Title: Analysis of non-Markovian batch service queue with second optional service under transient and steady state domain

Authors: P. Vijaya Laxmi; Andwilile Abrahamu George

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam, India

Abstract: This paper analyses the transient and steady state behaviour of a non-Markovian batch service queue with second optional service. The transient state probabilities are computed using the probability generating function, Rouche's theorem, and Laplace transform (L.T.) methods. The Tauberian property in the L.T. expressions is used to get steady state probabilities. Also, we obtain various performance measures along with cost optimisation and numerical results are presented by taking special cases of the service times. The results show the standard observation that the Erlang-k type distribution reduces to an exponential distribution when k = 1 and when k takes a large value, it becomes deterministic.

Keywords: non-Markovian; transient and steady state analysis; batch service queue; first essential service; second optional service.

DOI: 10.1504/IJMOR.2023.129496

International Journal of Mathematics in Operational Research, 2023 Vol.24 No.3, pp.387 - 407

Received: 29 Jan 2022
Accepted: 15 Feb 2022
Published online: 10 Mar 2023 *

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