The Variance of the Number of Customers in a Queue

Voorkant
University of California, Berkeley, 1970 - 76 pagina's
A queueing system is considered for which the arrival process is stationary and has the orderliness property, and for which the queue discipline is first-in-first-out. If, for all t> s> tau, the waiting time of a customer who arrives at time tau and the number of customers who arrive in the interval (s, t) are independent, then the steady state variance of the queue size is obtained in terms of the stationary waiting time distribution. It is shown that the steady state variance of the queue size is equal to the variance of the number of customers who arrive during a time interval w sub q, a random variable, distributed as stationary waiting time. For the situation of infinite channel queues, a formula for the variance of the number of customers in the system is obtained (without any assumption about the arrival process). This formula is specialized to the case where the customers arrive in batches and arrival of batches forms a stationary batch arrival process. (Author).

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