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Light Traffic Approximations in Queues

For a stationary waiting time random variable W ≡ W ( S , T ) in a GI / G /1 queueing system with generic service and inter-arrival time random variables S and T respectively, with ES < ET , performance characteristics including Pr{ W > 0} and EW are studied in light traffic conditions. One way of attaining these conditions, as considered in a previous paper, is to replace T by γ T for large γ; another way is to thin the arrival process with small but positive retention probability π. These two approaches are compared, the thinning approach being applied to queues with either a renewal or a periodic Poisson arrival process. Results are also given for GI / M / k and GI / D / k queues. The variety of queueing systems studied is reflected in the different behaviour both of the quantities calculated directly and of the derived quantity E ( W | W > 0). The dominant feature of light traffic characteristics is their dependence on the clustering tendency and related properties of the arrival process. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics of Operations Research INFORMS
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