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

摘要

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 λ_0, 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.