Multi-Server Queueing Systems with Multiple Priority Classes

Mor Harchol-Balter (), Takayuki Osogami (), Alan Scheller-Wolf () and Adam Wierman ()
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Mor Harchol-Balter: Carnegie Mellon University
Takayuki Osogami: Carnegie Mellon University
Alan Scheller-Wolf: Carnegie Mellon University
Adam Wierman: Carnegie Mellon University

Queueing Systems: Theory and Applications, 2005, vol. 51, issue 3, No 5, 360 pages

Abstract: Abstract We present the first near-exact analysis of an M/PH/k queue with m > 2 preemptive-resume priority classes. Our analysis introduces a new technique, which we refer to as Recursive Dimensionality Reduction (RDR). The key idea in RDR is that the m-dimensionally infinite Markov chain, representing the m class state space, is recursively reduced to a 1-dimensionally infinite Markov chain, that is easily and quickly solved. RDR involves no truncation and results in only small inaccuracy when compared with simulation, for a wide range of loads and variability in the job size distribution. Our analytic methods are then used to derive insights on how multi-server systems with prioritization compare with their single server counterparts with respect to response time. Multi-server systems are also compared with single server systems with respect to the effect of different prioritization schemes—“smart” prioritization (giving priority to the smaller jobs) versus “stupid” prioritization (giving priority to the larger jobs). We also study the effect of approximating m class performance by collapsing the m classes into just two classes.

Keywords: M/GI/k; M/PH/k; multi-server queue; priority queue; matrix analytic methods; busy periods; multi-class queue; server farm; preemptive priority (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11134-005-2898-7

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