137 research outputs found
Moments of Conditional Sojourn Times in Finite Capacity M/M/1/N-PS Processor Sharing Queues
Cataloged from PDF version of article.Moments of sojourn times conditioned on the length
of an admitted job are derived for a finite capacity M/M/1/NPS
processor sharing queue. The mean conditional sojourn time
is given in closed form whereas an expression is provided for
the conditional variance in such systems involving matrix-vector
operations
Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues
We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for an egalitarian PS queue with customer classes, we show that the marginal queue length distribution for class factorizes over the number of other customer types. The factorizing coefficients equal the queue length probabilities of a PS queue for type in isolation, in which the customers of the other types reside \textit{ permanently} in the system. Similarly, the (conditional) mean sojourn time for class can be obtained by conditioning on the number of permanent customers of the other types. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian processor-sharing 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. \u
On Sojourn Times in the Finite Capacity Queue with Processor Sharing
We consider a processor shared queue that can accommodate at most a
finite number of customers. We give an exact expression for the sojourn
time distribution in the finite capacity model, in terms of a Laplace
transform. We then give the tail behavior, for the limit , by
locating the dominant singularity of the Laplace transform.Comment: 10 page
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