Explicit formulas for the steady-state probabilities of the two-class FIFO M/M/1 queue
Conference: MMB 2006 - 13th GI/ITG Conference Measuring, Modelling and Evaluation of Computer and Communication Systems
03/27/2006 - 03/29/2006 at Nürnberg, Germany
Proceedings: MMB 2006
Pages: 12Language: englishTyp: PDFPersonal VDE Members are entitled to a 10% discount on this title
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.