Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues

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Cheung, Sing-Kong and Berg van den, Hans and Boucherie, Richard J. (2005) Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues. Performance Evaluation, 62 (1-4). pp. 100-116. ISSN 0166-5316

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Abstract:We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for multi-class egalitarian PS queues, we show that the marginal queue length distribution for each class equals the queue length distribution of an equivalent single class PS model with a random number of permanent customers. Similarly, the mean sojourn time (conditioned on the initial service requirement) for each class can be obtained by conditioning on the number of permanent customers. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian PS models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights. (Keywords: Processor-sharing queues; Queue length; Decomposition; Permanent customers; Approximation; Generalized discriminatory processor-sharing)
Item Type:Article
Copyright:© 2005 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65584
Official URL:http://dx.doi.org/10.1016/j.peva.2005.07.009
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