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Journals ACM SIGMETRICS Performance Evaluation Review Volume 29 Issue 3

Simulating Tail Probabilities in GI/GI/1 Queues and Insurance Risk Processes with Subexponential Distributions (Extended Abstract) Nam Kyoo Boots 1 Perwez Shahabuddin 2 This study deals with estimating tail probabilities of the steady-state waiting-time random variable in a GI/GI/1 queue with heavy-tailed service times. In particular, if W is the steady-state waiting-time random variable, then the problem is to estimate P(W > u) where z~ is large. The GI/GI/1 queue is strongly related to the single-source fluid queue. This is a buffer with a constant out-flow rate and fed by a fluid source which alternates between the onstate and the off-state. In the on-state, the source sends fluid into the queue at a certain fixed rate. Assume the times in the on-state to be subexponentially distributed and the times in the off-state to be generally distributed. Then with proper re-interpretation, the techniques in this study can be used to estimate the steady-state probability that the buffer content in the fluid queue exceeds u at the beginning of an on-period. Problems like estimating P(W > u) for the GI/GI/1 queue for large u and the above measure for fluid queues, arise, for example, while estimating probabilities of extreme delays and

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Simulating tail probabilities in GI/GI/1 queues and insurance risk processes with subexponential distributions (extended abstract)

Boots, Nam Kyoo; Shahabuddin, Perwez
ACM SIGMETRICS Performance Evaluation Review , Volume 29 (3)
Association for Computing Machinery – Dec 1, 2001

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