Abstract
For the M/G/1 model, we look into a preemptive priority scheme in which the priority level is decided by a lottery. Such a scheme has no effect on the mean waiting time in the non-preemptive case (in comparison with the First Come First Served (FCFS) regime, for example). This is not the case when priority comes with preemption. We derived the resulting mean waiting time (which is invariant with respect to the lottery performed) and show that it lies between the corresponding means under the FCFS and the Last Come First Served with Preemption Resume (LCFS-PR) (or equivalently, the Egalitarian Processor Sharing (EPS)) schemes. We also derive an expression for the Laplace-Stieltjes transform for the time in the system in this model. Finally, we show how this priority scheme may lead to an improvement in the utilization of the server when customer decide whether or not to join.
Highlights
The M/G/1 queueing model is one of the most researched model in operations research and in the performance evaluation area of computer sciences
Two other well-known service regimes are that of Last Come First Served with Preemption Resume (LCFS-PR) and Egalitarian Processor Sharing (EPS)
Under the EPS regime, the server splits its service capacity evenly among all those who are present in the system at any given time instant
Summary
The M/G/1 queueing model is one of the most researched model in operations research and in the performance evaluation area of computer sciences. Minding the trade-off between length of wait and the level of payment, and noticing that other customers face a similar dilemma, their equilibrium behavior is to pay a random amount (having some specific distribution) resulting overall in the PRP regime. In the latter model some will opt out and, interestingly, in the case of an exponential service time (i.e., an M/M/1 model), the fraction of those who join coincide with the socially optimal joining rate. The reader is referred to Part VII of [3] for a comprehensive summary on various queueing regimes
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