Departures from Many Queues in Series
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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This paper considers a queueing model that could be used to represent the start-up behavior of a long production line or the transient flow of messages over a long path in a communication network. In particular, we consider a series of n single-server queues, each with unlimited waiting space and the first-in first-out service discipline. Initially, the system is empty then k sub n customers are placed in the first queue. The service times of all the customers at all queuses are i.i.d. with a general distribution having mean 1 and finite positive variance delta squared. Our object is to describe the departure process from the n to the th power queue as n gets large. Equivalently, since customers are served in order of arrival, we can consider infinitely many queues in series with infinitely many customers in the first queue we are still interested in the departure times of the first k sub n customers from the n to the th power queue as n yields infinity. We may have k sub n constant, independent of n, or k sub n yields infinity as n yields infinity.
- Operations Research