Variable length packet switches: delay analysis of crossbar switches under Poisson and self similar traffic

We consider crossbar switches for switching variable length packets. Analysis of such switches is important in the context of IP switches where the packet interarrival times and packet lengths are drawn from continuous distributions. Assuming a single stage M×N switch we obtain a very general throughput delay model for Poisson packet arrivals and exponential service times. We then analyze an M×N switch for self similar packet arrivals and exponential packet lengths. An MMPP (Markov modulated Poisson process) based self similar arrival process model corresponding to the arrival rate, the autocorrelation, the Hurst parameter and the time scales over which burstiness exists in the input process is first obtained using results from Andersen and Nielsen (1998). We then use queuing theory available for MMPP/G/1 queues to model the switch performance for self similar packet arrivals. The results from the analytical model are compared against those from a simulation model that is driven by traces that are statistically similar to the Bellcore traces. We also analyse the effect of link multiplicities (speedup) to the output and asymmetries in the input traffic