IoT 15(3): e1

Research Article

The M/G/1 queueing model with preemptive random priorities

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  • @ARTICLE{10.4108/icst.valuetools.2014.258240,
        author={Moshe Haviv},
        title={The M/G/1 queueing model with preemptive random priorities},
        journal={EAI Endorsed Transactions on Internet of Things},
        volume={1},
        number={3},
        publisher={EAI},
        journal_a={IOT},
        year={2015},
        month={2},
        keywords={priority queues, preemption, performance evaluation},
        doi={10.4108/icst.valuetools.2014.258240}
    }
    
  • Moshe Haviv
    Year: 2015
    The M/G/1 queueing model with preemptive random priorities
    IOT
    EAI
    DOI: 10.4108/icst.valuetools.2014.258240
Moshe Haviv1,*
  • 1: The Hebrew University of Jerusalem
*Contact email: moshe.haviv@gmail.com

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.