Explicit formulas for the steady-state probabilities of the two-class FIFO M/M/1 queue

Konferenz: MMB 2006 - 13th GI/ITG Conference Measuring, Modelling and Evaluation of Computer and Communication Systems
27.03.2006 - 29.03.2006 in Nürnberg, Germany

Tagungsband: MMB 2006

Seiten: 12Sprache: EnglischTyp: PDF

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Ny, Louis-Marie Le (Irisa, University of Rennes, Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France)

In this paper, we consider a queue with two classes of customers and a FIFO-single server. Class-i (i = 1,2) customers arrive according to a Poisson process with rate λ i; there is no priority between the two classes. The service of class-i (i = 1,2) customers is exponential with rate μ i. Exact formulas are proven for the stationary probability of each ordered state and the steady-state distribution of the number (total or per class) of customers in the queue.