Analysis of priority queues with session-based arrival streams

In this paper, we analyze a discrete-time priority queue with session-based arrivals. We consider a user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over the packets of the other class. The model is motivated by a web server handling delay-sensitive and delay-insensitive content. By using probability generating functions, some performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is shown by some numerical examples

Transient Analysis of Two- Class Priority Queuing System

A transient solution of Two-class priority queuing system was discussed in this paper, the first class with high priority and the second one with low priority and the capacity of the system is infinite. Various performance measures are examined. Some numerical analyses are discussed and some special cases are deduced and confirmed the results

Sample-path large deviations for tandem and priority queues with Gaussian inputs

This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower bound on the exponential decay rate of this overflow probability and present an explicit condition for the lower bound to match the exact decay rate. Examples show that this condition holds for a broad range of frequently used Gaussian inputs. The last part of the paper concentrates on a model for a single node, equipped with a priority scheduling policy. We show that the analysis of the tandem queue directly carries over to this priority queueing system.Comment: Published at http://dx.doi.org/10.1214/105051605000000133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transient bayesian inference for short and long-tailed GI/G/1 queueing systems

In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues