Burst ratio for a versatile traffic model

by Andrzej Chydzinski

We deal with a finite-buffer queue, in which arriving jobs are subject to loss due to buffer overflows. The burst ratio parameter, which reflects the tendency of losses to form long series, is studied in detail. Perhaps the most versatile model of the arrival stream is used, i.e. the batch Markovian arrival process (BMAP). Among other things, it enables modeling the interarrival time density function, the interarrival time autocorrelation function and batch arrivals. The main contribution in an exact formula for the burst ratio in a queue with BMAP arrivals and arbitrary service time distribution. The formula is presented in an explicite, ready-to-use form. Additionally, the impact of various system parameters on the burst ratio is demonstrated in numerical examples. The primary application area of the results is computer networking, where the complex nature of traffic has a deep impact on the burst ratio. However, due to the versatile arrival model, the results can be applied in other fields as well.