Submitted to IASTED International Conference on Communication Systems and Applications, July 19-21, Banff, Alberta, Canada
A Lexicographically Optimized Routing Algorithm for AllOptical Networks Wenhao Lin, Richard S. Wolff Department of Electrical and Computer Engineering, Montana state university, Bozeman, MT 59717 (Phone) 406-9947172 (Email)
[email protected],
[email protected]
Abstract: In this paper, we propose and demonstrate a new adaptive routing algorithm based on lexicographical optimization applicable to all-optical multi-wavelength networks. Such an algorithm appeared in [1] for IP packet routing. But because of its time complexity and the peculiarities of all-optical networks, we can’t apply it directly in all-optical networks. Here we develop a new approach that addresses routing and wavelength assignment (RWA) under conditions where the signal is optical end-to-end, with no wavelength conversion. The algorithm is particularly designed to enable highly dynamic RWA anticipated in burst-mode and customercontrolled networks. We also anticipate the need to constrain end-to-end routing based on other factors including link performance, transient effects in switches and amplifiers, and other physical layer factors.
Keywords: Fiber optics and optical communications; Networks RWA algorithms, Lexicographical optimization. 1.
Introduction
Next generation optical networks will use ondemand resource allocation to increase the overall network performance and meet application requirements for on-demand connections. These multiple wavelength, alloptical networks will use optical switches and optical amplifiers to achieve the overall network performance. On-demand resource allocation may be implemented through wavelength conversion at intermediate nodes in the physical layer of the network. The successful deployment of these next generation optical networks may require a routing and wavelength assignment (RWA) strategy that takes into account wavelength conversion at these intermediate nodes along with constraints due to the
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performance of the physical layer. It is equally feasible to envision all-optical networks where there is no wavelength conversion, thereby eliminating the need for costly wavelength converters, but at the same time adding further constraints and complexity to RWA. RWA strategies for networks with and without wavelength conversion at intermediate nodes have been studied and presented in the literature. Extensive work has been done in network topologies where wavelength conversion is possible at intermediate nodes, thereby alleviating the wavelength continuity constraint [2]. The extension of MPLS to include optical routing (e.g., GMPLS) takes into account certain attributes associated with optical networks [3-5], and a technique to take these factors into account in routing has been proposed as a modification to SPF algorithms [6]. However, the light path characteristics explicitly identified in the GMPLS framework are logical and ideal: interface switch capability, interface bandwidth, link protection type, traffic engineering metric, hop count limit, priority and preemption, etc. There is currently no inclusion of optical layer behavior and performance factors such as number of wavelengths on a fiber, signal power levels, noise levels, end-to-end bit error rate, etc. in GMPLS, although there is considerable discussion in the IETF to consider these factors. These factors could be constraints in selecting optical paths and should be considered in RWA. Our own research on all-optical network routing has led to the development of new algorithms for RWA. We have been addressing the problem where a single wavelength must be used end-to-end (e.g., no wavelength conversion is possible) and designed an algorithm that is particularly well-suited to enable highly-dynamic RWA anticipated in burst-mode and customercontrolled all-optical networks. In a transparent, all-optical network, an end-to-end path and wavelength needs to be chosen for each
Submitted to IASTED International Conference on Communication Systems and Applications, July 19-21, Banff, Alberta, Canada connection request that minimizes connection request blocking probability and maximizes resource utilization. The solution is state dependent, meaning that that the current traffic load (e.g., assignment of traffic to wavelengths and links) affects the optimum RWA for a particular connection request. For a large network, a common way to solve the RWA problem is to separate it into two sub-problems, first finding a path from the source to destination, and then assigning a wavelength that is free on each fiber link of the computed path. In this paper, we assume that a single wavelength is used end-to-end (e.g., there is no wavelength conversion) and that each photonic switch or routing node only knows how many wavelengths are used on each connecting link. Switches will broadcast such usage information periodically. With the development of DWDM, it is possible that there are hundreds of wavelengths on each fiber. So, in large network photonic switches will not broadcast the state of each wavelength. Optical routing algorithms can be classified into two categories: static routing and adaptive routing. Static routing algorithms include Fixed routing [7], Fixed-Alternative routing [7]. Several possible paths for all possible (source, destination) pairs are pre-computed. Adaptive routing algorithms usually use Dijkstra Algorithm to compute a minimal cost path from source to destination. Link cost function is critical for such algorithms. In [8], the cost of a link l is defined as 1/F l , where F l is the number of free wavelengths on a link. In [9], the link cost of a link l is defined as exp(1/ F l ). In [10], the authors proposed a lexicographically optimized routing algorithm for a WDM network. Their algorithm uses a heuristic iterative method that tries to precompute optimal paths for all pairs of nodes assuming the demand matrix is known in advance. In this paper, we proposed a new adaptive routing algorithm inspired by the lexicographical optimization idea. We are mainly concerned how to compute a path based on current network state to decrease system connection request blocking probability. After path computation, reservation signaling procedures are executed to establish a connection. we use the Backward Reservation technique [11], in which we use First-fit wavelength selection [7], to create a connection from the
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source to destination node if a free wavelength exists along the computed path. We are mainly concerned with how to compute a path based on the current network state that decreases system connection request blocking probability. 2.
Proposed algorithm
2.1 Notation definitions Given an n dimension vector x, Φ(x) is defined as a non-increasing sorting of x’s coordinates, i.e., Φ(x) = 〈 x i1 , x i 2 , x i 3 , K , x in 〉 , such that x i1 ≥ x i 2 ≥ x i 3 ≥ K ≥ x in
Given two vectors x and y, x is lexicographically smaller than y, iff Φ(x) ≤ Φ(y), i.e., x i1 = y i1 , K , x i ( k −1) = y i ( k −1) , but x ik < y ik . = number of used The usage of a link Ul wavelength on link l. The availability of a link Fl = number of free wavelengths on link l. The congestion of a link Cl = 1/ Fl. Erlang is defined as (average connection duration time)/(average connection request interarrival time), where a connection uses a wavelength.
2.2 Lexicographical Optimization Routing Algorithm (LORA) In [1] a lexicographic routing algorithm is proposed for distributing the IP traffic load among all links to avoid the bottleneck problem of OSPF routing. However, its time complexity is exponential in network size for a general link cost function. Additionally, for a connection request, its solution usually consists of several paths, so the traffic from source to destination will split. This is not applicable to wavelength routing in an all-optical network. Following the lexicographical optimization approach, we define our optimization objective function as follows: Given the current network state, for each computed path from source to destination node, we create a vectorν i , called a usage vector in this paper, whose elements are the wavelength usage of each link along the path. We then find an optimal path such that its corresponding usage vector is the lexicographical minimum among all the possible paths.
Submitted to IASTED International Conference on Communication Systems and Applications, July 19-21, Banff, Alberta, Canada As in [1], by using this optimization objective function, we distribute the traffic load among all links. By the definition of lexicographical comparison, the lexicographically optimized routing algorithm should find a path first by using the least used links, then the intermediately used links and at last the most used links. In other words, links with different usage values have different powers. A natural way to express this idea is to
Theorem 1: For a given network with n nodes, if β > n-1, then LORA will return the lexicographically minimal path. Proof: Let’s assume the minimal cost path returned by LORA is P1. It has i k links with
set the link cost function as β l , and β ≥ 1 is a parameter we want to change dynamically. We illustrate the lexicographic approach in the following example. Consider a source S and destination D, which could be connected by two paths: P1=S-A-B-C-D and P2=S-E-F-G-H-D, as indicated in figure 1. The numbers associated with each link in each path indicate the number of wavelengths in use on the link. We then form ordered vectors for P1 and P2 corresponding to the number of wavelengths in use on each link, ordered with the highest number first: P1= P2= By the lexicographic approach, we choose P2 as the preferred route, because the highest link usage (4) on P1 exceeds the highest link usage on P2 (3). The preferred route is P2 despite the fact that P2 is longer than P1, in terms of hops.
0. Notice that i k ≥ j k and P2 can’t have links
u
usage k, …, i 0 links with usage 0. Let’s also assume the lexicographically minimal path P2 has j k links with usage k, …, j 0 links with usage with usage more than k. Also notice that ∑ 0 ii is k
the length of path P1 and ∑ 0 ji is the length of k
path P2. We claim i k = j k . Else we have i k > j k , then, k
Cost(P1)- Cost(P2) = = (i k - j k )*
≥β k
∑j
i =0 k −1
+
∑ (i i =0
k −1 i =0
β
βk
∑i i
*β i
i
k
∑j i =0
i
*βi
− ji ) * β i k −1
* β ≥ β - ( ∑ ji ) β k −1 ≥ i
i
k
i =0
- (n-1) β > 0. But this contradicts our assumption that P1 is the minimal cost path. So i k = j k . By using the k
k −1
same method, we can prove i k −1 = j k −1 ,…, i 0 = j0. ■
Figure 1. Two paths between S and D with different wavelength utilization The following pseudo-code describes the algorithm (LORA) Function LORA (State, S, D) Input: State, current network state; S, source node; D, destination node. Output: A path from S to D. {Decide the value of parameter β according to current network traffic load. Set cost of each link as β l . Return the minimal cost path by calling the Dijkstra algorithm. } u
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Theorem 1 clarifies our intuition that by using large β , we can search for a less congested path in a larger area than when a smaller β is used. We notice that with LORA there are two extreme situations, when β > n-1 the algorithm finds a lexicographically minimal path globally, when β =1 this algorithm degrades to the Shortest Path. In an all-optical network, distributing the traffic load among links is not our only consideration. We also need to allocate wavelengths efficiently. LORA usually returns a path longer than the shortest path. But a longer path will use more network resources. We can dynamically change β to control the lengths of paths returned by LORA using an off-line method. For a given network topology, we obtain the optimal β values under several traffic
Submitted to IASTED International Conference on Communication Systems and Applications, July 19-21, Banff, Alberta, Canada loads by simulation using the Hill-Climbing algorithm. By interpolation, we obtain a curve for optimal β under different traffic loads. Such a curve can be stored in photonic switches. When a connection request arrives, an edge photonic switch will first compute the optimal β value for the current network traffic load, which can be obtained from historic data or by information broadcast by all edge photonic switches. We can also change the optimal β traffic load curve to optimal β - network mean link congestion level curve, which is defined as ∑ l C l / (number of links in network). 3.
Numerical results
We use the NSF network, which has 16 nodes, as our experiment network topology, as shown in Figure 2. We assume that each link has 10 wavelengths. We use the Backward Reservation method [11] and First-fit wavelength allocation [7] for the reservation procedure in the simulations. Edge switchers use Source Routing. No wavelength conversion is assumed in this network Figure 3 shows the optimal β values we obtained under different traffic loads for the NSF network.
Figure 2
NSF network
optimal beta
1.5 1.38
beta 1.25 1.13 1 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115
load erlang
Figure 3 Optimal β - traffic load with hill climbing step resolution 0.1
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Figure 4 Performance comparison. X axis is traffic load, in erlangs, and Y axis is blocking probability. Figure 3 shows that when the traffic load is low (below 30 erlangs), the optimal β value is 1. Of course, under such light load conditions, we can also use a larger β value to achieve low blocking probability. As we increase the traffic, we find that 1.3 is a good value for β . When the traffic load is above 105 erlangs, we find that using a large value of β doesn’t help decrease blocking probability. Based on these simulation results, we use the following rule for selecting the optimal value for β , which is a piecewise linear function. When the traffic load is less than 105 erlangs, β =1.3. When the traffic load is greater than 105 erlangs, β = 1.1. We compare the performance of LORA with three other algorithms: Shortest Path, minimal cost path with cost (l) = Cl (named Least Congested (LC) in this paper), and minimal cost path with cost (l) = exp(Cl) (named Enhanced Least Congested (ELC) in this paper. Figure 4 shows the results of the comparison. Our simulation experiments show that LORA works well compared to other algorithms. The blocking probability achieved with LORA is at least as low or lower at all network traffic loads than with any of the other RWA algorithms tested. The results obtained with LORA are significantly better than those obtained with least cost (LC) methods, with at least a 25% reduction in blocking probability. This work forms a foundation for our research designing RWA algorithms under additional constraints such as link performance, transient effects in switches and amplifiers, and other physical layer factors.
Submitted to IASTED International Conference on Communication Systems and Applications, July 19-21, Banff, Alberta, Canada 4. Conclusion and future work In this paper we proposed a new adaptive routing algorithm for all-optical network. It is simple to implement. By simulation, we can obtain an optimal β value curve for a given network topology. Such a curve would be stored in the network nodes, which consist of photonic switches. Switches can dynamically change the parameter β based on the current network load when computing an end-to-end wavelength path. Our experiments show that LORA works well compared to other algorithms. Our future work will include designing RWA algorithms under additional constraints such as link performance, transient effects in switches and amplifiers, and other physical layer factors. Note that LORA does not provide a means of selecting the best wavelength to assign among the available wavelengths on the selected path. Our current research is examining approaches to wavelength selection that minimize blocking probability while at the same time taking other constraints into consideration. In such new algorithms, Algorithm LORA will be a useful subroutine.
References [1] L. Georgiadis, P. Georgatsos, S. Sartzetakis, K. Floros, “Lexicographically Optimal Balanced Networks”, IEEE Infocom 2001, (April 2001). [2] E. Karasan and E. Ayanoglu, “Effects of Wavelength Routing and Selection Algorithms on Wavelength Conversion Gain in WDM Optical Networks”, IEEE/ACM Transactions on Networking, Vol. 6, No. 2, pp. 186-196, (April, 2002) [3] IETF RFC 3471,“Generalized Multi-Protocol Label Switching (GMPLS)Signaling Functional Description”, (January, 2003). [4] IETF RFC 3472,“Generalized Multi-Protocol Label Switching (GMPLS )Signaling Constraintbased Routing Protocol Extensions (CR-LDP)”, (January, 2003). [5] E. Oki, et. al., “Dynamic Multilayer Routing Schemes in GMPLS-Based IP+Optical Networks”, IEEE Communications Magazine, January 2005, pp. 108-113. [6]B. Gao, Y. Yang, C. Chen, “Implementing A Constraint-based Shortest Path First Algorithm
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in Intelligent Optical Networks”, Mahi Networks White Paper, (May 2003). [7] Hui Zang, Jason P. Jue, Biswanath Mukheriee, “A review of Routing and Wavelength Assignment Approaches for Wavelength-Routed Optical WDM networks”., Optical Networks Magazine, vol. 1, no. 1, (January 2000). [8] Arjan Durresi et.al., “Quality Based Optical Routing Protocols”, Proceedings of Optical Transmission System and Eqipment for WDM Networking II, SPIE vol. 4247, pp. 410-420, (September 2003) [9] Yan Zhang, “Virtual Circuit Routing”, Class Report, (October 2003). [10] Stelios Sartzetakis, Chrysostomos I.Tziouvaras and Leonidas Georgiadis, “Adaptive Routing Algorithm for Lambda Switching Networks”, SPIE OPTICAL NETWORKS Magazine (July/August 2002) [11] Feifei Fang, Xiaoping Zheng, Hanyi Zhang, “Performance Study of Distributed Wavelength Reservation Protocols within both Single and Multi-Fiber WDM Networks”, Photonic Network Communications, vol. 6, no. 2, (September 2003).
