Multiprocessor systems with preemptive priorities

Mitrani, Isi; King, Peter J. B.

doi:10.1016/0166-5316(81)90014-6

Cited by 57 publications

(27 citation statements)

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“…The only papers not restricted to two priority classes are coarse approximations based on assuming that the multi-server behavior is related to that of a single server system [2] or approximations based on aggregating the many priority classes into two classes [19,22].…”

Section: Prior Workmentioning

confidence: 99%

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Multi-Server Queueing Systems with Multiple Priority Classes

et al. 2005

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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 results 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, preemptive priority.

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Section: Prior Workmentioning

confidence: 99%

“…In general these yield complicated mathematical expressions susceptible to numerical instabilities at higher loads. See King and Mitrani [19]; Gail, Hantler, and Taylor [8,9]; Feng, Kowada, and Adachi [7]; and Kao and Wilson [11].…”

Section: Two Priority Classesmentioning

confidence: 99%

Multi-Server Queueing Systems with Multiple Priority Classes

et al. 2005

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“…The first-passage probabilities f 3;i 2 ,i 1 can be recursively calculated using the equations (20), starting with f 3;0,i 1 = g 3;i 1 . The last two terms in (20) need some explanation: this is the probability of first passage to class-2 levels less than or equal to q 2 + i 2 in state (0, q 2 + i 2 , q 1 + i 1 ) when starting an excursion in state (2, q 2 , q 1 ), so with two instead of one class-3 customer.…”

Section: Three-class Systemmentioning

confidence: 99%

“…This is feasible, since the order in which the customers are served does not alter the duration of a high-priority busy period, cf. (20). The remaining first-passage probabilities for the case n = 1 are computed as, for k ≥ 2,…”

Section: N-class Systemmentioning

confidence: 99%

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Joint queue length distribution of multi-class, single-server queues with preemptive priorities

et al. 2015

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In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments, we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an M/M/1 queueing system with non-preemptive priorities between customer classes.

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