Steady-state Waiting Time Distribution Research Articles

A generalized pollaczek-khinchine formula for the gi/gi/1/k queue and its application to approximation

This paper deals with the steady-state waiting time distribution in the GI/GI/1/k {GI/GI/1 with k waiting places) queue. Marshall[8]'s generalized Pollaczek-Khinchine formula is generalized to the GI/GI/1/k model. From the resulting formulas, we obtain approximation formulas for the waiting time distribution and for the probabilities of the system being empty and of customer loss. The quality of those approximations is shown by numerical examples.

On an exponential server with general cyclic arrivals

A E n¦ M ¦ 1 queue is defined as a single server queue with exponential service time and general cyclic arrival distributions of cycle length n. The waiting time distribution for such a queue is proved to be a sum of n exponential terms; this is a generalization of G ¦ M ¦ 1 queue results. Based on this a method for obtaining the steady-state waiting time distributions for E n¦ M ¦ 1 queues is introduced. An example is presented to show an application of E n¦ M ¦ 1 queues in deterministic routing.

Comparison of Two Scheduling Systems

The delays that outpatients have to undergo before getting their medical treatment are often excessively long. The most commonly used patterns of scheduling appointments to patients are classified into three categories: (1) Pure Block Appointment systems, (2) Individual Appointment Systems, and (3) Mixed Block-Individual Appointment Systems. Several analytical studies have been concerned with the comparison of some of these appointment systems, and their highlights are described briefly. There are many other possible ways of assigning appointments to patients; one such way, referred to as the Two-at-a-Time Appointment System, is described. The advantages of the Two-at-a-Time Appointment System over any of the commonly used ones are discussed. Finally, the steady-state waiting time distribution functions that will correspond to the Two-at-a-Time Appointment System and the Individual Appointment System, as applied to the Wilmer Outpatient Clinic, have been obtained and are compared.