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Asymptotic analysis and computational methods for a class of simple, circuit-switched networks with blocking

Published online by Cambridge University Press:  01 July 2016

Debasis Mitra
Debasis Mitra*
Affiliation:
AT & T Bell Laboratories
*
∗Postal address: AT & T Bell Laboratories, Murray Hill, NJ 07974, USA.
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Abstract

We consider the following circuit-switching problem which is one of the simplest possible extensions of the classical M/M/K/K model: there are p source centers connected to a hub by channels of various line-capacities and the hub is connected to a destination center by a common channel with its own line-capacity. A circuit requires a line from its source to the hub and another line from the hub to the destination. The holding times of circuits are independent, arbitrarily distributed random variables with means which depend on their source, and requests for circuits arrive in Poisson streams. Blocked calls are cleared. The problem is to calculate the blocking probabilities at each of the sources. The formal solution is well known but its calculation is exponentially hard in p.

We have developed a technique which extends recent results on integral representations and their asymptotic expansions to obtain the full expansion for the blocking probabilities in inverse powers of a large parameter N. The power of the method derives from two sources: first, an efficient recursive formula for calculating the general term of the expansion; second, tight upper and lower bounds which accompany the estimates. The computational complexity is polynomial in p. We report on computations.

Keywords

ASYMPTOTICSMULTIDIMENSIONAL INTEGRALSQUASI-REVERSIBLE STOCHASTIC NETWORKS
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 219 - 239
Copyright
Copyright © Applied Probability Trust 1987 

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