Title: Transient analysis of an M/M/c queuing system with retention of reneging customers

Authors: Rakesh Kumar; Sapana Sharma

Addresses: Department of Mathematics, Shri Mata Vaishno Devi University, Katra, Sub-Post Office, University Campus-182320, Jammu and Kashmir, India ' Department of Mathematics, Shri Mata Vaishno Devi University, Katra, Sub-Post Office, University Campus-182320, Jammu and Kashmir, India

Abstract: In this paper, we study the transient behaviour of an M/M/c queuing system with reneging and retention of reneging customers. The probability generating function technique along with Bessel function properties is used to derive the time-dependent state probabilities explicitly. The transient behaviour of system size probabilities, the expected system size, the average reneging rate, and the average retention rate is studied with the help of a numerical example.

Keywords: transient analysis; M/M/c queuing system; expected system size; operational research; reneging; retention.

DOI: 10.1504/IJOR.2019.102071

International Journal of Operational Research, 2019 Vol.36 No.1, pp.78 - 91

Received: 01 Aug 2016
Accepted: 28 Oct 2016
Published online: 06 Sep 2019 *

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