Title: Analysis of non-pre-emptive priority retrial queueing system with two-way communication, Bernoulli vacation, collisions, working breakdown, immediate feedback and reneging

Authors: G. Ayyappan; J. Udayageetha; B. Somasundaram

Addresses: Department of Mathematics, Pondicherry Engineering College, Puducherry, India ' Department of Mathematics, Perunthalaivar Kamarajar Arts College, Puducherry, India ' Department of Mathematics, Pondicherry Engineering College, Puducherry, India

Abstract: In this study, we investigate a single server priority retrial queueing system including two-way communication, collision, working breakdown, repair, immediate feedback, Bernoulli vacation and reneging. Incoming requests (calls) appear at the service station according to a compound Poisson process. During the idle time, the server can make an outgoing call with an exponentially distributed time. The incoming call that identifies the server occupied will join an orbit or collide with the call currently in service. The server renders the service following a non-pre-emptive priority service rule. The server takes a Bernoulli vacation. The server may become inactive due to normal breakdown and the call currently in service will get the remaining service at a moderate service rate. The repair process starts instantly. After the completion of service, vacation and repair the server is in an idle state. We allow reneging to happen at the orbit. Using the supplementary variable technique, the stability condition is derived.

Keywords: priority queueing systems; two-way communication; retrial queue; working breakdown; collisions; Bernoulli vacation.

DOI: 10.1504/IJMOR.2020.108420

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.4, pp.480 - 498

Received: 04 Feb 2019
Accepted: 19 Mar 2019
Published online: 13 Jul 2020 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article