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Nelson, R. (1995) Probability, Stochastic Processes and Queueing Theory. Springer-Verlag New York, Inc.

has been cited by the following article:

  • TITLE: Minimizing the Loss Probability in M/M/2/1 Queueing System with Ordered Entry

    AUTHORS: Eman Ahmed Kamel

    KEYWORDS: Loss Probability, Heterogeneous Servers, Semi-Markov Process, Laplace-Stieltjes Transform

    JOURNAL NAME: American Journal of Operations Research, Vol.8 No.1, January 17, 2018

    ABSTRACT: This study analyzed the M/M/2/1 queueing model with queue of length one (waiting room of capacity just one), heterogeneous servers and ordered entry using the method of semi-Markov process. The customers who arrive in the system enter the free server; if the two servers are free, the customers enter the first server. If the two servers are busy, just one customer can wait at the waiting room. If the two servers are busy and the waiting room has a customer, the following customers will leave the system without receiving any service. Such a customer is called LOST COSTOMER. The probability of lost customers in the queueing system under examination was computed. Furthermore, by using inequality obtained from Jensen’s inequality, it was shown that the loss probability was minimum when inter-arrival times fit deterministic distribution [1] [2].