A discrete-time queueing model with periodically scheduled arrival and departure slots

Authors:
Johan van Leeuwaarden;Dee Denteneer;Jacques Resing
Affiliations:
EURANDOM, MB Eindhoven, The Netherlands;Digital Signal Processing Group, Philips Research, AA Eindhoven, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, MB Eindhoven, The Netherlands
Venue:
Performance Evaluation
Year:
2006

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Abstract

We consider a time-slotted queueing model where each time slot can either be an arrival slot, in which new packets arrive, or a departure slot, in which packets are transmitted and hence depart from the queue. The slot scheduling strategy we consider describes periodically, and for a fixed number of time slots, which slots are arrival and departure slots. We consider a static and a dynamic strategy. For both strategies, we obtain expressions for the probability generating function of the steady-state queue length and the packet delay. The model is motivated by cable-access networks, which are often regulated by a request-grant procedure in which actual data transmission is preceded by a reservation procedure. Time slots can then either be used for reservation or for data transmission.