Title: Analysis of a finite retrial queueing system with orbital search using generalised inverses

Authors: R. Kalyanaraman; S.B. Pattabi Raman

Addresses: Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India ' Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India

Abstract: A simple, efficient, numerically stable algorithm to the analysis of a M/M/1/3/3 retrial queue with orbital search is given in terms of group generalised inverses. The interarrival time and service time are two different exponential distributions. There are three sources, each source generate primary customers. The primary arrivals first check whether the server is idle. If the server is idle, he enters the service station. Otherwise, he enters the orbit and retries, the inter retrial times follows negative exponential distribution. After being serviced, the customer returns to the source. Also, after completing service no one competing for service, with probability p, the server carries search for customers in the orbit and instantly picks up a customer, if available, directly from the orbit. Such a queue is called retrial queue with orbital search. Using the algorithm developed in Kalyanaraman and Raman (2010), the stationary distribution and mean first passage time distributions are obtained. Some operating chracteristics are calculated. Some particular models are also given.

Keywords: retrial queue; orbital search; generalised inverses; stationary distribution; mean first passage time; operating characteristics.

DOI: 10.1504/IJMOR.2026.153576

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.1, pp.54 - 72

Received: 10 Jan 2024
Accepted: 02 Feb 2024
Published online: 18 May 2026 *

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