Technical Report CS0374

Title: Queueing Systems with a Procrastinating Server
Authors: Micha Hofri
Abstract: Two related problems are analyzed and discussed:

a) 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.

b) 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 mi.

The treatment combines analytic and numerical methods. Only steady-state results are presented.

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