Loss Systems with Mixed Renewal and Poisson Inputs

A. Kuczura

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Advanced Queuing Theory Analysis Probability and Statistical Research Wireless Communication Networks Research

Abstract

When two independent streams of customers compete for the same servers, as happens for example when first-routed and overflow traffic streams share a single trunk-group, the state of the system seen by the two different types of arriving customers will in general be different. In a loss system with mixed renewal and Poisson inputs, the blocking experienced by the renewal-type customers can be markedly different from that seen by the Poissonian customers. This paper derives the distribution of the number of busy servers seen by the two streams, and outlines a numerical procedure for computing the distributions. Examples of blocking probabilities for two cases of the renewal stream are given.

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References

1963Stochastic Service Systems.1973The Interrupted Poisson Process As An Overflow Process 1968A Service System with Unfilled Requests Repeated 1972Queues With Mixed Renewal and Poisson Inputs

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1984On the Overflow Process from a Finite Markovian Queue 1984On the M/G/1 queue by additional inputs 1987The single-server queue with independent GI/G and M/G input streams 2003Analysis of a discrete-time single-server queue with bursty inputs for traffic control in ATM networks 1979Decomposition of Traffic in Loss Systems with Renewal Input 1985Individual Traffic Characteristics Queueing Systems with Multiple Poisson and Overflow Inputs 1983An Approximate Formula for Individual Call Losses in Overflow Systems 1980A Single Server Queueing Loss Model with Heterogeneous Arrival and Service

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