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November 2014 Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions
S. Maragatha Sundari, S. Srinivasan, A. Ranjitham
Missouri J. Math. Sci. 26(2): 189-205 (November 2014). DOI: 10.35834/mjms/1418931959


We study a batch arrival queueing system of phase vacation with two stages of service based on a Bernoulli schedule. A single server provides essential service to all arriving customers with service time following a general distribution. After two stages of service completion, the server leaves for phase one vacation of random length with probability $p$ or to continue staying in the system with probability $1-p$. As soon as the completion of phase one vacation, the server undergoes phase two vacation. On completion of two heterogeneous phases of vacation the server returns back to the system. The vacation times are assumed to be general. The server is interrupted and the service interruption follows an exponential distribution. The arrivals follow a Poisson distribution. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived. From this we deduce the steady state results. We also obtain the average queue size and average waiting time.


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S. Maragatha Sundari. S. Srinivasan. A. Ranjitham. "Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions." Missouri J. Math. Sci. 26 (2) 189 - 205, November 2014.


Published: November 2014
First available in Project Euclid: 18 December 2014

zbMATH: 1311.60107
MathSciNet: MR3293815
Digital Object Identifier: 10.35834/mjms/1418931959

Primary: 60K25
Secondary: 60K30

Keywords: batch arrival , Bernoulli schedule , queue size , random breakdown , steady state

Rights: Copyright © 2014 Central Missouri State University, Department of Mathematics and Computer Science


Vol.26 • No. 2 • November 2014
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