E. Nyberg, J. Virtamo, and S. Aalto. An exact algorithm for calculating blocking probabilities in multicast networks. Lecture Notes in Computer Science, 1815, 275-286, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem, depending on many parameters such as the type of application generating the trac and the service policy used for the group. Trac models for multicast sessions and algorithms for calculating blocking probabilities can be found in Karvo et al. KMVA01] and Nyberg, Virtamo, and Aalto [NVA00]. Since the unicast routing is given, the trac loads on all links can be computed for any given RP con guration. We seek to nd the RP con guration which minimizes the maximum link utilization anywhere in the network. It is assumed that the RPF path to the RP is chosen as the uplink path for all ....

E. Nyberg, J. Virtamo, and S. Aalto. An exact algorithm for calculating blocking probabilities in multicast networks. Lecture Notes in Computer Science, 1815, 275-286, 2000.

....static multicast calls. Their study suggests, that the reduced load approximation is not adequate for multicasting, and further work is needed. An exact algorithm with complexity for the network case with dynamic nonlayered multicast connections has been given in Nyberg et al. [9]. Efficient Monte Carlo simulation method for dynamic multicast networks has been developed by Lassila et al. 10] Aalto and Virtamo [11] developed an algorithm for the non layered case where all channels are statistically indistinguishable, using combinatorics to achieve complexity of ....

....Section V studies the insensitivity of the system, and the call blocking probabilities, when applying some basic user population models to the system. The results are summarised in section VI. II. MULTICAST LOSS SYSTEM We study the multicast loss system using notation presented in Nyberg et al. [9], adding multilayer specific properties to the model. Consider a network consisting of links, indexed with ) 1010102. 43 , link having a capacity of 576 resource units. The network is organized as a tree. The set denotes the set of user populations, located at the leaves of ....

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Eeva Nyberg, Jorma Virtamo, and Samuli Aalto, "An exact algorithm for calculating blocking probabilities in multicast networks, " in Networking

....for optimally allocating the number of samples to be used for each sub problem and give some numerical examples demonstrating the effectiveness of the method. Section 6 contains our conclusions. 2 II. The multicast loss system We define the multicast loss system in the same way as Nyberg et al. [9]. Consider a network consisting of J links, indexed with j = 1, J , link j having a capacity of C j resource units. The set of all links is denoted by J . The network is organized as a tree, where the root link is denoted by J . The set U denotes the set of user populations, ....

....links are independent, and that the leaf link distributions # u (y u ) P Y u = y u , u # U are known, and represent stationary distributions of reversible Markov processes satisfying the detailed balance equations. Several types of user population models of this kind have been discussed in [9]. In our work, we use a user population model for which traffic classes (u, i) are independent so that # u (y) # i#I p y i u,i (1 p u,i ) 1 y i , 3) where p u,i = P Y u,i = 1 is the probability that channel i is on on leaf link u. The probability p j,i of channel i to ....

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E. Nyberg, J. Virtamo, and S. Aalto, "An exact algorithm for calculating blocking probabilities in multicast networks," submitted for publication.

....the blocking probabilities was derived. This work was extended by Boussetta and Belyot [2] by adding unicast traffic to the system. Reduced load approximations of the blocking probabilities in a network were derived in [3] An exact algorithm for the network case has been given in Nyberg et al. [4]. A problem with the exact solution, however, is that it cannot be computed for networks with a large number of channels, I , due to the exponential growth of the size of the state space; the complexity of the algorithm is of order O(2 2I ) however, the complexity grows only linearly with ....

....new estimators are calculated for the s j and the procedure is repeated. B. Numerical examples Here some numerical examples are presented in order to illustrate the efficiency of the presented method in Monte Carlo simulation of the blocking probabilities. We consider the same network used in [4], 9] for which we know the exact results. The network is shown in figure 3. There is a root node, eight channels, I = 8, with d i = 1 for all channels. The capacity of the root link is C J = 7, for the others, C j = 6. Each leaf link has an infinite user population offering traffic to ....

[Article contains additional citation context not shown here]

E. Nyberg, J. Virtamo, and S. Aalto, "An exact algorithm for calculating blocking probabilities in multicast networks," in Proceedings of Networking 2000, Paris, May 2000, pp. 275--286.

....for optimally allocating the number of samples to be used for each sub problem and give some numerical examples demonstrating the effectiveness of the method. Section 6 contains our conclusions. II. The multicast loss system We define the multicast loss system in the same way as Nyberg et al. [9]. Consider a network consisting of J links, indexed with j =1, J, link j having a capacity of C j resource units. The set of all links is denoted by J . The network is organized as a tree, where the root link is denoted by J . The set U denotes the set of user populations, located at the ....

....leaf links are independent, and that the leaf link distributions # u (y u ) P Y u = y u ,u#U are known, and represent stationary distributions of reversible Markov processes satisfying the detailed balance equations. Several types of user population models of this kind have been discussed in [9]. In our work, we use a user population model for which traffic classes (u, i) are independent so that # u (y) # i#I p y i u,i (1 p u,i ) 1 y i , 3) where p u,i =P Y u,i =1 is the probability that channel i is ## on leaf link u. The probability p j,i of channel i to 3 be in the ## ....

[Article contains additional citation context not shown here]

E. Nyberg, J. Virtamo, and S. Aalto, \An exact algorithm for calculating blocking probabilities in multicast networks," submitted to IEEE/ACM Transactions on Networking.

....the blocking probabilities was derived. This work was extended by Boussetta and Belyot [2] by adding unicast traffic to the system. Reduced load approximations of the blocking probabilities in a network were derived in [3] An exact algorithm for the network case has been given in Nyberg et al. [4]. A problem with the exact solution, however, is that it cannot be computed for networks with a large number of channels, I , due to the exponential growth of the size of the state space; the complexity of the algorithm is of order O(2 I ) however, the complexity grows only linearly with ....

....new estimators are calculated for the s j and the procedure is repeated. ## ######### ######## Here some numerical examples are presented in order to illustrate the efficiency of the presented method in Monte Carlo simulation of the blocking probabilities. We consider the same network used in [4], 9] for which we know the exact results. The network is shown in figure 3. There is a root node, eight channels, I =8, with d i =1 for all channels. The capacity of the root link is C J =7, for the others, C j =6. Each leaf link has an infinite user population offering traffic to each channel ....

[Article contains additional citation context not shown here]

E. Nyberg, J. Virtamo, and S. Aalto, \An exact algorithm for calculating blocking probabilities in multicast networks," in #### ######## ## ########## ####, May 2000, pp. 275-286.

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