Workload in queues having priorities assigned according to service time |
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Authors: | Peter C Kiessler M A Wortman |
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Institution: | (1) Department of Mathematical Sciences, Clemson University, 29634-1907 Clemson, SC, USA;(2) Department of Industrial Engineering, Texas A&M University, 77843-3131 College Station, TX, USA |
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Abstract: | System designers often implement priority queueing disciplines in order to improve overall system performance; however, improvement is often gained at the expense of lower priority cystomers. Shortest Processing Time is an example of a priority discipline wherein lower priority customers may suffer very long waiting times when compared to their waiting times under a democratic service discipline. In what follows, we shall investigate a queueing system where customers are divided into a finitie number of priority classes according to their service times.We develop the multivariate generating function characterizing the joint workload among the priority classes. First moments obtained from the generating function yield traffic intensities for each priority class. Second moments address expected workloads, in particular, we obtain simple Pollaczek-Khinchine type formulae for the classes. Higher moments address variance and covariance among the workloads of the priority classes.This work was supported in part by National Science Foundation Grant DDM-8913658. |
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Keywords: | Priority queues scheduling semi-martingales Palm measures |
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