Limit Theorems for Generalized Single Server Queues. II. Cumulative Processes and Extreme Values.
TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES
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The paper is a sequel to a previous paper by the present author in which the limiting behavior of various stochastic processes arising from a generalized single server queueing system was studied. In this generalized system the first N customers of each busy period N random experience service times drawn from distributions u11,...,uN1, respectively, while all remaining customers of the busy period, if any, are serviced according to the distribution u01. Furthermore, the first N arrivals to the system, if any, after the initiation of the busy period occur at intervals drawn from distributions u12,...,uN2, respectively, while other arrivals, if any, during the busy period occur at intervals distributed as u02. This model is quite general.
- Operations Research