MMBP characterization of the departure process of a discrete-time queue arising in ATM networks

We consider networks of discrete-time finite capacity queues with cell loss. These kind of networks can be used to model the queueing within an ATM switch, or the queueing within a network of ATM switches. These networks do not lend themselves to an exact analysis. However, they can be analyzed approximately using the notion of decomposition. That is, the network is decomposed into individual queues, and each queue is then analyzed separately. The most importance aspect of such a decomposition is the characterization of the arrival process to an intermediate queue. In this thesis the departure process from one queue, which becomes the arrival process to the next downstream queue is characterized approximately by an Markov Modulated Bernoulli Process (MMBP) in order to capture both the burstiness and correlation of the departure process.We first obtain fitting models for characterizing the departure process of an IBP/Geo/1/K queue by an IBP. Their accuracy is examined through extensive validation tests. These fitting models are then used in a decomposition algorithm for the approximate analysis of a tandem queueing network with discrete-time finite capacity queues. Comparisons against simulation showed that the decomposition algorithm has a satisfactory accuracy. Approximation models for characterizing the departure process of an m-MMBP/Geo/1/K queue by an m-MMBP for m The departure process of a D-BMAP/Geo/1/K queue is also considered. We approximate the departure process by a k-MMBP. The tractable fitting model is proposed in order to not only approximate the stationary distribution but also follow the pattern of the autocorrelation coefficients of the interdeparture time. Its accuracy is examined through extensive validation tests.