Eugene Pinsky

Computational algorithms for blocking probabilities in circuit-switched networks

In this paper, we develop two new general purpose recursive algorithms for the exact computation of blocking probabilities in multi-rate product-form circuit-switched networks with fixed routing. The first algorithm is a normalization constant approach based on the partition function of the state distribution. The second is a mean-value type of algorithm with a recursion cast in terms of blocking probabilities and conditional probabilities. The mean value recursion is derived from the normalization constant recursion. Both recursions are general purpose ones that do not depend on any specific network topology. The relative advantage of the mean-value algorithm is numerical stability, but this is obtained at the expense of an increase in computational costs.

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

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.

Exact computation of blocking probabilities in state-dependent multi-facility blocking models

In this paper, we develop a new general-purpose recursive algorithm for the exact computation of blocking probabilities in multi-facility blocking models with some forms of state-dependent arrival rates. The recursion is cast in terms of the partition function of a product-form model. A dynamic scaling procedure is also proposed to avoid numerical overflow or underflow. The recursion is sufficiently general to be applied to a variety of different state-dependent arrival processes and service rate functions.

Blocking formulae for the Engset model

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 decomposition method for the exact analysis of circuit-switched networks

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.<<ETX>>

An asymptotic analysis of complete sharing policy

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.<<ETX>>

A simple approximation for the Erlang loss function

Abstract 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 ) −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.

Performance analysis of some channel access schemes in cellular communication systems

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.<<ETX>>

Performance analysis of an asynchronous multi-rate crossbar with bursty traffic

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 N 1 x N 2 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.

Modeling hot spots in database systems (extended abstract)

This paper presents an analytical performance model for a static locking policy in a database system. The model takes into consideration the impact of hot spots in databases, and offers an asymptotically accurate measure of throughput and probability of conflict in the system. The solution approach is based on a technique called ensemble aver-aging, which enables the solution to become computationally tractable, and is especially attractive when applied to database systems. Performance analysis of concurrency control and locking mechanisms in database systems has been