A new mean-value type of algorithm is developed for analyzing multi-facility blocking models with state-dependent arrival rates. It can be applied to a broad class of blocking systems with simultaneous resource possession including, for example, circuit-switched networks. The underlying recursion is cast in terms of blocking probabilities and marginal state probabilities. The developments made here generalize previous results that were restricted to the case of constant arrival rates.

Single-hop and multi-hop wavelength division multiplex (WDM) access systems have been proposed to take advantage of the large bandwidth available in lightwave mediums. In such systems, there are one or several transmitters and receivers at each node in the network. The receivers and transmitters may be tunable or set at particular wavelengths. The lightwave medium makes available a large number of channels at different wavelengths. Recently, the stochastic analysis of single-hop and multi-hop systems has been studied. The authors present a unified 'multi-facility blocking model' approach to the stochastic modeling and analysis of WDM networks of both the single-hop and multi-hop type. The developed model is amenable to exact analysis by an efficient recursive algorithm. The modeling and analysis technique enables one to study the performance of arbitrary access configurations under general traffic conditions including the case of uniform traffic and the case where there are 'hot spots.'.>

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.

In this paper, we present simple recursive algorithms for computing call and time congestion in the classical Engset model with M sources and N servers. The first recursion has the complexity of O(MN) and gives the blocking probabilities for all intermediate values of M and N. The second recursion assumes a particular value of M and has the complexity of O(N). It gives the blocking probabilities for all intermediate values of N. Both recursions are similar to the well-known recurrence for computing the Erlang loss function.

A general-purpose decomposition method is formulated for the exact analysis of blocking probabilities in multirate circuit-switched networks. The procedure is based on a decomposition and aggregation technique that exploits the sparsity that can be found in the routing matrix of a network. Use is also made of a recursive algorithm developed by the authors (see Ann. Oper. Res. vol.35, no.1-4, p.31-41, 1992). No special assumptions are made with regard to the structure of the network. By reducing the analysis to that of a set of interrelated subsystems and a reduced system, the overall dimensionality of the problem is diminished, and the computational costs are reduced significantly. This enables the efficient exact analysis of larger network models. An example is provided to illustrate the computational savings that can be realized.>

One of the most promising approaches to building high speed networks and distributed multiprocessors is the use of optical interconnections. The basic component of such a system is a switch (interconnection network) that has a capacity of interconnecting a large number of inputs to outputs. In this paper we present an analysis of an N1 x N2 asynchronous crossbar switch model for all-optical circuit-switching networks that incorporates multi-rate arrival traffic with varied arrival distributions. We compare the model behavior using traffic loads derived from the Binomial, Pascal, and Poisson statistical distributions. We give efficient algorithms to compute the performance measures. We analyze the effect of load changes from particular traffic distribution streams on system performance and give a simple “economic” interpretation.

In this paper we present a simple non-iterative computational procedure for approximating the Erlang loss function B(N, ϱ). It is applicable to the practical range 10−5<B(N, ϱ)<10−1 and gives results that are within 10% of the exact values. The formula can be computed on a pocket calculator in constant time and could be used to approximately compute B(N, ϱ) for systems of practically any size.

The quasi-optimal maximum packing policy which gives the lowest blocking rates for dynamic channel assignment is considered. The authors formulate the stochastic model and apply an efficient approximation to compute the performance measures. The authors have previously shown that the analysis of a stochastic model of a maximum packing policy is equivalent to that of a fixed-route circuit-switched network. Thus, some of the performance measures in cellular communication systems can be obtained by using the well-developed exact simulation and approximation methods used in analyzing circuit-switched networks. Formal costs associated with each connection are used to show how dynamic channel assignment with maximum packing can improve the service and increase the total revenue. The results support an argument for the realization of the dynamic channel assignment and rearrangement in cellular communication systems.>

A model is considered which has several classes of customers arriving in independent Poisson processes at a multiserver facility and requiring a specific number of servers for a random period of time (arbitrarily distributed with a finite mean). If these servers cannot be provided, the customers are cleared. The problem is to determine the blocking probabilities. The exact expression is available but is complicated. The authors apply a novel approximation method of ensemble averaging for the asymptotic analysis of blocking in such systems. The method gives simple expressions for the average performance measures without an explicit computation of the normalization constant of the steady-state probability distribution. The computation of blocking probability and of other performance measures is reduced to computing a root of a simple algebraic equation. The obtained expressions are shown to be asymptotically correct.>

The purpose of this paper is to present an asymptotic performance analysis of a class of multihop radio networks using the calculus of residues. The analysis provides a closed-form approximation of global performance measures, whose precision increases exponentially with the size of the system. The complexity of computing these approximations is independent of the problem size. The method is easily applicable to a variety of topologies and access protocols.