The Stationary Distribution of the M/M/1 Queue with Batch Reneging Triggered by Line Cutting
Keywords:
Foster’s criterion, M/M/1 queue, priority queue, reneging, stationary distribution.Abstract
We consider an extension of the M/M/1 queue where customers join the queue at
uniformly random positions upon arrival. Immediately after, each customer who has been
skipped over by a new arrival (or ‘cut’) leaves independently with the same probability. We
provide necessary and sufficient criteria for stability, as well as closed-form stationary results
for special cases, and an approximation method for the general case. We compare limiting
distribution simulation output with the approximations for the general case.
