Non-Markovian Bulk Service Queue with Unreliable Server and Multiple Vacation Under Restricted Admissibility Policy

G. Ayyappan; M. Nirmala

doi:https://doi.org/10.14445/22315373/IJMTT-V54P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 1 | Year 2018 | Article Id. IJMTT-V54P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P510

Non-Markovian Bulk Service Queue with Unreliable Server and Multiple Vacation Under Restricted Admissibility Policy

G. Ayyappan, M. Nirmala

Citation :

G. Ayyappan, M. Nirmala, "Non-Markovian Bulk Service Queue with Unreliable Server and Multiple Vacation Under Restricted Admissibility Policy," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 1, pp. 87-99, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P510

Abstract

This paper is concerned with the transient and steady state analysis of unreliable server batch arrival general bulk service queueing system with multiple vacation under a restricted admissibility policy of arriving batches. Arrivals occur in batches according to compound Poisson process. Unlike the usual batch arrival queueing system, the restricted admissibility policy differs during a busy period and a vacation period and hence all arriving batches are not allowed to join the system at all times. The service is done in bulk with minimum of ‘a’ customers and maximum of ‘b’ customers. The service time follows a general (arbitrary) distribution. In addition, the server subject to active breakdown. As soon as the breakdown occurs the server is sent for repair and the customer who was just being served before server breakdown waits for the remaining service to complete. In the proposed model, the transient and steady state results for queue size distribution by applying the supplementary variable technique are derived. Some performance measures, special and particular cases are also discussed. Numerical illustration is provided to see the effect and validity of the results.

Keywords

Bulk service, Unreliable server, Multiple vacation, Restricted admissibility, Mean queue size

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