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].