

(2)

According to P1 and P2 , equation (2) can be written as: iid

iid

Li = A(∆T ) − A(0) = A(∆T ),

(3)

iid

where = denotes i.i.d or “independently and identically distributed”. Substituting equation (1) in (3) results in the following: iid

Li = m∆T +

√ am · Z(t).

(4)

Because of the self-similar and Gaussian nature of Z(t), P3 , P4 , and P5 yield: √ iid Li = m∆T + am · ∆T H Z(1) ∼ N (m∆T, am∆T 2H ).

core switch such that every wavelength λi (1 ≤ i ≤ w) can be converted into any of the other w − 1 wavelengths. A burst entering an input link of a core switch is routed to the appropriate output link according to its destination address. On arriving at the output interface, the burst is allocated one of the free w wavelengths to be forwarded to the next node. If at the instant of arrival, no wavelength is found idle at the output interface, the burst is delayed in the optical buffer. On leaving the optical buffer, if any wavelength is made free, it is allocated to the burst for transmission. In the case when all resources (optical buffers and wavelengths) are busy, the burst is lost and is said to be dropped. In this subsection, we present an apposite model to calculate the burst loss probability for the traffic model mentioned in the preceding subsection. Let qij denote the routing probability of a burst from input link li to the output link lj0 of a single core switch. Thus, the traffic contribution of li to the total outgoing traffic from lj0 is equal to qij Bi (t). Therefore, the total outgoing traffic on lj0 , denoted by Cj (t), is the sum of the bursts routed to lj0 from each of the x input links. Thus, Cj (t) can be calculated as: Cj (t) =

x X

qij Bi (t).

(6)

i=1

(5)

4.2. The model of a core node We now introduce an analytical model for an optical core node. As shown in Figure 3, consider a core switch with x input interfaces and y output interfaces. Each interface is connected to an optical link with a capacity of w wavelengths. Also, we assume the presence of full WCs in the

As in equation (4), the incoming traffic on link li , which we denote by Bi (t), can be written as: √ (7) Bi (t) = mi t + ami · Z(t). A similar equality can be obtained for Cj (t) as follows: p Cj (t) = m ˆ j t + am ˆ j · Z(t), (8) P where m ˆ j = ki=1 qij mi . In order to model the burst transmission and optical buffer, we adapt the stationary storage

Pre-print 4.3. The model of an entire OBSN

model reported in [8]. Thus, the volume of traffic being served and held in the optical buffers can be written as: V = sup(A(t) − A(s) − Cw(t − s)),

(9)

s≤t

where C is the service rate of each wavelength, w is the number of wavelengths and t ∈ (−∞, ∞). According to [8], we have: H 1−H ! wC − m 1 x ¯ , P (V > x) ≈ φ √ am H 1−H (10) ¯ = P (Z(1) > y) is the residual distribution where φ(y) function of the standard Gaussian distribution. For an optical buffer of length x, the burst loss probability, PLoss , can be calculated as follows: PLoss = α · P (V > x),

(11) λl =

with α given as: 2 Z ∞ exp (C−m) 2 2σ −(y − m)2 √ α= (y − C)exp dy. 2σ 2 mσ 2π C (12) In the case of Gaussian traffic, with mean m and variance σ 2 = am, equation (12) is simplified as follows: a √ α= . 2π (wC − m + am)

(13)

m∆T · w. 2

(14)

Therefore, the probability of losing a burst on the j th link of a core node can be obtained as: mj ∆T P bj = αj · P V > L + ·w 2 = αj · φ¯

√

1 amj

wC−m H H

m ∆T L+ j2

1−H

·w

1−H !

.

(15)

Q X

P

λl j ,

(16)

j=1

l where Q is the cardinality of Pl . Further, λP l can be described recursively as follows:  Pj δ precPj (l) 6= null    precPj (l) P , (17) λl j =    λhead(l) otherwise |I|

where |I| is the total number of ingress nodes in the network and the burst departure rate δlPl is given as: P

Now, consider a core node with an optical buffer of length L for which the “busy queue” assumption made in the storage model of [8] holds. Since the average length of each burst is m∆T and each burst is served at a constant rate, the average amount of traffic to be served by each of the w wavelengths is m∆T /2. Hence, every core node can be modeled as a storage with limited capacity of: L+

In this subsection, we aim at calculating the blocking probability of an entire OBSN. As mentioned in the model for an ingress node (subsection 4.1), the input traffic has been modeled as an FBM process. Similarly, in the model proposed for a core node (subsection 4.2), the input traffic is taken to be an FBM process. The traffic leaving the core node is also an FBM process having the same variance coefficient (a) and Hurst value (H) as that of the incoming traffic into the core node. The traffic entering and leaving a core node only differ in their mean service rates (m). Therefore, the traffic model adapted to calculate the burst loss probability at each output link of a core node holds for the other links as well. Based on the notations defined in the earlier section, λl is the sum of the arrival rates of individual paths in Pl . Thus, we have:

P

δl j = λl j (1 − P bl ).

(18)

Before proceeding into the next section, we provide a more detailed explanation for the second case given in equation (17), i.e., when precPl (l) = null. Occurrence of this condition implies the fact that l is connected to an ingress switch and thus, λl = λhead(l) (as mentioned in the assumptions). Also, since we assumed that there exists a specified shortest path between each source and destination, and that the destination of a burst is uniformly distributed, the second case in equation (17) holds. The network blocking probability can be defined as the ratio of the total number of bursts not reaching the egress switches to the total number of bursts injected from ingress switches into the optical core at a long-run. Thus, P b can be defined in terms of δl and λl as: X δl Pb = 1 −

tail(l)∈E

X

head(l)∈I

λl

,

(19)

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The performance of the analytical model has been validated in terms of blocking probability for the network shown in Figure 4 in the Ptolemy environment. Each simulation was run until the network converged to steady state which is often very slow under self-similar traffic. Throughout this section, the dark lines in the figures denote the results obtained through analysis while the dotted lines represent the simulation results. Also, FBM has been modeled using the rmd33 method reported in [8]. Figure 5 illustrates the influence of the Hurst parameter (H) on the network blocking probability (P b). In this scenario, L = 10, C · w = 200 and a = 1. As shown in the figure, P b increases with increase in H. Such a behavior is not out of expectation as self-similar traffic is featured with inherent burstiness extended over a wide range of time scales. The peaks observed in the traffic trace are the result of such burstiness. Since the servers are unable to provide service to the incoming traffic at such peaky periods, a large fraction of bursts is lost during this period. With increase in the degree of self-similarity (H), the amount of traffic burstiness also increases. Such an event, in turn, adds to traffic burstiness, thus increasing the burst loss probability. From Figure 6, we observe that with increase in optical buffer length (L), the network blocking probability decreases. Over here, H = 0.8, C = 10000 and w = 10. This implies that by increasing the length of the buffers in the core nodes, more number of bursts can be delayed in the buffers and thus, prevented from being dropped in absence of any idle wavelength. In terms of the storage model, the storage capacity increases, resulting in lower burst overflow. This justifies the storage model adapted in the core node as an appropriate model for optical buffers in an OBSN. In Figure 7, the effect of the Hurst parameter on P b for different optical buffer lengths is depicted. As shown, networks with lower H value experience lesser burst loss than those with higher H values. The traces shown in Figure 7 summarize the results obtained in the previous two figures. Figure 8 represents the blocking probability for different values of C · w, which is the product of the service rate and the number of wavelengths. For this scenario, H = 0.8 and a = 50. As can be seen, for small values of C · w, the burst blocking probability is high. But as the value of C · w increases, this probability falls. For C · w = 400, the burst loss probability becomes almost negligible. This figure implies that P b can be reduced by either increasing the service rate or number of wavelengths, or even both. In Figures 9 and 10, we study the effect of burst aggregation time (∆T ) on the burst loss probability. We know

A

D

E1 I2

B

E2 E

I3

C

E3

I4

Figure 4. The simulated OBSN. Analysis Simulation

0.015

Blocking Probability (Pb)

5. Simulation and numerical results

I1

0.013 0.011 0.009 0.007 0.005 0.003 0.5

0.6

0.7

0.8

0.9

Hurst parameter value (H)

Figure 5. Network blocking probability (P b) in terms of the Hurst parameter (H) (L = 10, a = 1).

Analysis Simulation

0.003


where the departure rate of link l is computed as δl = λl (1 − P bl ).

0.0025

H = 0.8

0.002

0.0015 5

10

15

20

25

30

35

40

45

50

Buffer Length (L)

Figure 6. Network blocking probability (P b) in terms of optical buffer length (L) (H = 0.8, a = 50, Cw = 100000).

that with increase in aggregation time, the average burst size also increases. Since each control packet reserves the required resources for the corresponding burst regardless of its length, with increase in the average burst length, the average amount of traffic served by the wavelengths also increases. Thus, as shown in Figure 9, the loss probability


0.0026 0.0024 0.0022

H = 0.8

0.002 0.0018 0.0016 0.0014

H = 0.6

0.0012 0.001 5

10

15

20

30

25

35

40

45

50

Byte Loss Probability (10E-5)

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Analysis Simulation

0.0028

Analysis Simulation

18 16 14 12 10 8 6 4 2 0 0

2

Figure 7. Comparison of network blocking probability (P b) in terms of optical buffer length (L) for two different values of H.

Analysis Simulation


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10

20

30

40

50

60

4

6

8

10

12

Aggregation Time (ǻT) (10E-5)

Buffer Length (L)

70

80

90

100

Figure 10. Impact of aggregation time (∆T ) on byte loss probability (H = 0.8, a = 50).

length, more amount of information is packed in each burst. Thus, if such a burst is dropped, a large amount of information is lost. Since the decrease in burst loss probability due to increase in aggregation time is not as much as that due to increase in average burst length (which increases linearly), the average number of bytes lost due to burst loss is directly proportional to ∆T (Figure 10). Thus, keeping this in mind along with other factors such as header overhead, the aggregation time period should be selected with great care.

Service Rate (C)

6. Conclusions Figure 8. Network blocking probability (P b) in terms of service rate (C) (H = 0.8, a = 50).

Analysis Simulation

Packet Loss Probability (10E-05)

2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0

1

2

3

4

5

6

7

8

9

10

Aggregation Time (ǻT) (10E-5)

Figure 9. Impact of aggregation time (∆T ) on the packet loss probability (H = 0.8, a = 50).

experienced by every single burst is reduced with increase in ∆T (according to equation (15)). On the other hand, with increase in the average burst

Based upon several surveys conducted on the contemporary communication networks, traffic prevailing in such networks is reported to exhibit fractal nature with long-range dependence. This causes the traffic to look alike irrespective of time scales over a long range interval. Such behavior makes the traffic very bursty. Thus, adapting traditional models based on Poisson-related processes can therefore lead to erroneous conclusions in network performance evaluation. The search for an appropriate high-speed paradigm to support this burstiness as well as to fulfill the ever-growing bandwidth demand has gained great importance. As one of the main supporting technologies for nextgeneration optical Internet, optical burst switching (OBS) has been widely accepted as a suitable alternative to optical packet switching. In this paper, we presented an analytical model with QoS provisioning for an OBS network under the influence of multimedia traffic. The proposed mode has been studied at three abstract levels: ingress node, optical core node and the entire OBS network. Based upon the proposed model, we also have investigated the influence of burst aggregation time on the total burst loss probability. We have studied the performance of the model in terms of burst blocking probability and have evaluated its correct-

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ness through simulation experiments conducted at the network level. In future work, we tend to study the network performance of an OBS network in terms of latency and provide an improved mathematical model for the optical buffer so as to further reduce the blocking probability of the bursts in the core network.

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[16] B. Kantarci, S.F. Oktug, and T. Atmaca. Performance of OBS Techniques under Self-similar Traffic Based on Various Assembly Techniques. Computer Communications, 30(2):315–325, January 2007. [17] P.E. Boyer and D.P. Tranchier. A Reservation Principle with Applications to the ATM Traffic Control. Computer Networks and ISDN Systems, 24:321–334, May 1992.