Two-dimensional queueing model for a LAN gateway

Authors:
Hamed Nassar
Affiliations:
Suez Canal University, Department of Computer Science, Ismailia, Egypt
Venue:
ICCOM'06 Proceedings of the 10th WSEAS international conference on Communications
Year:
2006

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Abstract

In this article, we present a queueing model for a gateway linking two Ethernet-type LANs. Each LAN is assumed to be slotted and have a single-channel allowing for the transmission of only one packet at a time. It turns out that the gateway presents an interesting queueing model not widely seen in the literature. In particular, the model has two interfering, parallel, and back-to-back queues. The model is used to study the gateway occupancy. To this end, a state transition diagram is constructed and then used to extract a two-dimensional, second order difference equation, with eight boundary conditions characterizing the gateway dynamics. A probability generating function (PGF) technique is used to solve the difference equation, resulting in a rather challenging functional equation defining a two-dimensional PGF of the joint gateway occupancy distribution. Pointers are given on the techniques available in the literature to solve the equation and obtain the distribution.