On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in This work has been carried out partly in the Dutch BSIK/BRICKS project. I. Adan ( ) Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands e-mail: [email protected] I. Adan · M. Mandjes · E. Tzenova Eurandom, P.O. Box 513, 5600 MB Eindhoven, The Netherlands M. Mandjes Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands e-mail: [email protected] M. Mandjes · W. Scheinhardt CWI, Amsterdam, The Netherlands W. Scheinhardt Faculty of Electrical Engineering, Mathematics, and Computer Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands e-mail: [email protected] 38 Queueing Syst (2009) 61: 37–63 which it explicitly does. This dichotomy can be understood by using large-deviations heuristics.