New QoS Measures for Routing and Wavelength Assignment in WDM Networks

Transcription

1 New QoS Measures for Routing and Wavelength Assignment in WDM Networks Shi Zhong Xu and Kwan L. Yeung Department of Electrical & Electronic Engineering The University of Hong Kong Pokfulam, Hong Kong Abstract-A new class of quality of service (QoS) measures, EB(p), p 1 for WDM optical transport networks is proposed in this paper. Compared with the traditional overall average blocking probability (OABP), EB(p) is a composite measure that is unbiased, makes reference to the QOS requirements, onesided, and takes the potential revenue loss into consideration. In particular, EB(1) can be identified as (revenue) weighted average excessive blocking, and EB() as mean square (revenue) weighted excessive blocking. The effectiveness of this new composite measure is compared with OABP based on several existing routing and wavelength assignment algorithms. I. INTRODUCTION With the rapid growth of IP and multimedia services, the bandwidth requirement in the wide area networks is increasing dramatically. The huge potential capacity of one single fiber, which is in Tb/s range, can be exploited by applying WDM technology which transfers multiple data streams on multiple wavelengths simultaneously. More and more WDM lines are deployed around the world. To solve the electronic-bottleneck problem, WDM optical transport networks (OTN) that deploy wavelength routing in the nodes are considered as the backbone networks for the near future. Due to the limitation of optical components, optical packet switching is not a mature technology yet. Lots of works on research and test-beds [1] are pushing WDM OTN into reality. In WDM OTN, the nodes should add/drop wavelengths and/or cross-connect wavelengths in a way similar to traditional circuit switching. In a circuit switch network, a call will be blocked if there is no resource to carry the call to its destination. This is known as capacity blocking. In a WDM network, in addition to capacity blocking, a call may be blocked as a result of wavelength blocking. In order to carry a call in all-optical domain throughout the network, the same wavelength (channel) should be used at each hop along the path from the source to destination. (This is known as the wavelength continuity constraint.) If a call is rejected as a result of no common wavelength along the path (although the network capacity is available), it is said that a wavelength blocking occurs. The most intuitive QoS measure for WDM OTN is thus the overall average call blocking probability (OABP) [1]. To minimize the overall average call blocking probability, many routing and wavelength assignment (RWA) algorithms have been proposed for finding a suitable routewavelength pair to accommodate each new call [-8]. Due to both wavelength and capacity blocking, it can be shown that the longer the distance between a sourcedestination (SD) pair, the higher the blocking probability it suffers from. But according to the OABP measure, there is no difference in blocking a call with long SD distance and a call with short SD distance. Some papers studied this issue by obtaining the average blocking probabilities of SD pairs with different distances [3,4]. In particular, the results in [5] imply that the blocking probability alone is not a fair and sufficient performance measure. From service providers perspective, long distance calls are not equivalent to short distance calls. In general, tariff is proportional to the resources taken up by a call, e.g. the distance of a call. The loss of revenue associated with blocking a long call could be much bigger than blocking a short call. Here is a simple example. Suppose that the revenue for an accepted long call is 1 units and that for an accepted short call is 1 unit (assume the call duration is the same). Consider two routing and wavelength assignment (RWA) algorithms, A and B, where A results in rejecting 1 long calls and B results in rejecting 1 short calls. The overall average blocking probabilities are the same for both algorithms. But it is incorrect to say that these two algorithms give the same performance because the revenue loss using A is 1 units, which is 1 times of using B. It is obvious that a service provider would prefer algorithm B. However, the situation becomes more complicated if algorithm A gives a lower OABP than B, but algorithm B gives a higher revenue than A. If we take all those factors into account, the question of which algorithm is better becomes very difficult to answer. For service providers, it is a common practice that some performance commitments (or, service level agreements) will be provided to their customers. For example, a telephone company may offer a QoS guarantee of no more than.1 call blocking probability to their subscribers, whereas a cellular mobile phone operator may provide a similar guarantee of. blocking probability. Then the major goal for a service provider is to engineer their network such that all performance commitments are met. On the other hand, over-engineering a network to provide a performance better than their commitments is in general not desirable 1. In this paper, starting with a detail examining of the ineffectiveness of the traditional performance measure, overall average blocking probability (OABP), four criteria for a good QoS measure are proposed. Then a new class of composite performance measures EB(p), p 1, is designed 1 Consider a cellular phone network. There is no need to provide a call blocking probability less than, e.g..1. This is because a call dropping as a result of, e.g. signal fading, could be easily larger than //$17. IEEE 891

2 with the four criteria in mind. When p =, we focus our investigation on EB(), which can be interpreted as the root mean square weighted excessive blocking, and demonstrate its effectiveness by comparing with OABP on the relative merits of several well-known RWA algorithms. II. NEW QOS MEASURE A. Example 1 Fig. 1 shows a 5 5 mesh-torus network, with 5 nodes and 5 links. Each link consists of a pair of unidirectional fibers and each fiber consists of 8 wavelengths. Assume call arrival follows a Poisson process and the arrival rates for all node pairs are the same. Let the mean call holding time be exponentially distributed. When a call arrives, random wavelength assignment scheme is used to select an available wavelength along the fixed route obtained using the X-Y routing strategy [8]. If no free wavelength can be found, the call is blocked. This RWA algorithm is known as the fixed routing with random wavelength assignment. Fig. 1. A 5 5 Mesh-Torus network. Due to the regular network topology and homogeneous traffic assumption, the blocking probabilities for different Source-Destination (SD) pairs with the same hop distance will be the same. Fig. depicts the simulation results under different network loads. Let B=.1 be the QoS requirement on blocking for all node pairs. From Fig., we can see that the overall average blocking probability (OABP) is less than.1 when the offered load is less than 77 Erlangs. But for node pairs with different hop distances, their blocking rates are different even under the same offered load. For example, when load is 75 Erlangs, OABP =.81. The blocking probabilities for 1- hop, -hop, 3-hop and 4-hop SD pairs are BP1 =.6, BP =.3, BP3 =.96 and BP4 =.5 respectively. (Note that the shortest distance between two furthest away nodes in Fig. 1 is 4-hop.) We can see that the blocking probability for 4-hop SD pairs BP4 is much higher than BP1. BP4 could be kept under.1 only when the load is less than 6 Erlangs. But at this loading, the blocking probabilities for 1-hop and -hop SD pairs are both less than.1 (this may not be seen directly from the figure), which are unnecessarily lower than the QOS requirement. Similarly, for 3-hop, -hop and 1-hop SD pairs to have a blocking less than.1, the corresponding maximum loads are 76, 1 and 195 Erlangs. This service deviation among node pairs with different hop distances is hidden by the overall average blocking probability. Aiming at providing QoS guarantee for node pairs with different hop distances, the overall average blocking probability is therefore not a good performance measure. Blocking Probability.9.8 OABP BP1.7 BP BP3.6.5 BP Fig.. OABP and blocking probabilities for different node pairs. Besides, it is obvious that the link resource occupied by an accepted 4-hop call is 4 times of that occupied by a 1-hop call. Since both long-distance and short-distance calls are treated the same by overall average blocking probability, it cannot correctly reflect the amount of resources consumed by a call. B. Example Now we construct another example to show the service variation in blocking probability under different traffic patterns, while the total offered load is fixed. Consider an 8- node (p, k) ShuffleNet [9] (where p=, k=) with one fiber per link and eight wavelengths per fiber as shown in Fig. 3. (Note that the links in a ShuffleNet is unidirectional.) The following assumptions are adopted in our simulations: The offered loads to node pairs with the same shortest distance are the same. The RWA algorithm adopted is again fixed shortest path routing with random wavelength assignment. Like Example 1, the blocking probabilities for node pairs with the same (minimum) hop distance will be the same. Varying the total offered network load from 1 to Erlangs, Table I summarizes the overall average call blocking probability (OABP), the blocking probabilities for 1-hop (BP1), -hop (BP) and 3-hop (BP3) node pairs, under 4 different traffic patterns. A traffic pattern is defined by a tuple (a:b:c), where a, b and c are the relative weights for call arrival rates at a 1-hop, -hop and 3-hop node pair. As an example, consider node in Fig. 3. Let the total traffic load at node be λ. Since node has nodes 1-hop away from it, 3 nodes -hop away and In a ShuffleNet, there is always a unique shortest path from one node to another. The shortest distance between any two nodes that are furthest away in a ShuffleNet is k-1 hops. For the ShuffleNet in Fig., the maximum hop distance is thus 3. 89

3 nodes 3-hop away, with traffic pattern (1:1:1), the amount of loads from node to nodes 1 to 7 are the same and equals to λ/7 each. Thus pattern (1:1:1) corresponds to the uniform traffic pattern Fig. 3. A (,) ShuffleNet. From Table I, we can see that with the same total offered network load (i.e. a row in Table I), the blocking performance with respect to OABP, BP1, BP and BP3, varies under different traffic patterns. It can be seen that OABP increases as the weight for long distance calls increases. But this trend cannot be observed in BP1, BP and BP3. It is also interesting to note that the values of BP3 under traffic patterns (8:1:1) and (1:1:8) are quite similar. Table II summarizes the results when OABP=.1 for all four traffic patterns. We can see that 14., and 1.4 Erlangs of traffic can be carried under (1:1:1), (8:1:1), (1:8:1) and (1:1:8) patterns, respectively. One may conclude that the RWA algorithm performs the best under uniform traffic pattern as the traffic carrying capacity is the largest for a given OABP value. For a service provider, the revenue generated by the accepted calls is probably more important. Let the revenue generated by a k-hop call be kc, while assuming all calls with same mean call holding time. Then the total revenue generated under (1:1:1) uniform traffic pattern is 14./( )[16 1 (1-.1)C+4 1 (1-.61)C+16 1 (1-.5)3C]=8.C. Similarly, the revenues generated under (8:1:1), (1:8:1) and (1:1:8) patterns are found to be 18.41C, 4.63C and 3.55C. Therefore, in terms of the revenue, this RWA algorithm gives the best performance under pattern (1:1:8). Then overall speaking, we have a hard time to decide under which one of the four traffic situations, this algorithm gives the best overall performance. We need a new composite measure. C. Requirements for a new QoS measure From the two examples above, we can see that the overall average call blocking probability (OABP) alone is not a good performance measure. It hides the information of service deviation among node pairs, and it does not consider the revenue generated by different types of calls. As a result, it is difficult to judge based purely on OABP that which RWA algorithm is better, and under what kind of traffic condition is better. If a RWA algorithm is biased against calls with long distance either inherently or on purpose, it can usually give a 1 3 lower OABP. A trivial example is that when the call arrival rate to a network is sufficiently high (such that there are sufficient calls with 1-hop distance), one can construct a (non-work-conserving) RWA algorithm that rejects all calls with hop distance larger than 1. Then this trivial RWA algorithm is very likely to yield the lowest OABP as compared with any existing algorithms. However, it is obvious that such an algorithm is by no means a good one. We envision that a good QoS performance measure for RWA algorithms should satisfy the following four criteria: 1. Unbiased. What we mean by an unbiased measure is that the measure should reflect the QoS as seen by a randomly picked call in the system. As different sourcedestination (SD) pairs have different traffic rates, a SD pair with a higher traffic rate should therefore be weighted heavier in the measure. (In fact, OABP does meet this criterion. Please refer to Eqn. (1).). Make reference to the individual requirements of SD pairs. The QoS requirement is that the blocking probability of a SD pair should be smaller than B. Therefore an acceptable QoS measure must make reference to B. Note that the B for different pairs are not necessarily the same. 3. One-sided. Blocking probabilities of individual node pairs often deviate from their associated B. The penalty should be only on those that deviate above B. Note that those that deviate above B are the excess blockings and should be minimized, whereas those deviate below B should not be reckoned in the penalty function. 4. Take the potential revenue into consideration. For service providers, the revenue generated by a call is usually proportional to the call distance. Rejecting a long distance call is thus less desirable than rejecting a short one. Therefore, the penalty for rejecting a long distance call should be heavier. D. New Performance measure Let N be the number of source-destination pairs with different QoS requirements B, λ be the arrival rate for node pair, and B be the associated call blocking probability. Further let Λ = Σ λ. The conventional used overall average blocking probability (OABP) is given by 1 B = Λ λ (1) B With the four criteria of a good performance measure in mind, EB(p) a new class of composite performance measures is designed as follows, 1 1/ ( ) = [ ( ) ], 1,,... { p p EB p B B Lλ Λ p = () i, j} I where I is the set of node pairs with blocking probabilities exceeding their QoS requirements B ; L can be viewed as a punishing factor for node pair. L is proportional to the shortest distance between nodes i and j. One can treat it as the 893

4 tariff of using the wavelengths along the shortest path between the two nodes. The value of L should be independent of the actual path that a call is carried. Just like in a telephone network, an admitted call may be routed to a path other than the shortest one, e.g., as a result of using dynamic RWA algorithms [8]. Since routing is the responsibility of the network, the tariff should be set while only making reference to the shortest path. If an operator wants to ignore the difference between long and short calls, they can set L to 1 for all. When p=1, EB(1) can be considered as the (revenue) weighted average excessive blocking. It is based on the assumption that the customer unsatisfaction increases linearly with the excessive blocking. However, the degree of customer unsatisfaction usually increases faster than the blocking rates. (If their patience is used up, the customers might simply switch to another service provider.) EB(p) with p larger than 1 can reflect this trend. As we increase p, we are penalizing more and more on larger deviations of B over B. When p=, EB() can be considered as the mean square (revenue) weighted excessive blocking. In the limit p, only the maximum deviation term, i.e. the worst case, is penalized. The exact choice of p would depend on applications and can be decided by the network operators. Overall speaking, EB(p) is a composite performance measure. It considers not just excessive blocking, but also the potential revenue loss and the level of customer satisfaction. If there is no excessive blocking, set I will be empty and EB(p) will be zero, independent of the actual (negligible) amount of blocking for each source-destination pair. This helps to prevent the network from over-engineering. For example, in Fig., if the QoS requirements for all SD pairs are.1, when the offered load is 6 Erlangs, the blocking probabilities for all node pairs are less than.1. Thus EB(p)=. III. CASE STUDIES In this section, we use the new composite performance measure EB(p) to evaluate the effectiveness of five RWA algorithms, Least-Loaded Routing () [6], Fixed Path Least Congestion routing () [7], new Fixed Path Least Congestion routing (N) [7], Fixed Routing with Random Wavelength assignment (FR_RAND) [8], and SPREAD routing based on Layered Graph () Routing [1]. The first three algorithms are dynamic alternate routing strategies. Two alternate routes are prepared for each sourcedestination (SD) pair. When a call arrives, both routes will be checked for an available wavelength. A call will be blocked if and only if no wavelength is available on both routes. In FR_RAND, only one route is prepared for each SD pair, and one of available wavelengths will be randomly chosen when a new call arrives. In, route and wavelength are jointly chosen to achieve least impact on the rest of the network. Note that in multifiber networks, the channels associated with one wavelength will be equal to the number of fibers per link. EB( ) EB() OABP FR_RAND N Fig. 4. OABP using different algorithms N Fig. 5. EB() performance using different algorithms FR_RAND N Fig. 6. EB( ) performance of three routing algorithms ARPA backbone network is used in our simulation. Here we consider a multifiber scenario where each link has 4 pairs of fibers (4 for each direction) and each fiber contains 16 wavelengths. For simplicity, we assume The QoS requirements on blocking for all node pairs are the same and B =.1 L is set to the minimum hop distance from node i to j. Fig 4 shows the overall average blocking probability (OABP) versus the total offered load under a homogeneous 894

5 traffic condition, where call arrival rates to all nodes are the same and the destination of a call is uniformly distributed. We can see that N algorithm achieves the lowest OABP and performs better than the rest algorithms. Fig. 5 shows the performance using the new measure EB(). The EB() of FR_RAND is ranged from.16 to.34, which is not depicted in Fig. 5. We can still see that both and N perform better than others. But when the total offered network load is between 71 to 88 Erlangs, becomes better than N. This change cannot be observed when OABP is used. We can find that EB()= for both and N algorithms when the total load is less than or equal to 75 Erlangs (not shown in the figure). That means the requirements of all SD pairs are satisfied. The similar turning points for, and FR are 685, 715 and 45 Erlangs respectively. From (), we can get the definition of EB( ) as follows,, if B < B for allsd pair i-j EB( ) = (3) Max( B B ), otherwise The performance of the five algorithms using EB( ) is shown in Fig. 6. In this case, only the maximum deviation from the targeted QoS requirement is penalized. IV. CONCLUDSIONS In this paper, we have argued that the conventional overall average blocking probability (OABP) alone is not a good performance measure for WDM optical transport networks. Then a new class of composite measures EB(p) was proposed. Compared with OABP, EB(p) is unbiased, makes reference to the QOS requirements, one-sided, and takes the potential revenue loss into consideration. The effectiveness of this new measure was then compared with OABP based on several routing and wavelength assignment algorithms. REFERENCES [1] Special issue on protocols and architectures for next generation optical WDM networks, IEEE JSAC Oct.. [] H. Zang, J. P. Jue and B. Muhkerjee, A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks, Optical Networks Magn., Vol. 1,, no. 1, Jan.. [3] H. Harai, M. Murata and H. Miyahara, Performance of alternate routing methods in all-optical switching networks, INFOCOM97, pp: [4] A. Birman and A. Kershenbaum, Routing and wavelength assignment methods in single-hop all-optical networks with blocking, INFOCOM95, pp: [5] K.C. Lee and V.O.K. Li, A wavelength-convertible optical network, IEEE/OSA Journ. of Lightwave Tech., Vol.11, May 1993, pp [6] E. Karasan and E. Ayanoglu, Effects of wavelength of routing and selection algorithm in wavelength conversion gain in WDM networks, IEEE/ACM Trans. Networking, Vol.6., No., 1998 [7] L Li and A. K. Somani, S. Acampora, Performance analysis of fixed-path least-congestion routing in mulitfiber WDM networks, Proc. SPIE All Optical Networking [8] M. Kovacevic and A. Acampora, On wavelength translation in all-optical networks, INFOCOM95, pp: [9] S. Acampora, A Multichannel multihop local lightwave networks, GLOBECOM87, pp: [1] S. Xu, L. Li and S. Wang, Dynamic Routing and Assignment of Wavelength Algorithms in Multifiber WDM Networks, IEEE JSAC, Vol. 18, No.1, TABLE I OABP and BP for S-D pairs with different hop distance under different traffic patterns Load UNIFORM (1:1:1) NONUNIFORM (8:1:1) NONUNIFORM (1:8:1) NONUNIFORM (1:1:8) Erlang OABP BP1 BP BP3 OABP BP1 BP BP3 OABP BP1 BP BP3 OABP BP1 BP BP TABLE II BP for S-D pairs with different hop distance when OABP=.1, under different traffic pattern UNIFORM NON-UNI (8:1:1) NON-UNI(1 :8 :1) NON-UNI(1 :1 :8).156 Load OABP BP1 BP BP3 Load OABP BP1 BP BP3 Load OABP BP1 BP BP3 Load OABP BP1 BP BP