Efficient decomposition methods for the analysis of multi-facility blocking models

Abstract

Three new decomposition methods are developed for the exact analysis of stochastic multi-facility blocking models of the product-form type. The first is a basic decomposition algorithm that reduces the analysis of blocking probabilities to that of two separate subsystems. The second is a generalized M-subsystem decomposition method. The third is a more elaborate and efficient incremental decomposition technique. All of the algorithms exploit the sparsity of locality that can be found in the demand matrix of a system. By reducing the analysis to that of a set of subsystems, the overall dimensionality of the problem is diminished and the computational requirements are reduced significantly. This enables the efficient computation of blocking probabilities in large systems. Several numerical examples are provided to illustrate the computational savings that can be realized.

Nonstationary analysis of circuit-switched communication networks

“…8 gives the approximate time-dependent blocking probability function (FPA) and the upper and low values of the 95% confidence intervals (C.I.) obtained by simulation for the classes (1, 1), (1,2), (1,3), (1,4) and (1,5). In general, the approximation curves follow the shape of the time-dependent blocking probability functions obtained by simulation.…”

The Decomposition of a Blocking Model for Connection-Oriented Networks

“…Conway et al [18] partition a network into subnetworks and derive equations similar to those of (7) and (8). Since the partition is based on the network topology, it does not always give the maximum computational savings.…”

“…Conway et al proposed a topologybased general-purpose decomposition method similar to that of (7) and (8). They showed that large computational savings can be obtained [18]. In the second example, we compared the performance of our proposed methods with that of Conway et al using the same network topology and routing paths as that of [18] but with twice the number of call classes.…”

“…They showed that large computational savings can be obtained [18]. In the second example, we compared the performance of our proposed methods with that of Conway et al using the same network topology and routing paths as that of [18] but with twice the number of call classes. We showed that our proposed methods provided significant savings over that of [18].…”

“…In networks with regular topology, e.g., tree networks, decompositions have been used to develop efficient algorithms to compute the blocking probabilities [14]- [17]. General-purpose topologybased decomposition methods have been proposed to reduce the computational cost of exact blocking probability computation in product form models [18]. Numerical inversion of generating functions, normally used to compute the blocking probability exactly, have been used together with decomposition and truncation to speed up the computation [19].…”