Title: Transient analysis of a discrete-time infinite server queue with system disaster

Authors: R. Sebasthi Priya; R. Sudhesh

Addresses: Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, Tamilnadu 620-024, India ' Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, Tamilnadu 620-024, India

Abstract: This paper studies a discrete-time infinite server queue subject to system disaster. The exact time-dependent probabilities of the number of customers present in the system are obtained using generating functions, continued fractions and confluent hypergeometric functions. Further, the results are extended to obtain closed form expression for busy period distribution and steady state system size probabilities. Numerical illustrations are provided to visualise the effect of system size probabilities, both in steady state and transient state, and busy period distribution for different parameter values.

Keywords: discrete queue; time-dependent probability; generating functions; busy period; confluent hypergeometric functions; continued fractions.

DOI: 10.1504/IJMOR.2018.088580

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.1, pp.91 - 101

Received: 29 Mar 2016
Accepted: 29 Jul 2016
Published online: 12 Dec 2017 *

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