- Email: [email protected]
Dynamic burst discarding scheme for deflection routing in optical burst switching networks
Optical Switching and Networking 4 (2007) 106–120 www.elsevier.com/locate/osn
Dynamic burst discarding scheme for deflection routing in optical burst switching networks Kouji Hirata ∗ , Takahiro Matsuda, Tetsuya Takine Department of Information and Communications Technology, Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita 565-0871, Japan Received 12 May 2006; received in revised form 6 December 2006; accepted 1 January 2007 Available online 11 January 2007
Abstract This paper proposes a dynamic burst discarding scheme for deflection routing in optical burst switching networks. In general, deflection routing is effective in lightly loaded situations, whereas it has a contrary effect in congested networks because deflected bursts accelerate network congestion. Thus deflection routing should be employed in lightly loaded networks. Incoming traffic, however, varies in time and location, so that temporal and/or local congestion cannot be avoided. Our proposed scheme resolves this problem in the following way. Each node autonomously detects congestion with local information, and bursts to be deflected are discarded in a probabilistic manner, based on the degree of detected congestion and the numbers of elapsed and remaining hops of those bursts. Simulation experiments show that when congestion happens temporarily, the proposed scheme reduces the burst loss probability, and it utilizes network resources efficiently when local congestion happens. c 2007 Elsevier B.V. All rights reserved.
Keywords: Optical burst switching; Contention resolution; Deflection routing; Dynamic burst discarding
1. Introduction In recent years, optical networks are expected as a platform of next generation networks that support an explosive increase in traffic volume on the Internet [1]. In optical networks, one of the most important technical requirements is a switching technique such as optical circuit switching (OCS), optical packet switching (OPS), and optical burst switching (OBS). OCS is relatively easy to implement but lacks flexibility to cope with fluctuating traffic and link state. OPS is conceptually ideal, but it has some technological ∗ Corresponding author. Tel.: +81 6 6879 7742.
E-mail addresses: [email protected] (K. Hirata), [email protected] (T. Matsuda), [email protected] (T. Takine). c 2007 Elsevier B.V. All rights reserved. 1573-4277/$ - see front matter doi:10.1016/j.osn.2007.01.001
limitations at present, in terms of optical RAMs and all-optical processing of headers [2,3]. OBS possesses several advantages of both OCS and OPS, and it is under study as a promising solution to optical Internet backbone networks in the near future [4,5]. Fig. 1 illustrates an architecture of OBS networks. OBS is used in a core domain that interconnects electrical domains (i.e., IP subnetworks). There are two types of network nodes, edge nodes and core nodes, in OBS networks. Edge nodes fill the role of an interface between electrical domains and the OBS core network. IP packets arriving from IP subnetworks are assembled into bursts at ingress edge nodes [6]. Those bursts are sent to their destination edge nodes in an optical domain and disassembled into packets there. Wavelength and switching resources for each
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
107
Fig. 1. A optical burst switching (OBS) network.
Fig. 3. Deflection routing.
Fig. 2. Basic operation in JET.
burst are reserved according to a one-way reservation protocol such as Just-Enough-Time (JET) [7]. Fig. 2 illustrates the basic operation in JET. Before the transmission of a burst, its control packet, which includes the route information and burst length, is transmitted on a control channel. At each core node, the control packet is processed in an electrical domain in order to reserve a wavelength and set up a route for the corresponding burst. The burst follows the control packet on a data channel after an offset time, without any acknowledgements for the connection establishment. The offset time should be large enough to process the control packet electrically and set up the switching matrix for the burst at every OBS core node on the route. As a result, the switching matrix has been already set up when the burst arrives at core nodes, i.e., the burst is transmitted in a cut-through manner without O/E/O conversion. Wavelength reservation is released after the burst is transmitted. In OBS networks, contention occurs at switching nodes whenever two or more bursts with the same wavelength try to leave a switch fabric on the same output port at the same time. In electrical packetswitched networks, contention is resolved with storeand-forward technique that temporarily stores incoming packets in a memory bank, and those packets are sent out later when the desired output port becomes available. This is possible because of the availability of electronic RAM. However, no optical RAM technology
is available in OBS networks. Therefore, OBS switches should adopt different approaches to such an inevitable contention [8]. Contention resolution in OBS networks can be performed in three domains, i.e., wavelength, time, and space. In the wavelength domain, wavelength conversion avoids contention by converting one wavelength to another [9], and it improves the performance considerably. However, the wavelength conversion technology is still immature and it requires extra hardware (e.g., wavelength converters and lasers for wavelength conversion) and control software. For contention resolution in the time domain, fiber delay lines can be utilized, which store bursts temporarily until output ports become available [10,11]. At present, however, fiber delay lines are typically limited to providing a few tens of µs delay at most [12,13]. Thus it is not able to store a large number of optical bursts. Deflection routing is considered as contention resolution in the space domain [14–16], which can be implemented without any restrictions. Deflection routing is a sort of dynamic routing. When a burst arrives at an OBS core node and finds that the wavelength at the port on the primary path is not available, it will be switched to an alternative port (see Fig. 3). In this way, bursts arriving at a congested node are distributed to its neighboring nodes, and overall link utilization and network performance are expected to be improved. However, deflection routing has some faults. First of all, its performance depends strongly on the network topology, and deflection routing may not work effectively when there exists only a small number of alternative paths. Moreover, when the network is congested, the burst loss probability becomes large and eventually exceeds that in the case of no
108
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
deflection [15–17], because deflected bursts accelerate the network congestion in general. Note that this is the critical problem in OBS networks when contention resolution relies only on deflection routing. Thus OBS networks with deflection routing should be operated in lightly loaded situations. Incoming traffic, however, varies in time and location, so that temporal and/or local congestion cannot be avoided. In this paper, we propose a dynamic burst discarding scheme for deflection routing in OBS networks. Our scheme aims at controlling deflection routing when temporal and/or local congestion happens. A unique feature of the proposed scheme is that each core node independently controls deflection routing. Specifically, each node autonomously detects congestion with locally available information, and bursts to be deflected are discarded in a probabilistic manner, based on the estimated degree of congestion and the numbers of elapsed and remaining hops of those bursts. The rationale behind the proposed scheme might be similar to the concept of RED [18] that detects congestion through the queue length in the buffer. However, no buffer is available at core nodes in OBS networks. Thus we need a different method of detecting congestion. The proposed scheme utilizes a characteristic of deflection routing for detecting congestion. When a specific node is congested in an OBS network with deflection routing, its neighboring nodes are likely to be congested, too. Thus the proposed scheme uses the number of control packets arriving at each node as the index of congestion at its neighboring nodes. In addition, the proposed scheme does not discard deflected bursts randomly as in RED, but discards them selectively, based on the numbers of elapsed and remaining hops. Note that the control of deflection based on the numbers of elapsed and remaining hops was first proposed in [19]. Our proposed scheme controls superfluous deflection in order to use the network resource efficiently. As a result, the burst loss probability is expected to be reduced significantly by the proposed scheme when the network load increases temporarily and/or locally. The rest of this paper is organized as follows. Section 2 describes related works. In Section 3, we describe the proposed scheme in detail. Section 4 presents the result of simulation experiments and discusses the performance of the proposed scheme. Finally, we conclude the paper in Section 5.
congested networks. To resolve this problem, several schemes were proposed in the past. Wang et al. proposed a scheme to resolve this problem [17], where bursts can be stored electrically at ingress nodes. Further bursts are not allowed to transmit back and forth on the same link. Lee et al. focused on how to select an alternative path when contention occurs [19]. They proposed a scheme that selects a lightly loaded alternative path and dynamically determines if the burst should be deflected or retransmitted from its source node according to delay and blocking probability on the alternative path. However, this scheme requires a management database at OBS edge nodes, which stores the latest information on the status of the whole OBS network. Even though the performance of the OBS network is considerably improved, this scheme introduces significant overhead because periodic updates of the management database are required. On the other hand, the overhead of our proposed scheme is minimal because each node operates autonomously without any external controllers. In [20], Zalesky et al. showed that deflection routing had a destabilizing effect at high loads in OBS networks. To resolve this problem, they proposed and analyzed a technique called wavelength reservation to intentionally limit the amount of deflection by reserving several wavelengths on each link for the exclusive use of nondeflected bursts. In addition, they presented a reducedload Erlang fixed-point analysis of OBS networks with deflection routing and wavelength reservation. Note that this scheme requires several wavelengths, whereas our proposed scheme can be operated on a single wavelength. In [21], Cameron et al. proposed a routing protocol called SP-PRDR. In this scheme, non-deflected bursts have preemptive priority over deflected bursts. Thus a wavelength reservation for a deflected burst can be preempted by a non-deflected burst and the wavelength reservation for the non-deflected burst succeeds. As a result, this scheme suppresses superfluous deflection routing and reduces the burst loss probability effectively in heavily loaded situations. In lightly loaded situations, however, the burst loss probability of this scheme is higher than that of the conventional deflection routing. On the other hand, the burst loss probability of our proposed scheme in lightly loaded situations is expected to be almost the same as that of the conventional deflection routing.
2. Related works
3. Proposed scheme
As mentioned above, deflection routing accelerates the network congestion and has a contrary effect in
This section describes the proposed scheme to enhance the performance of deflection routing, especially
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
109
Table 1 Parameters in simulation experiments Parameter
Value
Number W of wavelengths Propagation delay d of a link Processing time ∆ of a control packet Mean arrival rate of bursts Transmission time L of a burst
1 0.01 (s) 0.001 (s) λ (bursts/s) 0.01 (s)
when the network is congested temporarily or locally. In normal situations, bursts are transmitted on the shortest path to the destination node. Further, contended bursts at core nodes are deflected to a shortest path among available alternative ones. When the network is congested, however, the proposed scheme selectively discards contended bursts. To do so, each node has to know the degree of congestion. Further, when congestion is detected, each node has to decide either to attempt deflection routing for contended bursts or to discard them simply, based on information available at the node. Note that it is not a good idea to discard all contended bursts even in heavily loaded situations. In such a case, the selective discarding of contended bursts can relax the degree of congestion and therefore some of the contended bursts can be delivered to their destination nodes by deflection routing. In what follows, we first discuss how to estimate the degree of congestion and how to discard contended bursts selectively, and then we show a specific implementation of our scheme. 3.1. Autonomous detection of congestion This subsection describes a rationale behind our autonomous congestion detection scheme. Suppose congestion happens at node i of an OBS network with deflection routing. Many contended bursts at node i are then re-routed to its neighboring nodes, so that they are expected to be involved in congestion, too. In order to confirm this observation, we conduct simulation experiments with an OBS network shown in Fig. 4. We assume that fixed length bursts are generated from each node according to a Poisson process and the destination node of a burst is independently chosen equally likely from among other nodes. The offered load at each node is set to be 0.4 (i.e., each ingress node generates 40 bursts per second on average). We will use this network model in Section 4 again and we explain it in more detail there. Other system parameters are listed in Table 1. Table 2 shows correlation coefficients of the numbers of control packets received at respective nodes every second, where the upper half and lower half tables
Fig. 4. Network model.
provide the results for OBS networks with the simple forwarding scheme (without deflection) and with deflection routing, respectively. We observe that the correlation coefficient for a pair of adjacent nodes are significantly larger in the network with deflection routing. This phenomenon suggests that when a specific node is congested in an OBS network with deflection routing, its neighboring nodes are likely to be congested, too. In other words, the degree of congestion at each node can be used as an estimator of those at its neighboring nodes. We also observe this phenomenon when a certain node is heavily loaded while its neighboring nodes are very lightly loaded. Thus we propose an autonomous congestion detection scheme, in which each node counts the number of arriving control packets every unit time, and based on it, each node indirectly estimates the degree of congestion at its neighboring nodes. Section 3.3 describes how this autonomous scheme is integrated into our dynamic burst discarding scheme. 3.2. Priority assignment to contended bursts Contended bursts are selectively discarded when congestion is detected. To do so, we assign priority to contended bursts and we may discard those with low priority. Specifically, we assign high priority to contended bursts whose elapsed hops are large. See Fig. 5. Note that this strategy is common in congestion control. At the same time, however, we are willing to assign high priority to contended bursts whose remaining hops are small, because they are more likely to be delivered to their destination, compared to those with a large number of remaining hops. A similar idea was employed in [19]. Note that in assigning priority to contended bursts, the above two measures can be inconsistent, so that we have to compromise between them in one way or another, which is discussed in the following subsection.
110
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Table 2 Correlation coefficients of the numbers of control packets
burst discarding probability p is given by p = p1 × p2 ,
(1)
3.3. Dynamic burst discarding scheme
where p1 (0 ≤ p1 ≤ 1) is determined based on the estimated degree of congestion and p2 (0 ≤ p2 ≤ 1) is determined by the numbers of elapsed and remaining hops of the control packet. As explained in the preceding subsection, factor p2 should increase with the number r of remaining hops to the destination node and also it should be a decreasing function of the number e of elapsed hops. Even though we have a choice of so many such functions, we assume in this paper that p2 is given by e+1 +1 , (2) p2 = 1 − log2 e+r
This subsection describes our dynamic burst discarding scheme. Suppose an arriving control packet cannot reserve the primary path at a core node. In our scheme, this control packet (and the corresponding burst) is discarded with probability p, instead of attempting deflection routing. As discussed above, the burst discarding probability p is a function of the estimated degree of congestion and priority based on the numbers of elapsed and remaining hops. Due to the nature of deflection routing, however, the actual number of remaining hops is uncertain. Thus we substitute the number of remaining hops on the shortest path to the destination for it, and we call the former the number of remaining hops hereafter. In the proposed scheme, we assume that the
where e and r denote the numbers of elapsed and remaining hops, respectively. Fig. 6 shows factor p2 as a function of the number e of elapsed hops. Note that p2 = 0 for bursts with r = 1, so that p = 0 (see (1)). Therefore bursts that can reach their destination nodes with one hop always attempt deflection routing. We expect that this feature will lead to the improvement of the throughput. Next, we consider factor p1 in (1). We assume that each node counts the number of arriving control packets every unit time τ , and estimates the current load by taking the exponentially-weighted moving average, from which factor p1 is determined. The detailed procedure of each node is as follows.
Fig. 5. Burst discarding according to the number of hops.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 6. Factor p2 as a function of the number e of elapsed hops.
(i) Count the number an (n = 1, 2, . . .) of control packets arriving in every interval ((n − 1)τ, nτ ]. (ii) Compute the exponentially-weighted moving average aˆ n of the sequence {an ; n = 1, 2, . . .} by aˆ n = αan + (1 − α)aˆ n−1 ,
(3)
where α (0 < α ≤ 1) is a parameter. (iii) Compute the offered load ρn per transmission channel by aˆ n L , (4) NW where L denotes the average burst length, N denotes the number of links at the node, and W denotes the number of wavelengths available per link. (iv) During interval (nτ, (n + 1)τ ], the following p1 is employed. (h i−1 (−β tan(πρn − π2 )) 1 + e , if ρn < 1, (5) p1 = 1, otherwise, ρn =
where β (β > 0) is a parameter. Note that p1 in (5) is a sigmoid function of ρn (ρn < 1). Fig. 7 shows factor p1 as a function of ρn , where β = 4. We observe that p1 increases rapidly when ρn becomes greater than 0.3. 4. Performance evaluation To evaluate the performance of the proposed scheme, we conduct simulation experiments with the OBS network in Fig. 4, assuming that OBS is used at core networks (see Fig. 1). It consists of 24 nodes and 43 bi-directional links. We assume that neither wavelength
111
Fig. 7. Factor p1 as a function of ρn (β = 4).
conversion nor buffering capability is available at any of the nodes. Note that under this assumption, bursts transmitted on different wavelengths do not interfere each other. Thus we focus on a specific wavelength and set W = 1 (see (4)). For simplicity, we assume that propagation delays d of all links are identical and equal to 0.01 (s), and the processing time ∆ of each control packet at every node is equal to 0.001 (s). At each node, bursts are generated according to a Poisson process with rate λ, and burst transmission times L are fixed to 0.01 (s). The destination of each burst is independently chosen equally likely among all possible nodes, and its primary route is set to be a shortest path between the source and destination. Table 1 summarizes values of those parameters. We choose one second as a unit time τ . Let H denote the number of hops on the primary path of a burst. The offset time given to the control packet is then set to be H × ∆ + 0.05 = 0.001H + 0.05 (s), where H × ∆ denotes the minimum offset time. Thus each burst can take (H + 50) hops at most. Parameter α of the exponentially-weighted moving average in (3) is set to be 1/8, unless stated otherwise. Further parameter β of the sigmoid function in (5) is fixed to 4. The proposed scheme aims to improve the performance of OBS networks when the network load increases temporarily and/or locally. Because we cannot consider all possible scenarios, we examine the performance of the proposed scheme in the following way. In Section 4.1, we consider static scenarios in order to reveal fundamental characteristics of the proposed scheme. We first examine the impact of system parameters on the burst loss probability and confirm the superiority of the proposed scheme in congested situations, regardless of specific values of system parameters. We
112
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 8. Burst loss probability in linear scale.
also examine the average end-to-end delay and goodput, in order to show that the proposed scheme can suppress superfluous deflection routing and use network resources efficiently. We then show, in Sections 4.2 and 4.3, that the proposed scheme works very well in locally and temporarily congested networks, respectively, which are our main concerns. For each set of parameters, we collect 30 independent samples from simulation experiments with 3000 s. We also show 95% confidence intervals in each figure unless stated otherwise, even though most of them are invisible. 4.1. Fundamental performance of the proposed scheme 4.1.1. Burst loss probability We first examine various characteristics of the burst loss probability in the proposed scheme. Note that the burst loss probability is defined as burst loss probability =
# of lost burst . # of transmitted bursts
Figs. 8 and 9 show the burst loss probability against the input load ρ = λL, where the vertical axis in Fig. 9 is in logarithmic scale. Readers are referred to Table 3 for explanatory notes in figures. We first observe that the burst loss probability in the conventional deflection routing (labeled “deflection”) increases rapidly with the input load, and in heavily loaded situations, it is greater than that in the simple forwarding scheme without deflection (labeled “w/o deflection”). Note that this observation agrees with those in [15–17]. Next we examine the proposed scheme. Recall that the burst discarding probability p is given by the
Fig. 9. Burst loss probability in logarithmic scale. Table 3 Explanatory notes in figures Explanatory notes
Burst discarding prob. p
Deflection w/o deflection Proposal (w/o p1 ) Proposal (w/o p2 ) Proposal
p p p p p
=0 =1 = p2 = p1 = p1 × p2
product of p1 and p2 , where p1 is closely related to network congestion and p2 to the numbers of elapsed and remaining hops. The result for “proposal (w/o p2 )” shows that the control of deflection routing based only on the degree of congestion is not so much effective. In fact, its performance merely lies between the conventional deflection routing and the simple forwarding scheme without deflection. The result for “proposal (w/o p1 )” indicates that in heavily loaded situations, it is effective to suppress deflection routing based on the numbers of elapsed and remaining hops. However, it does not work well when sufficient network resources are available. Thus the control of deflection routing based on the number of hops is effective only when network resources are insufficient. The proposed scheme controls deflection routing based on p = p1 × p2 . In other words, it controls deflection routing based on the number of hops only when the network is congested (i.e., sufficient network resources are not available). As shown in Figs. 8 and 9, the proposed scheme exhibits an excellent performance over a wide range of the input load. Note that the performance of the proposed scheme may be sensitive to the topology as well as the conventional deflection routing. Thus we also evaluated the performance of
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 10. Burst loss probability.
113
Fig. 11. The impact of the processing time (lightly loaded situation ρ = 0.1, logarithmic scale).
the proposed scheme in NSFNET which consists of 14 nodes and 21 links, and we observed that the proposed scheme works effectively in NSFNET. Due to the shortage of space, we omit these results. Next, in order to examine the fairness of the proposed scheme among bursts with different numbers of endto-end hops, we classify bursts in terms of the number of hops on the primary route and show their burst loss probabilities in Fig. 10, where the input load is set to be 0.6. We also show the burst loss probabilities (labeled “proposal (when e = 0)”) when (2) is replaced by 1 +1 , p2 = 1 − log2 r i.e., deflection routing is controlled based only on the number r of remaining hops. In this case, the burst loss probability decreases effectively when the number of end-to-end hops is small. As the number of end-toend hops increases, however, the burst loss probability increases. This is because bursts with a small number of end-to-end hops have high priority and bursts with a large number of end-to-end hops tend to be discarded when e = 0. On the other hand, we observe that the control based on both the numbers of elapsed and remaining hops can decrease the burst loss probability, regardless of the number of hops on the primary route. This result shows that, to some extent, the proposed scheme takes into account the fairness among bursts with the different numbers of end-to-end hops. 4.1.2. Robustness of the superior performance of the proposed scheme We now demonstrate the robustness of the superior performance of the proposed scheme against the change
Fig. 12. The impact of the processing time (heavily loaded situation ρ = 0.6, linear scale).
of system parameter values such as the processing time ∆, the propagation delay d, and the number W of wavelengths. Figs. 11 and 12 show the burst loss probability against the processing time ∆ of each control packet in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively, where L are fixed to 0.01 (s) and ∆ varies from 0.001 (s) to 0.02 (s). These figures show that regardless of the value of the processing time, the burst loss probability in the proposed scheme is almost the same as that in the conventional deflection routing when the input load is light, and in heavily loaded situations, it is smaller than that in the conventional deflection routing. Thus we conclude that the proposed scheme keeps the superior performance in any value of the processing time ∆. From Figs. 11 and 12, we also observe that the burst loss probability in any scheme is a non-decreasing
114
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
function of the processing time ∆ and it remains constant for ∆/L ≥ 1. We explain the cause of this phenomenon below. Suppose two bursts, b M and b N , contend for an output link at a node, where the number of remaining hops of burst b M (resp. b N ) at the node is equal to m (resp. n) and m > n. In this case, compared with burst b N , burst b M can attempt to reserve the link (m − n)∆ (s) in advance, even if those bursts are scheduled to arrive at the node simultaneously. Therefore burst b M has priority over burst b N . This tendency strengthens with ∆ and it is maximized for (m − n)∆ ≥ L. As a result, if ∆ ≥ L, any pair of bursts with the different numbers of remaining hops are differentiated at maximum. This differentiation affects the burst loss probability in the following way. Bursts with many remaining hops tend to succeed in reserving links. However, as traversing the network, the number of remaining hops decreases and therefore bursts are prone to fail the reservation. Because this tendency strengthens with ∆, bursts are more likely to be lost at nodes close to the destinations. This leads to a waste of network resources. As a result, the burst loss probability increases with ∆ and reaches the ceiling at ∆ = L. Figs. 13 and 14 show the burst loss probability against the propagation delay d of each link in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively, where L is fixed to 0.01 (s) and d varies from 0.001 (s) to 0.02 (s). These figures show that the burst loss probabilities in the proposed scheme and the conventional deflection routing are almost the same in lightly loaded situation, and when the network is congested, the burst loss probability in the proposed scheme is smaller than that in the conventional deflection routing. Thus we conclude that the proposed scheme keeps the superior performance in any value of the propagation delay d. We also observe that the burst loss probabilities in the proposed scheme and the conventional deflection routing are non-increasing functions of the propagation delay d and they touch bottom at d = L. We explain the cause of this phenomenon using Fig. 15. Suppose nodes A and B transmit bursts b A and b B , respectively, to node F and burst b B collides with b A at node C. Further burst b B takes the alternative route C → D → E → F. Because bursts are transmitted in a cut-through manner, it is possible for burst b B to collide with burst b A at node E if the difference between the propagation delays on the primary and alternative routes is less than the transmission time L. The possibility of this collision gets smaller with increasing propagation time d and it is eliminated when d = L. Note that a similar phenomenon was observed
Fig. 13. The impact of the propagation delay (lightly loaded situation ρ = 0.1, logarithmic scale).
Fig. 14. The impact of the propagation delay (heavily loaded situation ρ = 0.6, linear scale).
Fig. 15. Collision of deflected burst.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 16. The impact of the wavelength (lightly loaded situation ρ = 0.1, logarithmic scale).
115
Fig. 18. Burst loss probability in linear scale (hyper exponential transmission time).
Fig. 17. The impact of the wavelength (heavily loaded situation ρ = 0.6, linear scale).
in [17], where exponential transmission times were assumed. In congested networks, deflected bursts are likely to be discarded at alternative routes because the conventional deflection routing accelerates the network congestion. As a result, the conventional deflection routing cannot work well and propagation delay can hardly affect the burst loss probability in congested networks. On the other hand, the proposed scheme can work effectively in any case. Figs. 16 and 17 show the burst loss probability when the number of wavelengths W varies from 1 to 8 in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively. In these figures, the input load ρ is defined as ρ = λL/W . We observe that the performance of every scheme improves with increasing the number of wavelengths because a wavelength to transmit bursts can be selected among all unused wavelengths at
Fig. 19. Burst loss probability in logarithmic scale (hyper exponential transmission time).
ingress nodes and contention can be avoided. We also observe that the proposed scheme exhibits an excellent performance in any case. So far we have assumed that the transmission time L is constant. We now examine the impact of the variation in transmission times on the burst loss probability. For this purpose, we assume that burst transmission times follow a balanced hyper exponential distribution with mean L = 0.01 and the coefficient of variation Cv = 2.0. Figs. 18 and 19 show the burst loss probability against the input load ρ = λL, where the vertical axis in Fig. 19 is in logarithmic scale. We observe that the qualitative behavior of the proposed scheme is very similar to the case of constant transmission times given in Figs. 8 and 9.
116
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 20. Average end-to-end delay.
Fig. 21. Goodput performance.
In summary, the superiority of the proposed scheme is quite robust in a wide range of system parameters. Thus, in what follows, we assume that burst transmission times are set to be constant and system parameter values are fixed to those in Table 1. 4.1.3. End-to-end delay and goodput To show that the proposed scheme can suppress superfluous deflection routing, we evaluate the average end-to-end delay. Fig. 20 plots the average end-toend delay against the input load. We observe that the average end-to-end delay decreases with the input load when the input load is greater than 0.4. This phenomenon comes from the fact that bursts with longer hops are more likely to be lost as the input load increases. Note that, in lightly and moderately loaded situations, deflection routing makes the average endto-end delay increase because it causes the increase of the number of hops. We also observe that the average end-to-end delay of the proposed scheme decreases slightly in moderately loaded situations, compared with the conventional deflection routing. This phenomenon suggests that superfluous deflection is suppressed. Next we investigate to what extent network resources are efficiently used in the proposed scheme. To do so, we define the goodput of a link as the average number of bursts transmitted on the link per unit time, which eventually reach their destinations. Fig. 21 shows the average goodput over links as a function of the input load. We observe that the average goodput in the proposed scheme increases with the input load, whereas the average goodput in the conventional deflection routing decreases when the network is congested. This observation supports our claim that the proposed
Fig. 22. Normalized goodput.
scheme uses network resources efficiently when the network is congested. We now define the normalized goodput as , X X normalized goodput = Gi Ti , all link i
all link i
where G i denotes the goodput of link i and Ti denotes the average number of bursts transmitted on link i per unit time. The normalized goodput is plotted against the input load in Fig. 22. This figure shows that the conventional deflection routing cannot use network resources efficiently when the network is congested. We again observe the excellent performance of the proposed scheme, which is considered to come from an efficient use of network resources. In Fig. 23, we examine the normalized goodput in terms of the number of hops on the primary route.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 23. Normalized goodput.
117
Fig. 24. Burst loss probability when node 2 is heavily loaded.
This figure indicates that the proposed scheme surpasses the conventional deflection routing, regardless of the number of hops and the input load. 4.2. Performance in locally congested networks This subsection investigates the performance of the proposed scheme when the network is locally congested, i.e., input loads at some nodes are greater than others. For this purpose, we assume that the input load of each node is set to be 0.1, unless stated otherwise, and we choose nodes 2, 12, and 22 as candidates for heavily loaded nodes. Note that node 2 and 22 are representatives of nodes located in peripheral areas of the network, while node 12 is a representative of nodes in the central area. We define the loss probability of bursts generated from node i as the ratio of the number of loss bursts generated from node i to the total number of bursts generated from node i. Fig. 24 shows the loss probability of bursts generated from each node, where the input load of node 2 is set to be 1.5. In this scenario, nodes with low indices are relatively congested (see Fig. 4). We observe that the loss probability of bursts generated from node 2 is greater than that in deflection routing. Owing to this, however, loss probabilities of bursts from all other nodes significantly decrease when the proposed scheme is employed. This phenomenon implies that the proposed scheme suppresses the increasing of the network load by restricting deflection routing of bursts generated from heavily loaded nodes. Therefore the proposed scheme fulfills a function of congestion control. The same observation can be made in Figs. 25–27, where the input loads at node 12 and node 22 are set to be 1.5 in Figs. 25 and 26, respectively,
Fig. 25. Burst loss probability when node 12 is heavily loaded.
and the input loads at nodes 2 and at node 22 are set to be 1.5 in Fig. 27. Fig. 28 shows the loss probability of bursts generated from node 22 against the input load of node 2, where the input loads of all nodes except for node 2 are set to be 0.1. We observe that in the conventional deflection routing, heavily loaded node 2 affects the performance of node 22 (which is located far from node 2) significantly. On the other hand, the proposed scheme reduces the influence of node 2 on node 22 and decreases the loss probability of bursts generated from node 22 effectively. In summary, the proposed scheme utilizes network resources efficiently when local congestion happens. 4.3. Response to temporarily increasing load Finally, we examine the dynamic behavior of the proposed scheme when the network load temporarily
118
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 26. Burst loss probability when node 22 is heavily loaded.
Fig. 28. The burst loss probability of node 22 against the input load of node 2.
Fig. 27. Burst loss probability when node 2 and 22 are heavily loaded. Fig. 29. Sample path of throughput.
increases. To do so, we assume that the input load at each node is fixed to 0.2 during time intervals [0,1010] (s) and [1040, 3000] (s), and it increases to 0.8 during time interval [1010, 1040] (s). Because we are concerned with the dynamic behavior, no confidence intervals are shown in the following figures. Fig. 29 shows a typical sample path of the throughput per unit time. We observe that the proposed scheme adequately reacts to the increase of the input load and its throughput eventually becomes greater than that in the simple forwarding scheme without deflection. On the other hand, the throughput of the conventional deflection routing degrades when the input load increases. Note that these observations coincide with the fundamental characteristics discussed in Section 4.1. We also observe from this figure that the simple forwarding scheme reacts to the increase of the
input load immediately, whereas the proposed scheme suffers from some delay in reacting to it. To see this phenomenon more closely, we define the average load as the average of the number of control packets arriving at each node per unit time. Fig. 30 plots the sample path of the average load, which corresponds to the sample path in Fig. 29. We observe that the average loads in the proposed scheme and the conventional deflection routing increase in a very similar manner, as soon as the input load increases. After that, the average load in the proposed scheme decreases gradually, whereas the average load in the conventional deflection routing remains almost constant. Recall here that we choose one second as a unit time τ and the parameter α in the exponentiallyweighted moving average (3) is set to be 1/8.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
119
autonomously at each node, and it was shown to be effective when congestion occurred temporarily and/or locally. Note that in many cases, the proposed scheme can be combined with other proposals that enhance the performance of deflection routing. For example, [17,19] independently proposed the use of electrical buffering capability at ingress nodes in OBS networks. Combining this with our proposed scheme, the performance of deflection routing can be further improved. Acknowledgement
Fig. 30. Sample path of the average load.
This research was supported in part by Grant-in-Aid for Scientific Research (C) of the Japan Society for the Promotion of Science under Grant No. 18560377. References
Fig. 31. Transient response to the increase in input load.
Therefore it takes about ten seconds to react to the increase in the input load in this scenario. Apparently, the response time to the increase of the input load can be improved if we set α to be a larger value. Fig. 31 shows sample paths of the throughput for α = 1/4, 1/8, and 1/16. We observe that the response time improves with the increase of α, whereas the proposed scheme becomes sensitive to a slight variation of the input load. This is a well-known tradeoff and we have to arrange a compromise between them, depending on the situation. 5. Conclusion This paper proposed a dynamic burst discarding scheme that controlled deflection routing in OBS networks. The proposed scheme can be operated
[1] F.J. Westphal, M. Jager, H.M. Foisel, A. Gladisch, Evolution of optical networks and management aspects, in: Proc. of the Fourth International Topical Workshop on Contemporary Photonic Technologies, Tokyo, Japan, Jan. 2001, pp. 35–38. [2] R.S. Tucker, W.D. Zjpmg, Photonic packet switching: An overview, IEICE Transactions on Communications E82-B (1999) 254–264. [3] M. Kovacevic, A. Acampora, On wavelength translation in alloptical networks, in: Proc. of INFOCOM, Boston, MA, Apr. 1995, pp. 413–422. [4] M. Yoo, M. Jeong, C. Qiao, A high speed protocol for bursty traffic in optical networks, in: Proc. of SPIE’s All-Optical Communications Systems: Architecture, Control and Network Issues, Dallas, TX, 1997, pp. 79–90. [5] C. Qiao, M. Yoo, Optical burst switching (OBS): A new paradigm for an optical Internet, Journal of High Speed Networks 8 (1999) 69–84. [6] S. Oh, H.H. Hong, M. Kang, A data burst assembly algorithm in optical burst switching networks, ETRI Journal 24 (2002) 311–322. [7] M. Yoo, C. Qiao, Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks, in: Proc. of IEEE/LEOS Technologies for a Global Information Infrastructure, Montreal, Canada, Aug. 1997, pp. 26–27. [8] S. Yao, B. Mukherjee, S. Dixit, A unified study of contentionresolution schemes in optical packet-switched networks, Journal of Lightwave Technology 21 (2003) 672–683. [9] S.L. Danielsen, P.B. Hansen, K.E. Stubkjear, Wavelength conversion in optical packet switching, Journal of Lightwave Technology 16 (1998) 2095–2108. [10] D.K. Hunter, M.C. Chia, I. Andonovic, Buffering in optical packet switches, Journal of Lightwave Technology 16 (1998) 2081–2094. [11] S. Bregni, G. Guerra, A. Pattavina, Optical switching of IP traffic using input buffered architectures, Optical Networks Magazine 3 (2002) 20–29. [12] P. Bayvel, M. Dueser, Optical burst switching: Research and applications, in: Proc. of OFC, Los Angeles, CA, Feb. 2004, pp. 23–27.
120
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
[13] Y. Liu, M.T. Hill, R. Geldenhuys, N. Calabretta, H. de Waardt, G.D. Khoe, H.J.S. Dorren, Demonstration of a variable optical delay for a recirculating buffer by using all-optical signal processing, IEEE Photonics Technology Letters 16 (2004) 1748–1750. [14] J. Fehrer, J. Sauer, L. Ramfelt, Design and implementation of a prototype optical deflection network, in: Proc. of SIGCOMM, London, UK, Aug. 1994, pp. 191–200. [15] F. Borgonovo, L. Fratta, J.A. Bannister, Unslotted deflection routing in all-optical networks, in: Proc. of GLOBECOM, Houston, TX, Nov. 1993, pp. 119–125. [16] F. Borgonovo, L. Fratta, J.A. Bannister, On the design of optical deflection-routing networks, in: Proc. of INFOCOM, Toronto, Canada, Jan. 1994, pp. 120–129. [17] X. Wang, H. Morikawa, T. Aoyama, Burst optical deflection routing protocol for wavelength routing WDM networks,
[18]
[19]
[20]
[21]
in: Proc. of SPIE/IEEE OPTICOMM, Dallas, TX, Oct. 2000, pp. 257–266. S. Floyd, V. Jacobson, Random early detection gateways for congestion avoidance, IEEE/ACM Transactions on Networking 1 (1993) 397–413. S. Lee, K. Sriram, H.S. Kim, J.S. Song, Contention-based limited deflection routing in OBS networks, in: Proc. of GLOBECOM, San Francisco, CA, Dec. 2003, pp. 2633–2637. A. Zalesky, H.L. Vu, Z. Rosberg, E.W.M. Wong, M. Zukerman, Modelling and performance evaluation of optical burst switched networks with deflection routing and wavelength reservation, in: Proc. of INFOCOM, Hong Kong, China, Mar. 2004, pp. 1864–1871. C. Cameron, A. Zalesky, M. Zukerman, Prioritized deflection routing in optical burst switching networks, IEICE Transactions on Communications E88-B (2005) 1861–1867.
Dynamic burst discarding scheme for deflection routing in optical burst switching networks Kouji Hirata ∗ , Takahiro Matsuda, Tetsuya Takine Department of Information and Communications Technology, Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita 565-0871, Japan Received 12 May 2006; received in revised form 6 December 2006; accepted 1 January 2007 Available online 11 January 2007
Abstract This paper proposes a dynamic burst discarding scheme for deflection routing in optical burst switching networks. In general, deflection routing is effective in lightly loaded situations, whereas it has a contrary effect in congested networks because deflected bursts accelerate network congestion. Thus deflection routing should be employed in lightly loaded networks. Incoming traffic, however, varies in time and location, so that temporal and/or local congestion cannot be avoided. Our proposed scheme resolves this problem in the following way. Each node autonomously detects congestion with local information, and bursts to be deflected are discarded in a probabilistic manner, based on the degree of detected congestion and the numbers of elapsed and remaining hops of those bursts. Simulation experiments show that when congestion happens temporarily, the proposed scheme reduces the burst loss probability, and it utilizes network resources efficiently when local congestion happens. c 2007 Elsevier B.V. All rights reserved.
Keywords: Optical burst switching; Contention resolution; Deflection routing; Dynamic burst discarding
1. Introduction In recent years, optical networks are expected as a platform of next generation networks that support an explosive increase in traffic volume on the Internet [1]. In optical networks, one of the most important technical requirements is a switching technique such as optical circuit switching (OCS), optical packet switching (OPS), and optical burst switching (OBS). OCS is relatively easy to implement but lacks flexibility to cope with fluctuating traffic and link state. OPS is conceptually ideal, but it has some technological ∗ Corresponding author. Tel.: +81 6 6879 7742.
E-mail addresses: [email protected] (K. Hirata), [email protected] (T. Matsuda), [email protected] (T. Takine). c 2007 Elsevier B.V. All rights reserved. 1573-4277/$ - see front matter doi:10.1016/j.osn.2007.01.001
limitations at present, in terms of optical RAMs and all-optical processing of headers [2,3]. OBS possesses several advantages of both OCS and OPS, and it is under study as a promising solution to optical Internet backbone networks in the near future [4,5]. Fig. 1 illustrates an architecture of OBS networks. OBS is used in a core domain that interconnects electrical domains (i.e., IP subnetworks). There are two types of network nodes, edge nodes and core nodes, in OBS networks. Edge nodes fill the role of an interface between electrical domains and the OBS core network. IP packets arriving from IP subnetworks are assembled into bursts at ingress edge nodes [6]. Those bursts are sent to their destination edge nodes in an optical domain and disassembled into packets there. Wavelength and switching resources for each
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
107
Fig. 1. A optical burst switching (OBS) network.
Fig. 3. Deflection routing.
Fig. 2. Basic operation in JET.
burst are reserved according to a one-way reservation protocol such as Just-Enough-Time (JET) [7]. Fig. 2 illustrates the basic operation in JET. Before the transmission of a burst, its control packet, which includes the route information and burst length, is transmitted on a control channel. At each core node, the control packet is processed in an electrical domain in order to reserve a wavelength and set up a route for the corresponding burst. The burst follows the control packet on a data channel after an offset time, without any acknowledgements for the connection establishment. The offset time should be large enough to process the control packet electrically and set up the switching matrix for the burst at every OBS core node on the route. As a result, the switching matrix has been already set up when the burst arrives at core nodes, i.e., the burst is transmitted in a cut-through manner without O/E/O conversion. Wavelength reservation is released after the burst is transmitted. In OBS networks, contention occurs at switching nodes whenever two or more bursts with the same wavelength try to leave a switch fabric on the same output port at the same time. In electrical packetswitched networks, contention is resolved with storeand-forward technique that temporarily stores incoming packets in a memory bank, and those packets are sent out later when the desired output port becomes available. This is possible because of the availability of electronic RAM. However, no optical RAM technology
is available in OBS networks. Therefore, OBS switches should adopt different approaches to such an inevitable contention [8]. Contention resolution in OBS networks can be performed in three domains, i.e., wavelength, time, and space. In the wavelength domain, wavelength conversion avoids contention by converting one wavelength to another [9], and it improves the performance considerably. However, the wavelength conversion technology is still immature and it requires extra hardware (e.g., wavelength converters and lasers for wavelength conversion) and control software. For contention resolution in the time domain, fiber delay lines can be utilized, which store bursts temporarily until output ports become available [10,11]. At present, however, fiber delay lines are typically limited to providing a few tens of µs delay at most [12,13]. Thus it is not able to store a large number of optical bursts. Deflection routing is considered as contention resolution in the space domain [14–16], which can be implemented without any restrictions. Deflection routing is a sort of dynamic routing. When a burst arrives at an OBS core node and finds that the wavelength at the port on the primary path is not available, it will be switched to an alternative port (see Fig. 3). In this way, bursts arriving at a congested node are distributed to its neighboring nodes, and overall link utilization and network performance are expected to be improved. However, deflection routing has some faults. First of all, its performance depends strongly on the network topology, and deflection routing may not work effectively when there exists only a small number of alternative paths. Moreover, when the network is congested, the burst loss probability becomes large and eventually exceeds that in the case of no
108
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
deflection [15–17], because deflected bursts accelerate the network congestion in general. Note that this is the critical problem in OBS networks when contention resolution relies only on deflection routing. Thus OBS networks with deflection routing should be operated in lightly loaded situations. Incoming traffic, however, varies in time and location, so that temporal and/or local congestion cannot be avoided. In this paper, we propose a dynamic burst discarding scheme for deflection routing in OBS networks. Our scheme aims at controlling deflection routing when temporal and/or local congestion happens. A unique feature of the proposed scheme is that each core node independently controls deflection routing. Specifically, each node autonomously detects congestion with locally available information, and bursts to be deflected are discarded in a probabilistic manner, based on the estimated degree of congestion and the numbers of elapsed and remaining hops of those bursts. The rationale behind the proposed scheme might be similar to the concept of RED [18] that detects congestion through the queue length in the buffer. However, no buffer is available at core nodes in OBS networks. Thus we need a different method of detecting congestion. The proposed scheme utilizes a characteristic of deflection routing for detecting congestion. When a specific node is congested in an OBS network with deflection routing, its neighboring nodes are likely to be congested, too. Thus the proposed scheme uses the number of control packets arriving at each node as the index of congestion at its neighboring nodes. In addition, the proposed scheme does not discard deflected bursts randomly as in RED, but discards them selectively, based on the numbers of elapsed and remaining hops. Note that the control of deflection based on the numbers of elapsed and remaining hops was first proposed in [19]. Our proposed scheme controls superfluous deflection in order to use the network resource efficiently. As a result, the burst loss probability is expected to be reduced significantly by the proposed scheme when the network load increases temporarily and/or locally. The rest of this paper is organized as follows. Section 2 describes related works. In Section 3, we describe the proposed scheme in detail. Section 4 presents the result of simulation experiments and discusses the performance of the proposed scheme. Finally, we conclude the paper in Section 5.
congested networks. To resolve this problem, several schemes were proposed in the past. Wang et al. proposed a scheme to resolve this problem [17], where bursts can be stored electrically at ingress nodes. Further bursts are not allowed to transmit back and forth on the same link. Lee et al. focused on how to select an alternative path when contention occurs [19]. They proposed a scheme that selects a lightly loaded alternative path and dynamically determines if the burst should be deflected or retransmitted from its source node according to delay and blocking probability on the alternative path. However, this scheme requires a management database at OBS edge nodes, which stores the latest information on the status of the whole OBS network. Even though the performance of the OBS network is considerably improved, this scheme introduces significant overhead because periodic updates of the management database are required. On the other hand, the overhead of our proposed scheme is minimal because each node operates autonomously without any external controllers. In [20], Zalesky et al. showed that deflection routing had a destabilizing effect at high loads in OBS networks. To resolve this problem, they proposed and analyzed a technique called wavelength reservation to intentionally limit the amount of deflection by reserving several wavelengths on each link for the exclusive use of nondeflected bursts. In addition, they presented a reducedload Erlang fixed-point analysis of OBS networks with deflection routing and wavelength reservation. Note that this scheme requires several wavelengths, whereas our proposed scheme can be operated on a single wavelength. In [21], Cameron et al. proposed a routing protocol called SP-PRDR. In this scheme, non-deflected bursts have preemptive priority over deflected bursts. Thus a wavelength reservation for a deflected burst can be preempted by a non-deflected burst and the wavelength reservation for the non-deflected burst succeeds. As a result, this scheme suppresses superfluous deflection routing and reduces the burst loss probability effectively in heavily loaded situations. In lightly loaded situations, however, the burst loss probability of this scheme is higher than that of the conventional deflection routing. On the other hand, the burst loss probability of our proposed scheme in lightly loaded situations is expected to be almost the same as that of the conventional deflection routing.
2. Related works
3. Proposed scheme
As mentioned above, deflection routing accelerates the network congestion and has a contrary effect in
This section describes the proposed scheme to enhance the performance of deflection routing, especially
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
109
Table 1 Parameters in simulation experiments Parameter
Value
Number W of wavelengths Propagation delay d of a link Processing time ∆ of a control packet Mean arrival rate of bursts Transmission time L of a burst
1 0.01 (s) 0.001 (s) λ (bursts/s) 0.01 (s)
when the network is congested temporarily or locally. In normal situations, bursts are transmitted on the shortest path to the destination node. Further, contended bursts at core nodes are deflected to a shortest path among available alternative ones. When the network is congested, however, the proposed scheme selectively discards contended bursts. To do so, each node has to know the degree of congestion. Further, when congestion is detected, each node has to decide either to attempt deflection routing for contended bursts or to discard them simply, based on information available at the node. Note that it is not a good idea to discard all contended bursts even in heavily loaded situations. In such a case, the selective discarding of contended bursts can relax the degree of congestion and therefore some of the contended bursts can be delivered to their destination nodes by deflection routing. In what follows, we first discuss how to estimate the degree of congestion and how to discard contended bursts selectively, and then we show a specific implementation of our scheme. 3.1. Autonomous detection of congestion This subsection describes a rationale behind our autonomous congestion detection scheme. Suppose congestion happens at node i of an OBS network with deflection routing. Many contended bursts at node i are then re-routed to its neighboring nodes, so that they are expected to be involved in congestion, too. In order to confirm this observation, we conduct simulation experiments with an OBS network shown in Fig. 4. We assume that fixed length bursts are generated from each node according to a Poisson process and the destination node of a burst is independently chosen equally likely from among other nodes. The offered load at each node is set to be 0.4 (i.e., each ingress node generates 40 bursts per second on average). We will use this network model in Section 4 again and we explain it in more detail there. Other system parameters are listed in Table 1. Table 2 shows correlation coefficients of the numbers of control packets received at respective nodes every second, where the upper half and lower half tables
Fig. 4. Network model.
provide the results for OBS networks with the simple forwarding scheme (without deflection) and with deflection routing, respectively. We observe that the correlation coefficient for a pair of adjacent nodes are significantly larger in the network with deflection routing. This phenomenon suggests that when a specific node is congested in an OBS network with deflection routing, its neighboring nodes are likely to be congested, too. In other words, the degree of congestion at each node can be used as an estimator of those at its neighboring nodes. We also observe this phenomenon when a certain node is heavily loaded while its neighboring nodes are very lightly loaded. Thus we propose an autonomous congestion detection scheme, in which each node counts the number of arriving control packets every unit time, and based on it, each node indirectly estimates the degree of congestion at its neighboring nodes. Section 3.3 describes how this autonomous scheme is integrated into our dynamic burst discarding scheme. 3.2. Priority assignment to contended bursts Contended bursts are selectively discarded when congestion is detected. To do so, we assign priority to contended bursts and we may discard those with low priority. Specifically, we assign high priority to contended bursts whose elapsed hops are large. See Fig. 5. Note that this strategy is common in congestion control. At the same time, however, we are willing to assign high priority to contended bursts whose remaining hops are small, because they are more likely to be delivered to their destination, compared to those with a large number of remaining hops. A similar idea was employed in [19]. Note that in assigning priority to contended bursts, the above two measures can be inconsistent, so that we have to compromise between them in one way or another, which is discussed in the following subsection.
110
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Table 2 Correlation coefficients of the numbers of control packets
burst discarding probability p is given by p = p1 × p2 ,
(1)
3.3. Dynamic burst discarding scheme
where p1 (0 ≤ p1 ≤ 1) is determined based on the estimated degree of congestion and p2 (0 ≤ p2 ≤ 1) is determined by the numbers of elapsed and remaining hops of the control packet. As explained in the preceding subsection, factor p2 should increase with the number r of remaining hops to the destination node and also it should be a decreasing function of the number e of elapsed hops. Even though we have a choice of so many such functions, we assume in this paper that p2 is given by e+1 +1 , (2) p2 = 1 − log2 e+r
This subsection describes our dynamic burst discarding scheme. Suppose an arriving control packet cannot reserve the primary path at a core node. In our scheme, this control packet (and the corresponding burst) is discarded with probability p, instead of attempting deflection routing. As discussed above, the burst discarding probability p is a function of the estimated degree of congestion and priority based on the numbers of elapsed and remaining hops. Due to the nature of deflection routing, however, the actual number of remaining hops is uncertain. Thus we substitute the number of remaining hops on the shortest path to the destination for it, and we call the former the number of remaining hops hereafter. In the proposed scheme, we assume that the
where e and r denote the numbers of elapsed and remaining hops, respectively. Fig. 6 shows factor p2 as a function of the number e of elapsed hops. Note that p2 = 0 for bursts with r = 1, so that p = 0 (see (1)). Therefore bursts that can reach their destination nodes with one hop always attempt deflection routing. We expect that this feature will lead to the improvement of the throughput. Next, we consider factor p1 in (1). We assume that each node counts the number of arriving control packets every unit time τ , and estimates the current load by taking the exponentially-weighted moving average, from which factor p1 is determined. The detailed procedure of each node is as follows.
Fig. 5. Burst discarding according to the number of hops.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 6. Factor p2 as a function of the number e of elapsed hops.
(i) Count the number an (n = 1, 2, . . .) of control packets arriving in every interval ((n − 1)τ, nτ ]. (ii) Compute the exponentially-weighted moving average aˆ n of the sequence {an ; n = 1, 2, . . .} by aˆ n = αan + (1 − α)aˆ n−1 ,
(3)
where α (0 < α ≤ 1) is a parameter. (iii) Compute the offered load ρn per transmission channel by aˆ n L , (4) NW where L denotes the average burst length, N denotes the number of links at the node, and W denotes the number of wavelengths available per link. (iv) During interval (nτ, (n + 1)τ ], the following p1 is employed. (h i−1 (−β tan(πρn − π2 )) 1 + e , if ρn < 1, (5) p1 = 1, otherwise, ρn =
where β (β > 0) is a parameter. Note that p1 in (5) is a sigmoid function of ρn (ρn < 1). Fig. 7 shows factor p1 as a function of ρn , where β = 4. We observe that p1 increases rapidly when ρn becomes greater than 0.3. 4. Performance evaluation To evaluate the performance of the proposed scheme, we conduct simulation experiments with the OBS network in Fig. 4, assuming that OBS is used at core networks (see Fig. 1). It consists of 24 nodes and 43 bi-directional links. We assume that neither wavelength
111
Fig. 7. Factor p1 as a function of ρn (β = 4).
conversion nor buffering capability is available at any of the nodes. Note that under this assumption, bursts transmitted on different wavelengths do not interfere each other. Thus we focus on a specific wavelength and set W = 1 (see (4)). For simplicity, we assume that propagation delays d of all links are identical and equal to 0.01 (s), and the processing time ∆ of each control packet at every node is equal to 0.001 (s). At each node, bursts are generated according to a Poisson process with rate λ, and burst transmission times L are fixed to 0.01 (s). The destination of each burst is independently chosen equally likely among all possible nodes, and its primary route is set to be a shortest path between the source and destination. Table 1 summarizes values of those parameters. We choose one second as a unit time τ . Let H denote the number of hops on the primary path of a burst. The offset time given to the control packet is then set to be H × ∆ + 0.05 = 0.001H + 0.05 (s), where H × ∆ denotes the minimum offset time. Thus each burst can take (H + 50) hops at most. Parameter α of the exponentially-weighted moving average in (3) is set to be 1/8, unless stated otherwise. Further parameter β of the sigmoid function in (5) is fixed to 4. The proposed scheme aims to improve the performance of OBS networks when the network load increases temporarily and/or locally. Because we cannot consider all possible scenarios, we examine the performance of the proposed scheme in the following way. In Section 4.1, we consider static scenarios in order to reveal fundamental characteristics of the proposed scheme. We first examine the impact of system parameters on the burst loss probability and confirm the superiority of the proposed scheme in congested situations, regardless of specific values of system parameters. We
112
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 8. Burst loss probability in linear scale.
also examine the average end-to-end delay and goodput, in order to show that the proposed scheme can suppress superfluous deflection routing and use network resources efficiently. We then show, in Sections 4.2 and 4.3, that the proposed scheme works very well in locally and temporarily congested networks, respectively, which are our main concerns. For each set of parameters, we collect 30 independent samples from simulation experiments with 3000 s. We also show 95% confidence intervals in each figure unless stated otherwise, even though most of them are invisible. 4.1. Fundamental performance of the proposed scheme 4.1.1. Burst loss probability We first examine various characteristics of the burst loss probability in the proposed scheme. Note that the burst loss probability is defined as burst loss probability =
# of lost burst . # of transmitted bursts
Figs. 8 and 9 show the burst loss probability against the input load ρ = λL, where the vertical axis in Fig. 9 is in logarithmic scale. Readers are referred to Table 3 for explanatory notes in figures. We first observe that the burst loss probability in the conventional deflection routing (labeled “deflection”) increases rapidly with the input load, and in heavily loaded situations, it is greater than that in the simple forwarding scheme without deflection (labeled “w/o deflection”). Note that this observation agrees with those in [15–17]. Next we examine the proposed scheme. Recall that the burst discarding probability p is given by the
Fig. 9. Burst loss probability in logarithmic scale. Table 3 Explanatory notes in figures Explanatory notes
Burst discarding prob. p
Deflection w/o deflection Proposal (w/o p1 ) Proposal (w/o p2 ) Proposal
p p p p p
=0 =1 = p2 = p1 = p1 × p2
product of p1 and p2 , where p1 is closely related to network congestion and p2 to the numbers of elapsed and remaining hops. The result for “proposal (w/o p2 )” shows that the control of deflection routing based only on the degree of congestion is not so much effective. In fact, its performance merely lies between the conventional deflection routing and the simple forwarding scheme without deflection. The result for “proposal (w/o p1 )” indicates that in heavily loaded situations, it is effective to suppress deflection routing based on the numbers of elapsed and remaining hops. However, it does not work well when sufficient network resources are available. Thus the control of deflection routing based on the number of hops is effective only when network resources are insufficient. The proposed scheme controls deflection routing based on p = p1 × p2 . In other words, it controls deflection routing based on the number of hops only when the network is congested (i.e., sufficient network resources are not available). As shown in Figs. 8 and 9, the proposed scheme exhibits an excellent performance over a wide range of the input load. Note that the performance of the proposed scheme may be sensitive to the topology as well as the conventional deflection routing. Thus we also evaluated the performance of
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 10. Burst loss probability.
113
Fig. 11. The impact of the processing time (lightly loaded situation ρ = 0.1, logarithmic scale).
the proposed scheme in NSFNET which consists of 14 nodes and 21 links, and we observed that the proposed scheme works effectively in NSFNET. Due to the shortage of space, we omit these results. Next, in order to examine the fairness of the proposed scheme among bursts with different numbers of endto-end hops, we classify bursts in terms of the number of hops on the primary route and show their burst loss probabilities in Fig. 10, where the input load is set to be 0.6. We also show the burst loss probabilities (labeled “proposal (when e = 0)”) when (2) is replaced by 1 +1 , p2 = 1 − log2 r i.e., deflection routing is controlled based only on the number r of remaining hops. In this case, the burst loss probability decreases effectively when the number of end-to-end hops is small. As the number of end-toend hops increases, however, the burst loss probability increases. This is because bursts with a small number of end-to-end hops have high priority and bursts with a large number of end-to-end hops tend to be discarded when e = 0. On the other hand, we observe that the control based on both the numbers of elapsed and remaining hops can decrease the burst loss probability, regardless of the number of hops on the primary route. This result shows that, to some extent, the proposed scheme takes into account the fairness among bursts with the different numbers of end-to-end hops. 4.1.2. Robustness of the superior performance of the proposed scheme We now demonstrate the robustness of the superior performance of the proposed scheme against the change
Fig. 12. The impact of the processing time (heavily loaded situation ρ = 0.6, linear scale).
of system parameter values such as the processing time ∆, the propagation delay d, and the number W of wavelengths. Figs. 11 and 12 show the burst loss probability against the processing time ∆ of each control packet in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively, where L are fixed to 0.01 (s) and ∆ varies from 0.001 (s) to 0.02 (s). These figures show that regardless of the value of the processing time, the burst loss probability in the proposed scheme is almost the same as that in the conventional deflection routing when the input load is light, and in heavily loaded situations, it is smaller than that in the conventional deflection routing. Thus we conclude that the proposed scheme keeps the superior performance in any value of the processing time ∆. From Figs. 11 and 12, we also observe that the burst loss probability in any scheme is a non-decreasing
114
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
function of the processing time ∆ and it remains constant for ∆/L ≥ 1. We explain the cause of this phenomenon below. Suppose two bursts, b M and b N , contend for an output link at a node, where the number of remaining hops of burst b M (resp. b N ) at the node is equal to m (resp. n) and m > n. In this case, compared with burst b N , burst b M can attempt to reserve the link (m − n)∆ (s) in advance, even if those bursts are scheduled to arrive at the node simultaneously. Therefore burst b M has priority over burst b N . This tendency strengthens with ∆ and it is maximized for (m − n)∆ ≥ L. As a result, if ∆ ≥ L, any pair of bursts with the different numbers of remaining hops are differentiated at maximum. This differentiation affects the burst loss probability in the following way. Bursts with many remaining hops tend to succeed in reserving links. However, as traversing the network, the number of remaining hops decreases and therefore bursts are prone to fail the reservation. Because this tendency strengthens with ∆, bursts are more likely to be lost at nodes close to the destinations. This leads to a waste of network resources. As a result, the burst loss probability increases with ∆ and reaches the ceiling at ∆ = L. Figs. 13 and 14 show the burst loss probability against the propagation delay d of each link in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively, where L is fixed to 0.01 (s) and d varies from 0.001 (s) to 0.02 (s). These figures show that the burst loss probabilities in the proposed scheme and the conventional deflection routing are almost the same in lightly loaded situation, and when the network is congested, the burst loss probability in the proposed scheme is smaller than that in the conventional deflection routing. Thus we conclude that the proposed scheme keeps the superior performance in any value of the propagation delay d. We also observe that the burst loss probabilities in the proposed scheme and the conventional deflection routing are non-increasing functions of the propagation delay d and they touch bottom at d = L. We explain the cause of this phenomenon using Fig. 15. Suppose nodes A and B transmit bursts b A and b B , respectively, to node F and burst b B collides with b A at node C. Further burst b B takes the alternative route C → D → E → F. Because bursts are transmitted in a cut-through manner, it is possible for burst b B to collide with burst b A at node E if the difference between the propagation delays on the primary and alternative routes is less than the transmission time L. The possibility of this collision gets smaller with increasing propagation time d and it is eliminated when d = L. Note that a similar phenomenon was observed
Fig. 13. The impact of the propagation delay (lightly loaded situation ρ = 0.1, logarithmic scale).
Fig. 14. The impact of the propagation delay (heavily loaded situation ρ = 0.6, linear scale).
Fig. 15. Collision of deflected burst.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 16. The impact of the wavelength (lightly loaded situation ρ = 0.1, logarithmic scale).
115
Fig. 18. Burst loss probability in linear scale (hyper exponential transmission time).
Fig. 17. The impact of the wavelength (heavily loaded situation ρ = 0.6, linear scale).
in [17], where exponential transmission times were assumed. In congested networks, deflected bursts are likely to be discarded at alternative routes because the conventional deflection routing accelerates the network congestion. As a result, the conventional deflection routing cannot work well and propagation delay can hardly affect the burst loss probability in congested networks. On the other hand, the proposed scheme can work effectively in any case. Figs. 16 and 17 show the burst loss probability when the number of wavelengths W varies from 1 to 8 in lightly and heavily loaded situations (ρ = 0.1 and 0.6), respectively. In these figures, the input load ρ is defined as ρ = λL/W . We observe that the performance of every scheme improves with increasing the number of wavelengths because a wavelength to transmit bursts can be selected among all unused wavelengths at
Fig. 19. Burst loss probability in logarithmic scale (hyper exponential transmission time).
ingress nodes and contention can be avoided. We also observe that the proposed scheme exhibits an excellent performance in any case. So far we have assumed that the transmission time L is constant. We now examine the impact of the variation in transmission times on the burst loss probability. For this purpose, we assume that burst transmission times follow a balanced hyper exponential distribution with mean L = 0.01 and the coefficient of variation Cv = 2.0. Figs. 18 and 19 show the burst loss probability against the input load ρ = λL, where the vertical axis in Fig. 19 is in logarithmic scale. We observe that the qualitative behavior of the proposed scheme is very similar to the case of constant transmission times given in Figs. 8 and 9.
116
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 20. Average end-to-end delay.
Fig. 21. Goodput performance.
In summary, the superiority of the proposed scheme is quite robust in a wide range of system parameters. Thus, in what follows, we assume that burst transmission times are set to be constant and system parameter values are fixed to those in Table 1. 4.1.3. End-to-end delay and goodput To show that the proposed scheme can suppress superfluous deflection routing, we evaluate the average end-to-end delay. Fig. 20 plots the average end-toend delay against the input load. We observe that the average end-to-end delay decreases with the input load when the input load is greater than 0.4. This phenomenon comes from the fact that bursts with longer hops are more likely to be lost as the input load increases. Note that, in lightly and moderately loaded situations, deflection routing makes the average endto-end delay increase because it causes the increase of the number of hops. We also observe that the average end-to-end delay of the proposed scheme decreases slightly in moderately loaded situations, compared with the conventional deflection routing. This phenomenon suggests that superfluous deflection is suppressed. Next we investigate to what extent network resources are efficiently used in the proposed scheme. To do so, we define the goodput of a link as the average number of bursts transmitted on the link per unit time, which eventually reach their destinations. Fig. 21 shows the average goodput over links as a function of the input load. We observe that the average goodput in the proposed scheme increases with the input load, whereas the average goodput in the conventional deflection routing decreases when the network is congested. This observation supports our claim that the proposed
Fig. 22. Normalized goodput.
scheme uses network resources efficiently when the network is congested. We now define the normalized goodput as , X X normalized goodput = Gi Ti , all link i
all link i
where G i denotes the goodput of link i and Ti denotes the average number of bursts transmitted on link i per unit time. The normalized goodput is plotted against the input load in Fig. 22. This figure shows that the conventional deflection routing cannot use network resources efficiently when the network is congested. We again observe the excellent performance of the proposed scheme, which is considered to come from an efficient use of network resources. In Fig. 23, we examine the normalized goodput in terms of the number of hops on the primary route.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 23. Normalized goodput.
117
Fig. 24. Burst loss probability when node 2 is heavily loaded.
This figure indicates that the proposed scheme surpasses the conventional deflection routing, regardless of the number of hops and the input load. 4.2. Performance in locally congested networks This subsection investigates the performance of the proposed scheme when the network is locally congested, i.e., input loads at some nodes are greater than others. For this purpose, we assume that the input load of each node is set to be 0.1, unless stated otherwise, and we choose nodes 2, 12, and 22 as candidates for heavily loaded nodes. Note that node 2 and 22 are representatives of nodes located in peripheral areas of the network, while node 12 is a representative of nodes in the central area. We define the loss probability of bursts generated from node i as the ratio of the number of loss bursts generated from node i to the total number of bursts generated from node i. Fig. 24 shows the loss probability of bursts generated from each node, where the input load of node 2 is set to be 1.5. In this scenario, nodes with low indices are relatively congested (see Fig. 4). We observe that the loss probability of bursts generated from node 2 is greater than that in deflection routing. Owing to this, however, loss probabilities of bursts from all other nodes significantly decrease when the proposed scheme is employed. This phenomenon implies that the proposed scheme suppresses the increasing of the network load by restricting deflection routing of bursts generated from heavily loaded nodes. Therefore the proposed scheme fulfills a function of congestion control. The same observation can be made in Figs. 25–27, where the input loads at node 12 and node 22 are set to be 1.5 in Figs. 25 and 26, respectively,
Fig. 25. Burst loss probability when node 12 is heavily loaded.
and the input loads at nodes 2 and at node 22 are set to be 1.5 in Fig. 27. Fig. 28 shows the loss probability of bursts generated from node 22 against the input load of node 2, where the input loads of all nodes except for node 2 are set to be 0.1. We observe that in the conventional deflection routing, heavily loaded node 2 affects the performance of node 22 (which is located far from node 2) significantly. On the other hand, the proposed scheme reduces the influence of node 2 on node 22 and decreases the loss probability of bursts generated from node 22 effectively. In summary, the proposed scheme utilizes network resources efficiently when local congestion happens. 4.3. Response to temporarily increasing load Finally, we examine the dynamic behavior of the proposed scheme when the network load temporarily
118
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
Fig. 26. Burst loss probability when node 22 is heavily loaded.
Fig. 28. The burst loss probability of node 22 against the input load of node 2.
Fig. 27. Burst loss probability when node 2 and 22 are heavily loaded. Fig. 29. Sample path of throughput.
increases. To do so, we assume that the input load at each node is fixed to 0.2 during time intervals [0,1010] (s) and [1040, 3000] (s), and it increases to 0.8 during time interval [1010, 1040] (s). Because we are concerned with the dynamic behavior, no confidence intervals are shown in the following figures. Fig. 29 shows a typical sample path of the throughput per unit time. We observe that the proposed scheme adequately reacts to the increase of the input load and its throughput eventually becomes greater than that in the simple forwarding scheme without deflection. On the other hand, the throughput of the conventional deflection routing degrades when the input load increases. Note that these observations coincide with the fundamental characteristics discussed in Section 4.1. We also observe from this figure that the simple forwarding scheme reacts to the increase of the
input load immediately, whereas the proposed scheme suffers from some delay in reacting to it. To see this phenomenon more closely, we define the average load as the average of the number of control packets arriving at each node per unit time. Fig. 30 plots the sample path of the average load, which corresponds to the sample path in Fig. 29. We observe that the average loads in the proposed scheme and the conventional deflection routing increase in a very similar manner, as soon as the input load increases. After that, the average load in the proposed scheme decreases gradually, whereas the average load in the conventional deflection routing remains almost constant. Recall here that we choose one second as a unit time τ and the parameter α in the exponentiallyweighted moving average (3) is set to be 1/8.
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
119
autonomously at each node, and it was shown to be effective when congestion occurred temporarily and/or locally. Note that in many cases, the proposed scheme can be combined with other proposals that enhance the performance of deflection routing. For example, [17,19] independently proposed the use of electrical buffering capability at ingress nodes in OBS networks. Combining this with our proposed scheme, the performance of deflection routing can be further improved. Acknowledgement
Fig. 30. Sample path of the average load.
This research was supported in part by Grant-in-Aid for Scientific Research (C) of the Japan Society for the Promotion of Science under Grant No. 18560377. References
Fig. 31. Transient response to the increase in input load.
Therefore it takes about ten seconds to react to the increase in the input load in this scenario. Apparently, the response time to the increase of the input load can be improved if we set α to be a larger value. Fig. 31 shows sample paths of the throughput for α = 1/4, 1/8, and 1/16. We observe that the response time improves with the increase of α, whereas the proposed scheme becomes sensitive to a slight variation of the input load. This is a well-known tradeoff and we have to arrange a compromise between them, depending on the situation. 5. Conclusion This paper proposed a dynamic burst discarding scheme that controlled deflection routing in OBS networks. The proposed scheme can be operated
[1] F.J. Westphal, M. Jager, H.M. Foisel, A. Gladisch, Evolution of optical networks and management aspects, in: Proc. of the Fourth International Topical Workshop on Contemporary Photonic Technologies, Tokyo, Japan, Jan. 2001, pp. 35–38. [2] R.S. Tucker, W.D. Zjpmg, Photonic packet switching: An overview, IEICE Transactions on Communications E82-B (1999) 254–264. [3] M. Kovacevic, A. Acampora, On wavelength translation in alloptical networks, in: Proc. of INFOCOM, Boston, MA, Apr. 1995, pp. 413–422. [4] M. Yoo, M. Jeong, C. Qiao, A high speed protocol for bursty traffic in optical networks, in: Proc. of SPIE’s All-Optical Communications Systems: Architecture, Control and Network Issues, Dallas, TX, 1997, pp. 79–90. [5] C. Qiao, M. Yoo, Optical burst switching (OBS): A new paradigm for an optical Internet, Journal of High Speed Networks 8 (1999) 69–84. [6] S. Oh, H.H. Hong, M. Kang, A data burst assembly algorithm in optical burst switching networks, ETRI Journal 24 (2002) 311–322. [7] M. Yoo, C. Qiao, Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks, in: Proc. of IEEE/LEOS Technologies for a Global Information Infrastructure, Montreal, Canada, Aug. 1997, pp. 26–27. [8] S. Yao, B. Mukherjee, S. Dixit, A unified study of contentionresolution schemes in optical packet-switched networks, Journal of Lightwave Technology 21 (2003) 672–683. [9] S.L. Danielsen, P.B. Hansen, K.E. Stubkjear, Wavelength conversion in optical packet switching, Journal of Lightwave Technology 16 (1998) 2095–2108. [10] D.K. Hunter, M.C. Chia, I. Andonovic, Buffering in optical packet switches, Journal of Lightwave Technology 16 (1998) 2081–2094. [11] S. Bregni, G. Guerra, A. Pattavina, Optical switching of IP traffic using input buffered architectures, Optical Networks Magazine 3 (2002) 20–29. [12] P. Bayvel, M. Dueser, Optical burst switching: Research and applications, in: Proc. of OFC, Los Angeles, CA, Feb. 2004, pp. 23–27.
120
K. Hirata et al. / Optical Switching and Networking 4 (2007) 106–120
[13] Y. Liu, M.T. Hill, R. Geldenhuys, N. Calabretta, H. de Waardt, G.D. Khoe, H.J.S. Dorren, Demonstration of a variable optical delay for a recirculating buffer by using all-optical signal processing, IEEE Photonics Technology Letters 16 (2004) 1748–1750. [14] J. Fehrer, J. Sauer, L. Ramfelt, Design and implementation of a prototype optical deflection network, in: Proc. of SIGCOMM, London, UK, Aug. 1994, pp. 191–200. [15] F. Borgonovo, L. Fratta, J.A. Bannister, Unslotted deflection routing in all-optical networks, in: Proc. of GLOBECOM, Houston, TX, Nov. 1993, pp. 119–125. [16] F. Borgonovo, L. Fratta, J.A. Bannister, On the design of optical deflection-routing networks, in: Proc. of INFOCOM, Toronto, Canada, Jan. 1994, pp. 120–129. [17] X. Wang, H. Morikawa, T. Aoyama, Burst optical deflection routing protocol for wavelength routing WDM networks,
[18]
[19]
[20]
[21]
in: Proc. of SPIE/IEEE OPTICOMM, Dallas, TX, Oct. 2000, pp. 257–266. S. Floyd, V. Jacobson, Random early detection gateways for congestion avoidance, IEEE/ACM Transactions on Networking 1 (1993) 397–413. S. Lee, K. Sriram, H.S. Kim, J.S. Song, Contention-based limited deflection routing in OBS networks, in: Proc. of GLOBECOM, San Francisco, CA, Dec. 2003, pp. 2633–2637. A. Zalesky, H.L. Vu, Z. Rosberg, E.W.M. Wong, M. Zukerman, Modelling and performance evaluation of optical burst switched networks with deflection routing and wavelength reservation, in: Proc. of INFOCOM, Hong Kong, China, Mar. 2004, pp. 1864–1871. C. Cameron, A. Zalesky, M. Zukerman, Prioritized deflection routing in optical burst switching networks, IEICE Transactions on Communications E88-B (2005) 1861–1867.