A Steady State Behavior of M/M/1 Queue with an Optional Differentiated Working Vacation and Arrival Restriction

Authors

  • S. Muthukumar Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, Tamil Nadu, India; Department of Mathematics, Ramco Institute of Technology (affiliated to Anna University), Rajapalayam 626117, Tamil Nadu, India https://orcid.org/0009-0007-1320-6082
  • J. Ebenesar Anna Bagyam Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, Tamil Nadu, India
  • S. Keerthana Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, Tamil Nadu, India

DOI:

https://doi.org/10.26713/cma.v16i1.2815

Keywords:

Single server queue, Multiple variants working vacations, Stationary analysis, Optimization and arrival restriction

Abstract

In this paper, we aim to study the steady-state behaviour of an M/M/1 queue with an optionally differentiated working vacations I and II. After finishing a busy period, the server takes either an optional working vacation I or an optional working vacation II. Customer arrivals are restricted when the server is either on an optional working vacation I or an optional working vacation II. The model’s stable solution is derived using the probability generating function. Additionally, specific expressions are used to discuss several performance measurements for the provided model. For cost optimization analysis, the Particle Swarm Optimization (PSO) method is also employed to reduce the total cost. We minimize the total cost of providing the best service by using the PSO optimization method. A few numerical examples are provided to illustrate the effects of different arrival rates, service rates, server vacation times, and customer waiting times.

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Published

01-07-2025
CITATION

How to Cite

Muthukumar, S., Bagyam, J. E. A., & Keerthana, S. (2025). A Steady State Behavior of M/M/1 Queue with an Optional Differentiated Working Vacation and Arrival Restriction. Communications in Mathematics and Applications, 16(1), 277–291. https://doi.org/10.26713/cma.v16i1.2815

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

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