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 γT 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.