The generalised state-dependent queue: the busy period Erlangian

B. W. Conolly

17 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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.

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1959The busy period in relation to the queueing process GI/M/1 1969On the Improvement of the Operational Characteristics of Single-Server Queues by the Use of a Queue-Length-Dependent Service Mechanism

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2017A state-dependent queueing system with asymptotic logarithmic distribution 1974Busy period of queues with state dependent arrival and service rates 2002Two-Class Priority Queueing System with State-Dependent Arrivals 1975On the waiting-time and busy period distributions for a general birth-and-death queueing model 1977Generalised birth and death queueing processes: recent results

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