Abstract
In this paper, we obtain strong approximation theorems for a single server queue withr priority classes of customers and a head-of-the-line-first discipline. By using priority queues of preemptive-resume discipline as modified systems, we prove strong approximation theorems for the number of customers of each priority in the system at timet, the number of customers of each priority that have departed in the interval [0,t], the work load in service time of each priority class facing the server at timet, and the accumulated time in [0,t] during which there are neither customers of a given priority class nor customers of priority higher than that in the system.
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Research supported by the National Natural Science Foundation of China.
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Zhang, HQ., Hsu, GH. Strong approximations for priority queues; head-of-the-line-first discipline. Queueing Syst 10, 213–233 (1992). https://doi.org/10.1007/BF01159207
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DOI: https://doi.org/10.1007/BF01159207