A Markov-modulated M/G/1 queue I: Stationary distribution

Knessl, Charles; Matkowsky, B. J.; Schuss, Z.; Tier, Charles

doi:10.1007/bf01150670

Cited by 14 publications

(2 citation statements)

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“…The evaluation of performance measures in stochastic models is a key problem that has been widely studied in the literature [1,8,19,35]. In this paper, we focus on the evaluation of the workload distribution of a single server queue where customers arrive according to a Markovian Arrival Process (MAP) [9,25] and their service times follow some general distribution.…”

Section: Introductionmentioning

confidence: 99%

Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment

et al. 2014

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2 We develop accurate approximations for the delay distribution of the MArP/G/1 queue that capture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.

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Section: Introductionmentioning

confidence: 99%

Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment

et al. 2014

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“…Through the BAR, we find the first moment of the stationary distribution, and when the service times are exponentially distributed, we find formulas for all the moments. Knessl et al [26] considered a more general state-dependent M͞G͞1, and an asymptotic method employing singular perturbation is proposed to approximate the stationary distribution of the workload process. Bambos and Walrand [5] and Browne and Sigman [8] studied the conditions under which the workload process in a state-dependent queue is positive recurrent.…”

Section: Introductionmentioning

confidence: 99%