Limit Theorems for Generalized Single Server Queues. IV. The Case N identically equal to 1 and Applications.
TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES
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The single server queueing system studied in this paper operates as follows. The first customer of each busy period is serviced according to a distribution nu, while all remaining customers of the busy period are serviced according to the distribution nu. Furthermore, the first arrival to the system after the initiation of the busy period occurs at interval distributed as nu, while other arrivals during the busy period occur at intervals distributed as nu. This model is referred to as the exceptional system. For this system the author discusses weak convergence results, and properties of the various weak limits, for the basic processes Wn, n or 0, Wt, t or 0 and Qt, t or 0, where Wn is the waiting time of customer n prior to commencing service, Wt is the workload of the server at time t, and Qt is the number of customers in the system at time t. Using the notion of an exceptional system, the author considers the limiting behavior of two additional variants of the single server queque. Author
- Statistics and Probability