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Calculation of the Steady State Waiting Time Distribution in GI/PH/c and MAP/PH/c Queues

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References

1953On the distribution of queueing times195 cited
1989Markov processes whose steady state distribution is matrix-exponential with an application to theGI/PH/1 queue108 cited
1992Computational methods in risk theory: A matrix-algorithmic approach86 cited
1986An algorithm for Ph/Ph/c queues85 cited
1992Phase-Type Representations in Random Walk and Queueing Problems84 cited
2000The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution64 cited
1983The queue GI/M/s with customers of different types or the queue GI/Hm/s57 cited
1983The queue GI/M/s with customers of different types or the queue GI/H m /s52 cited
1992On cycle maxima, first passage problems and extreme value theory for queues50 cited
1996Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload47 cited

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2015Beyond the mean in fork-join queues: Efficient approximation for response-time tails32 cited
2006Fundamental characteristics of queues with fluctuating load27 cited
2013Applications in Queueing Theory26 cited
2007Bayesian prediction of the transient behaviour and busy period in short- and long-tailed queueing systems23 cited

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2014Performance evaluation of a multi-product production line: An approximation method17 cited

2008Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods16 cited

2005Solving the ME/ME/1 queue with state–space methods and the matrix sign function16 cited

2006Fundamental characteristics of queues with fluctuating load15 cited