Title: A steady state analysis of an optional differentiated working vacation queue with working breakdown

Authors: S. Muthukumar; J. Ebenesar Anna Bagyam

Addresses: Department of Mathematics, Ramco Institute of Technology, Rajapalayam – 626117, Tamilnadu, India; Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore – 641021, Tamil Nadu, India ' Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore – 641021, Tamil Nadu, India

Abstract: In this work, we study the steady state behaviour of the M/M/1 queue with working breakdown and optionally differentiated working vacations. After each busy time, the server takes either an optional working vacation I or II. If a server breaks down during busy periods, it will provide the minimum number of services until it is repaired. The probability-generating function is used to determine the model's steady-state solution. Moreover, various indicators of the performance of the specified model are discussed in explicit form. The PSO algorithm is also used for cost optimisation analysis. The effects of parameters are demonstrated with numerical examples.

Keywords: single server queue; differentiated working vacations; working breakdown; repair; stationary analysis and optimisation.

DOI: 10.1504/IJMOR.2026.156087

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.4, pp.506 - 523

Received: 08 Aug 2024
Accepted: 20 Aug 2024
Published online: 03 Sep 2026 *

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