Title: M/G/1 queue with regular and optional phases of services and vacations

Authors: R. Kalyanaraman; K. Vidya

Addresses: Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India ' Department of Mathematics, Government College of Engineering, Thanjavur, Tamil Nadu, India

Abstract: This paper deals with a non-Markovian single server queue with phase type service and phase type vacation. The service time and vacation time of each phase is generally distributed. The probability generating function of number of customers in the system at an arbitrary time point and at departure point is obtained in steady state. Some important performance measures are derived. Some numerical illustrations are also provided.

Keywords: phase type service; phase type vacation; probability generating function; performance measures.

DOI: 10.1504/IJMOR.2026.152321

International Journal of Mathematics in Operational Research, 2026 Vol.33 No.3, pp.391 - 411

Received: 01 Mar 2024
Accepted: 21 Apr 2024
Published online: 16 Mar 2026 *

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