Vol. 6 No. 1 (2022): Special Issue in Honor of Professor Ravi P. Agarwal
Articles

Analysis of a single server serving three queues m[x 1 ] /g1/1, m[x 2 ] /g2/1 , m[x 3 ] /g3/1 with priority services, working breakdown, modified bernoulli vacation

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  • GEETHA PRIYA K,
  • FRANCIS RAJ L
GEETHA PRIYA K
Assistant Professor in Mathematics, D.K.M. College for Women,Vellore-1.
FRANCIS RAJ L
Assistant Professor and Guide, P.G and Research Department of Mathematics, Voorhees College, Vellore-1.
DOI: https://doi.org/10.26524/cm130
Published March 25, 2022
Keywords
  • Preemptive priority queueing systems , modified Bernoulli vacation, working breakdown, supplementary variable technique.
How to Cite
K, G. P., & L, F. R. (2022). Analysis of a single server serving three queues m[x 1 ] /g1/1, m[x 2 ] /g2/1 , m[x 3 ] /g3/1 with priority services, working breakdown, modified bernoulli vacation. Journal of Computational Mathematica, 6(1), 210 - 221. https://doi.org/10.26524/cm130

Abstract

In this paper considers M[X1]/G1/1, M[X2]/G2/1 , M[X3]/G3/1 general queueing system with priority services . Three types of customers from different classes arrive at the system in different independent Poisson process. The server follows the non preemptive priority rule subject to working breakdown, and modified Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there is no high priority customers present in the system. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained. Also the average number of customer in the priority and non priority, preemptive priority queue and the average waiting time are derived.

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