Non-Markovian bulk queueing system with state dependent arrivals and multiple vacations - a simulation approach

K.S. Ramaswami and S. Jeyakumar

International Journal of Mathematics in Operational Research, 2014, vol. 6, issue 3, 344-356

Abstract: We considered a non-Markovian bulk arrival general bulk service queueing system with state dependent arrivals and multiple vacations in this paper. The arrivals occur in bulk with a rate λ, when the server is busy and with a rate λ₀, when the server is on vacation. Using a supplementary variable technique and difference differential equations method we derive the queue size distribution, expected length of idle and busy periods and expected queue size of a M^x/G(a, b)/1 queueing system with state dependent arrivals and multiple vacations. We study the same through simulation using ARENA, a powerful manufacturing system simulation software and obtained some performance measures, which are mandatory for the study and analysis of the said queueing model. The simulated results for a few cases are presented.

Keywords: fast arrivals; slow arrivals; bulk service; simulation; supplementary variables; bulk queueing; state dependent arrivals; multiple vacations; simulation; queue size. (search for similar items in EconPapers)
Date: 2014
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