Sojourn Times In Queues Research Articles

Alternating server with non-zero switch-over times and opposite-queue threshold-based switching policy

A single server alternates between two Markovian queues with non-zero switch-over times. The server’s switching instants are determined by the number of customers accumulated at the unattended queue. Specifically, when queue i(i=1,2) is attended and the number of customers in queue j(j=1,2;j≠i) reaches a threshold, the server starts an exponentially distributed switch-over time to queue j, unless the number of customers in queue i is equal to or above queue i’s threshold. However, if during a switch-over period from queue i to queue j the former reaches its threshold, the switch-over is aborted, and the server immediately returns to queue i and continues to serve the customers there. We analyze the system mainly via Matrix Geometric (MG) methods while deriving explicitly the rate matrix R, and thus eliminating the need for successive substitutions. We further reveal connections between the entries of R and the roots of polynomials related to the Probability Generating Functions (PGFs) of the system states. Expressions for the system’s performance measures are obtained (e.g. mean queue size and mean sojourn time in queue 1, PGF and mean of the queue size in queue 2, as well as the Laplace Stieltjes transform and mean of the sojourn time in queue 2). Numerical results are presented and the effects of the various parameters, as well as the switch-over times, on the performance measures are examined. Seemingly counter-intuitive phenomena are discussed. Finally, various extreme cases are investigated.

Mean sojourn times in two-queue fork-join systems: bounds and approximations

This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the ‘system’s sojourn time’ S: with S i denoting a job’s sojourn time in queue i, S is defined as max{S 1, S 2}. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number of approximations, that are extensively tested by simulation and turn out to perform remarkably well.

Sojourn times in queues with instantaneous tri-route decision process

In this paper, we study the total sojourn time in a queueing system with an instantaneous tri-route decision process. Even though the computations are more difficult, we give here the structure of the sojourn time process for the M/ G/1 queue with tri-route decision process. A numerical study is carried out in this paper.

Sojourn times in queues with a pair of instantaneous independent bernoulli feedback

In this paper we study the total sojourn time in a queueing system with a pair of instantaneous independent Bernoulli feedback processes. As the details of the computations are difficult, we give only the structure of the sojourn time process for the M/G2/l queue with a pair of Bernoulli feedback. We have also carried out a numerical study in this paper