Efficient simulation of a queueing system fed by general on/off inputs

We study a discrete-time system consisting of N independent queues sharing a common server of fixed capacity. Each queue is fed by an on/off packet flow. Flows are i.i.d. with generally distributed on and off-periods. In particular this allows us to deal with power-law distributed periods, which are commonly used to model the size of files in the Internet. Known results for such a system are only asymptotic. Simulations are the only means of capturing the entire distribution of a generic queue. When N is large (e.g. more than 1,000), simulations may require excessive computational efforts. In order to overcome this drawback we present an innovative algorithm, which is shown to be accurate and computationally efficient. This algorithm follows an iterative procedure fixed-point basis. It simulates one queue only, served at a non-constant rate which is determined by the state of the other queues - the interfering system. We applied the algorithm to the system described above, assuming that the scheduling discipline treats all the queues equally, e.g. a round robin. The correctness of our approach is confirmed through comparison with known asymptotic results. A practical example of its use is provided, i.e. the evaluation of the capacity of an access system in the framework of the IST European project EMBRACE (Efficient Millimeter Broadband Radio Access for Convergence and Evolution).