On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers

P.H. Brill, M.L. Huang and M. Hlynka

European Journal of Operational Research, 2020, vol. 283, issue 1, 235-243

Abstract: We consider an M/G/1 queue with a workload barrier at finite level K > 0. Arriving customers are accepted into the system only if their waiting time plus service time does not exceed K; otherwise they are blocked and cleared immediately. This ‘accept/block’ regulation causes the pre-arrival ‘prior’ pdf (probability density function) of service time for all arrivals, to transform into the pdf of the ‘posterior’ service time reflecting the effect of the barrier at level K on both accepted and blocked customers. We derive the pdf of the posterior service time, its expected value, the expected numbers of customers accepted or blocked in a busy cycle, and a specific value of K which is greater than the median of the prior pdf, where equal expected numbers of customers are accepted and blocked in a busy cycle. We propose an expression for distance, to measure the discrepancy between the posterior and prior pdfs. Examples are given. This service-time viewpoint is of theoretical interest, and has potential applications in various related stochastic models.

Keywords: Queueing; Workload barrier; Prior and posterior service times; Distance between distributions; Level crossing method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:283:y:2020:i:1:p:235-243

DOI: 10.1016/j.ejor.2019.10.028

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