Analysis of a dynamic assignment queueing model with Poisson cluster arrival processes

We consider a dynamic assignment queueing model with multiple packet classes, which has a number of queues, each with its own server. This model arises from the output buffer control of an ATM-based packet switching system, which is connected to another system via multiple links. Each packet is divided into cells and transmitted by cell-by-cell transmission through the links. Such packet arrival processes can be modeled as Poisson cluster arrival processes. An arriving packet is assigned to one of the queues according to a dynamic packet assignment scheme, which is a variation of the shortest queue policy and tries to assign buffer space and/or transmission bandwidth fairly to each class when the system is congested. We derive an approximation of the packet loss probability by using a decomposition method and an asymptotic of the cell loss probability. Its accuracy is examined in comparison with simulation results. The results of this paper can be used for dimensioning the buffer sizes of the ATM-based packet switching systems.