The generalised state-dependent queue: the busy period Erlangian

Author:

Conolly B. W.

Abstract

A continued fraction representation is presented of the Laplace transform of the generating function of the fundamental joint probability and density of busy period length measured in customers served and duration in time. The setting is the single server Erlang queueing system where the parameters of negative exponentially distributed arrival and service times have a general dependence on instantaneous system state.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference8 articles.

1. The busy period in relation to the queueing process GI/M/1;Conolly;Biometrika,1959

2. On the Improvement of the Operational Characteristics of Single-Server Queues by the Use of a Queue-Length-Dependent Service Mechanism

3. Natvig B. (1974) A queueing model where potential customers are discouraged by queue length. Scard. J. Statist. 1, To appear.

4. Busy period of queues with state dependent arrival and service rates

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