Burst ratio for a versatile traffic model

Abstract

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.

Impact of the Dropping Function on Clustering of Packet Losses

“…This phenomenon was confirmed by direct measurements in a lab and in a real network, [ 2 , 3 ]. It was also explained theoretically, by the derivation of the burst ratio for tail-drop queueing models with various arrival stream types [ 20 , 21 , 22 ]. It is equally easy to understand why the dropping function mechanism can decrease the burst ratio.…”

“…Therefore, to obtain precise results, we have to to use the general distribution of the interarival time, as stated here. Other previous studies on the burst ratio, e.g., [ 20 , 21 , 22 , 24 , 25 ], do not incorporate the dropping function, which is the crucial component herein.…”