Title: Bernoulli vacation bulk queue with essential, optional service, unreliable server and state dependent arrival rates

Authors: R. Kalyanaraman; R.V. Sivasuprajha

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

Abstract: This paper presents the steady state analysis of a single server, bulk arrival, fixed batch service, Bernoulli vacation queue. The arrival follows compound Poisson process with state dependent arrival rates. The service time follows general distribution and services are given in batches of fixed size. The server provides two types of services called, essential and optional service to each batch. At each service completion point, the server takes vacation of Bernoulli type. The vacation period is generally distributed. In addition, during the server's busy state, the server may breakdown immediately, the server is sent for repair. The number of breakdowns follows Poisson process whereas the repair period follows general distribution. For this queueing system the steady state probabilities are derived in terms of probability generating function. The expected number of customers and mean waiting times at various server states are derived. Numerical illustrations are given.

Keywords: non-Markovian queue; bulk arrival queue; fixed batch size; Bernoulli vacation; essential and optional service; unreliable server; state dependent rates.

DOI: 10.1504/IJMOR.2026.155541

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.3, pp.354 - 381

Received: 04 Aug 2024
Accepted: 16 Aug 2024
Published online: 05 Aug 2026 *

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