Queueing systems with a procrastinating server

Abstract

Two related problems are analyzed and discussed: A queueing system that differs from the standard M/G/1 only in that at the end of a busy-period the server takes a sequence of vacations, inspecting the state of the queue at the end of each. When the length of the queue exceeds a predetermined level m it returns to serve the queue exhaustively. Two queues, with Poisson arrivals and general service-time distributions are attended by a single server. When the server is positioned at a certain queue it will serve the latter exhaustively, and at busy-period end will only switch to the other if the queue length there exceeds in size a predetermined threshold m i . The treatment combines analytic and numerical methods. Only steady-state results are presented.