Time-dependent analysis of an M / M / c preemptive priority system with two priority classes

Jori Selen () and Brian Fralix
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Jori Selen: Eindhoven University of Technology
Brian Fralix: Clemson University

Queueing Systems: Theory and Applications, 2017, vol. 87, issue 3, No 8, 379-415

Abstract: Abstract We analyze the time-dependent behavior of an M / M / c priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace transforms of the transition functions when the system is initially empty. The Laplace transforms corresponding to states with at least c high-priority customers are expressed explicitly in terms of the Laplace transforms corresponding to states with at most $$c - 1$$ c - 1 high-priority customers. We then show how to compute the remaining Laplace transforms recursively, by making use of a variant of Ramaswami’s formula from the theory of M / G / 1-type Markov processes. While the primary focus of our work is on deriving Laplace transforms of transition functions, analogous results can be derived for the stationary distribution; these results seem to yield the most explicit expressions known to date.

Keywords: Static priority; Time-dependent analysis; Laplace transforms; Multi-dimensional Markov process; 60J27; 60J35; 60K25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-017-9541-2

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