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Open AccessArticle

Continuous-Service M/M/1 Queuing Systems

Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA
Appl. Syst. Innov. 2019, 2(2), 16; https://doi.org/10.3390/asi2020016
Received: 29 March 2019 / Revised: 24 April 2019 / Accepted: 24 April 2019 / Published: 28 April 2019
In this paper, we look into a novel notion of the standard M/M/1 queueing system. In our study, we assume that there is a single server and that there are two types of customers: real and imaginary customers. Real customers are regular customers arriving into our queueing system in accordance with a Poisson process. There exist infinitely many imaginary customers residing in the system. Real customers have service priority over imaginary customers. Thus, the server always serves real (regular) customers one by one if there are real customers present in the system. After serving all real customers, the server immediately serves, one at a time, imaginary customers residing in the system. A newly arriving real customer presumably does not preempt the service of an imaginary customer and hence must wait in the queue for their service. The server immediately serves a waiting real customer upon service completion of the imaginary customer currently under service. All service times are identically, independently, and exponentially distributed. Since our systems are characterized by continuous service by the server, we dub our systems continuous-service M/M/1 queueing systems. We conduct the steady-state analysis and determine common performance measures of our systems. In addition, we carry out simulation experiments to verify our results. We compare our results to that of the standard M/M/1 queueing system, and draw interesting conclusions. View Full-Text
Keywords: queueing systems; simulation; operations research; optimization queueing systems; simulation; operations research; optimization
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Chew, S. Continuous-Service M/M/1 Queuing Systems. Appl. Syst. Innov. 2019, 2, 16.

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