Non-Markovian bulk queueing system with state dependent arrivals and multiple vacations -- a simulation approach (Q1635405)

Summary: 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 \(\lambda\), when the server is busy and with a rate \(\lambda_0\), 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\(^{\mathrm{x}}\)/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.