How Large Delays Build Up in a GI/G/1 Queue

Representing Workloads in GI/G/1 Queues Through the Preemptive-Resume LIFO Queue Discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: We study the long-run “state” behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, tog...

Error Bounds for Perturbing Nonexponential Queues

A general framework is provided to derive analytic error bounds for the effect of perturbations and inaccuracies of nonexponential service or arrival distributions in singleand multi-server queues. The general framework is worked out in detail for the three types of finite or infinite buffer queues: GI/G/1/N , M/G/c/N , and GI/M/c/N . First, for the standard GI/G/1/N queue, it is illustrated ho...

Mean Time for the Development of Largeworkloads and Large Queue Lengths in the Gi/g/1 Queue

We consider the GI/G/1 queue described by either the workload (unfinished work) or the number of customers in the system. We compute the mean time until reaches or exceeds the level , and also the mean time until reaches 0. For the M/G/1 and GI/M/1 models, we obtain exact contour integral representations for these mean first passage times. We then compute the mean times asymptotically, as and 0...

A Fluid Model for the Many-Server Gt/GI/st +GI Queue

In a recent paper we introduced and analyzed a deterministic GIt/M/st + GI fluid modelthat can be used to show how queue lengths and waiting times depend on model parameters ina large-scale queueing system that experiences periods of overloading. The main feature of themodel is time-varying arrival rate and staffing, but the model also includes the realistic feature of anon-expo...

HOW LARGE DELAYS BULD UP IN A GIiGil QUEUE