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Multicasting with Physical-Layer Constraints in Metropolitan Area Networks G. Ellinas1, T. Panayiotou1, N. Antoniades2, A. Hadjiantonis3, and A. M. Levine2 1 University of Cyprus, Nicosia 1678, Cyprus 2 College of Staten Island, The City University of New York, New York, USA 3 University of Nicosia and SignalGeneriX, Nicosia, Cyprus Tel: (357)22892273, Fax: (357)22892260, e-mail:
[email protected] ABSTRACT This paper investigates the problem of designing, engineering and evaluating metropolitan area transparent optical networks for the provisioning of multicast sessions. Apart from finding the minimum cost tree, our proposed technique utilizes a metric on the physical performance of the system, namely the Q-factor of the system, by calculating Q-penalties for impairments via a Q-budgeting approach, to investigate whether a multicast connection should be admitted to the network. It uses “tree balancing techniques” for the multicast sessions aiming at maximizing the multicast connections that can be admitted to the network. Keywords: optical networks, multicasting, metropolitan area networks. 1. INTRODUCTION Bandwidth-intensive applications and rich multimedia and real-time services are becoming very popular in today’s networks (e.g., video-conferencing, interactive online computer games, etc.). Next generation networks must have the capability and build-in intelligence to support all types of traffic (unicast, multicast, groupcast) and all kinds of applications. Multicasting has been investigated in the research community since the early days of optical networking [1, 2], but has only recently received considerable attention from the service providers, mainly because now many applications exist that can utilize the multicasting feature. Wavelength-routed networks are now widely deployed in order to accommodate the bandwidth requirements of next-generation networks and they provide the flexibility to serve multicast or groupcast connections. In these networks, optical splitters can be used to split the incoming signal to multiple output ports thus enabling a source node to establish connections with multiple destinations. In this case a light-tree is created to serve the multicast request. A light-tree is a set of lightpaths from the source to all destination nodes and there exist several heuristics on finding these lighttrees [1, 2]. 2. MODELING THE PHYSICAL IMPAIRMENTS In a fiber-optic communications system we are mostly concerned with the Bit Error Rate (BER) of the system. However, as the BER is a difficult parameter to evaluate, we can derive the required system Q factor for a target BER using Eq. (1) [3]: −Q
1 ⎛ Q ⎞ e2 BER = erfc ⎜ ⎟≈ 2 ⎝ 2 ⎠ Q 2π
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I1− I 0 σ 1+σ 0
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σ i2 = σ th2 +σ 2shot −i + σ 2ASE − ASE + σ 2s − ASE −i + σ 2RIN −i + σ 2ASE − shot
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The above assumes a baseline system with various receiver noise terms as well as Amplified Spontaneous Emission (ASE) noise from the optical amplifiers. To include other common physical layer impairments such as crosstalk, fiber nonlinearities, distortion due to optical filter concatenation and dispersion/chirp among others, a simple Q-budgeting approach is used as described in [3]. We start from the Q value for the baseline system and budget Q-penalties for the various physical layer impairments present. The Q penalty (QdB) associated with each physical layer impairment in a system is commonly expressed in dB and in this work we use the following definition: QdB = 10log (Qlinear). The Q penalty is calculated as the QdB without the impairment in place minus the QdB with the impairment present. This approach enables a network designer to calculate the impact of physical layer effects, such as non-linear effects, polarization effects, optical crosstalk, etc, in the design of an optical network.
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The modeling based on the Q performance of the connection is used during the provisioning phase to decide whether a multicast connection will be admitted in the network or rejected [4]. In an optical network there are effects that are inter-depended to the number of channels present at each instance in the system (optical crosstalk cross-phase modulation, four wave mixing are some examples) and there are others that only depend on the one channel under investigation. Our modelling allows for both cases since for the latter case the Q constraint is applied for new calls only, with the above calculation done for these new calls. For the former case, the Q calculation will be performed for the new call and each affected existing connection (call). To conclude, if any of these tests fail, meaning the Q for any path on the calculated tree is below a pre-determined threshold, then the new call will be blocked. In our case, a Q threshold of 8.5 dB is assumed which corresponds to a BER of 10-12. 3. MULTICASTING WITH PHYSICAL IMPAIRMENTS Constructing a cost-effective light-tree (also known as the Steiner-tree problem) along with the wavelength assignment problem for these light-trees is proven to be an NP-complete problem [1]. Several ILP formulations have been proposed for designing optimum light-trees [5]-[6] and several heuristics have been proposed for solving the multicast routing and wavelength assignment (MC-RWA) problem [7]-[8]. However, algorithms that find the minimum cost multicast tree and assign an available wavelength are not enough to guarantee the viability of the multicast session, as it may violate the physical layer constraints. This paper improves on the MC-RWA algorithms by also including physical layer constraints utilizing the Q factor discussed in section 2. 3.1 Algorithms This paper extends the results presented in [9] on light-tree routing with power-budget constraints. The work presented in [9] is based on the balanced light-tree (BLT) approach where the balanced light-tree algorithm takes as input an initial tree T spanning the source s and the destination nodes in the multicast group. The key part of the BLT algorithm is the tree balancing procedure. Consider a light-tree T, and let u (respectively, v) denote the leaf node with maximum (respectively, minimum) split ratio. The idea behind the BLT algorithm is to delete the node with the maximum split ratio (node u) from T, and add it back to the tree by connecting it to the node with the minimum split ratio (node v) in the path from source s to node v. By doing so, it reduces the split ratio of node u, but it also increases the split ratio of all nodes below node v in the tree. Therefore, this pair of delete/add operations is performed only if it does not increase the split ratio of any node beyond that of node u. Thus, after each iteration of the algorithm, the split ratio of the node with the maximum value is decreased. While the split ratio of some other node(s) is increased, it does not increase beyond the previous maximum value. As a result, the difference between the maximum and minimum split ratio values also decreases with each iteration. The algorithm terminates after a certain number of iterations. If more than one nodes with the same maximum and minimum split ratio exist, we let U denote the set of nodes with the maximum split ratio and V denote the set of nodes with the minimum split ratio. We consider the shortest path BLT algorithm (BLT-SP) [9] and we compute all shortest paths between any node in set U and any node in set V. We select node u such that the path from v to u is shortest among the paths from any node in V to any node in U. The main idea of BLT is to consider the tree node with the largest total splitting loss and attempt to reduce that loss by moving that node closer to the source node in the logical light-tree. This may increase the attenuation loss (the node may be added to the tree on a longer path) but it will also decrease its splitting loss, possibly resulting in a smaller total loss. The balanced light-tree_Q (BLT_Q) technique takes as input an initial tree T spanning the source s and the destination nodes in the multicast group. The key part of the BLT_Q algorithm is the tree balancing procedure taking into account now the Q factor. Consider a light-tree T, and let u (respectively, v) denote the node with the minimum (respectively, maximum) split ratio. The idea behind the BLT_Q algorithm is to delete the node with minimum Q u from T, and add it back to the tree by connecting it to node with the maximum Q v in the path from source s to node v. This results in an increase of the Q factor of node u, but it also reduces the Q factor of all nodes below node v in the tree. Therefore, this pair of delete/add operations is performed only if it does not reduce the Q factor of any node beyond that of node u. Thus, after each iteration of the algorithm, the Q factor of the node with the minimum value is increased. While the Q factor of some other node(s) is decreased, it does not decrease beyond the previous minimum value. As a result, the difference between the minimum and maximum Q factor values also decreases with each iteration. The algorithm terminates after a certain number of iterations. As for the BLT algorithm, we consider the shortest path (BLT_Q-SP) in order to select the path from v to u amongst all the shortest paths that may exist between any two nodes in sets U and V. The BLT_Q algorithm tends to create trees that have more breadth than depth, in contrast to the BLT algorithm where the trees have more depth. The BLT_Q algorithm decreases the attenuation loss and the signals pass through a smaller number of optical amplifiers. However, it also increases the total number of links in the tree. In order to keep the number of recourses low (small total number of links on the tree, which in turn will mean less number of wavelengths used) the algorithm BLT_Q is modified to create algorithm BLT_Qtolerance (BLT algorithm based on minimum acceptable Q factor). Considering that the minimum acceptable Q factor for each path is q, the algorithm tries to maximize the Q factor only at those nodes where its value is lower than the
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acceptable value q, i.e., if after a number of iterations (or no iterations) the minimum Q value in some node in the tree is higher than q then the algorithm terminates. Table 1. Balanced Tree Algorithms. Balanced Light-Tree (BLT) Algorithm Input: A graph G = (V, A) representing the network, a source node s ∈ V, a destination set M ⊆ V, and an initial light-tree T0 spanning the set {s ∪ M}. T0 is pre-computed by the Steiner heuristic. Output: A light-tree Tf spanning the set {s ∪ M}, such that either (i) Tf is feasible, or (ii) the difference between the maximum and minimum split ratio of any two nodes in M is minimum. Balanced Light-Tree based on Q_factor (BLT_Q) Algorithm Input: A graph G = (V, A) representing the network, a source node s ∈ V, a destination set M ⊆ V, and an initial light-tree T0 spanning the set {s ∪ M}.T0 is pre-computed by the Steiner heuristic. Output: A light-tree Tf spanning the set {s ∪ M}, such that either (i) Tf is feasible, or (ii) the difference between the maximum and minimum Q of any two nodes in M is minimum. Balanced Light-Tree based on minimum acceptable Q_factor (BLT_Qtolerance) Algorithm Input: A graph G = (V, A) representing the network, a source node s ∈ V, a destination set M ⊆ V, a minimum acceptable Qtolerance, an initial light-tree T0 spanning the set {s ∪ M}.T0 is pre-computed by the Steiner heuristic. Output: A light-tree Tf spanning the set {s ∪ M}, such that either (i) Tf is feasible, or (ii) the minimum Q value in some node in the tree is higher than the predetermined threshold q. 3.2 Performance Results In order to evaluate the average performance of the balanced light-tree routing algorithms we simulated multicast connections on a network consisting of 50 nodes and 196 links, with an average node degree of 7.84 and an average distance between the links of 70 km. We used a dynamic traffic model where multicast call requests arrive at each node according to a Poisson process and the holding time is exponentially distributed with a unit mean. In each simulation 5,000 multicast requests were generated for each multicast group size (number of destinations for the multicast tree) for a total of 40,000 multicast requests, and the results were averaged over five simulation runs. Thirty-two (32) wavelengths per link were utilized to evaluate the blocking probability vs. the multicast group size for a network load of 100 Erlangs. 1
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Figure 1.(a) Blocking probability vs. Multicast group size. (b) Blocking probability vs. Multicast group size with reengineered network node characteristics. For each multicast request, the algorithm first solves the routing problem by finding a tree that can accommodate the request and then tries to assign a wavelength for that tree. Multicast requests are blocked if there is no available wavelength for the entire tree. If a wavelength assignment is possible, the Q-budget for each path on the tree is evaluated and the multicast request will now be blocked if there is at least one route on that tree with a Q value that falls below a predetermined threshold value. In these simulation runs, for specific network parameters and node design, the threshold for the Q factor was set to 8.5 (QdB). Thus, the blocking probability in this case will be the sum of the blocking probability because of a lack of available wavelengths (Pb(λ)) and the blocking probability because of routes that violate the Q constraint (Pb(Q)). For each algorithm we plotted the total blocking probability vs. the multicast group size to ascertain the factor that limits blocking. Fig. 1(a) shows the simulation results for the blocking probability versus the multicast group size when a number of multicast algorithms are used. The Steiner tree heuristic (a cost is assigned on each link and the heuristic tries to find the tree with the minimum cost based on shortest-path calculations) and the BLT algorithm that only takes power budget constraints into consideration have much higher blocking probability than the
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BLT_Q and BLT_Qtolerance algorithms. This is the case as with the new algorithms the trees tend to become “shallower” which means that the Q threshold is not exceeded. Fig. (1b) shows the results of the simulation when the network is reengineered so that the launched power into the fiber is 3 dB higher (3 dBm now versus 0dBm before) and each network node has more gain shifted from the post-amplifier to the pre-amplifier resulting in improved node noise figure. Fig. 2 shows the results of the simulation when we engineer the fiber links to include in-line amplifiers. In this case it is clear that all multicast algorithms provide approximately the same results. The reason is that the presence of in-line optical amplifiers improves the calculation of the Q factor and the limiting factor is now the number of wavelengths in the network. Thus, all blocking in this case occur only due to the lack of available wavelength channels. 1
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Figure 2. Blocking probability vs. Multicast group size with in-line amplifiers on the fiber links. 4. CONCLUSIONS As next generation networks are expected to support a host of multicast applications, finding algorithms to successfully provision multicast requests is of particular importance. This paper improves on the MC-RWA algorithms by also including physical layer constraints utilizing the Q factor. Modified BLT algorithms are designed and their performance is tested on a 50-node network. Results show that the blocking probability is improved compared to both the Steiner heuristic and the BLT algorithm that only takes the power budget into consideration. This approach enables the efficient design, engineering and evaluation of transparent metropolitan area optical networks for the provisioning of multicast sessions. ACKNOWLEDGEMENTS This work was performed in collaboration with SignalGeneriX and it was partially funded by the Cyprus Research Promotion Foundation. REFERENCES [1] T. Stern and K. Bala: Multiwavelength Optical Networks: A Layered Approach, Prentice Hall, 1999. [2] L. H. Sahasrabuddhe and B. Mukherjee: Light-trees: Optical multicasting for improved performance in wavelength-routed networks, IEEE Communications Magazine, vol. 37, no. 2, February 1999. [3] N. Antoniades, et al.: Performance Engineering and Topological Design of Metro WDM Optical Networks Using Computer Simulation, Journal on Selected Areas in Communications, vol. 20, no. 1, Jan. 2002. [4] C. Politi, et al.: Physical Layer Impairment Aware Routing Algorithms based on Analytically Calculated Q-factor, Proc. OFC/NFOEC Conference, Anaheim, CA, March 2006. [5] A. Kamal, R. Ul-Mustafa: Multicast Traffic Grooming in WDM Networks, Proc. SPIE/IEEE Opticom, Dallas, Texas, October 2003. [6] D-N. Yang and W. Liao: Design of Light-Tree Based Logical Topologies for Multicast Streams in Wavelength Routed Optical Networks, Proc. IEEE Infocom, San Francisco, March-April 2003. [7] Y. Sun, J. Gu, and D. H. K. Tsang: Multicast routing in all-optical wavelength-routed networks, SPIE Optical Networks Magazine, pp. 101-109, July - August 2001. [8] G. Sahin and M. Azizoglu: Multicast routing and wavelength assignment in wide-area networks, SPIE Proceedings, All Optical Networking, Boston, Massachusetts, November 1998. [9] Y. Xin and G. N. Rouskas: Multicast routing under optical layer constraints, Proc. IEEE Infocom, vol. 4, pp. 2731-2742, 2004.
