Burst ratio in the finite-buffer queue with batch Poisson arrivals

Abstract

We study the burst ratio in the queueing system with finite buffer and batch arrivals. The study is motivated by computer networking, in which packet losses occur due to queueing mechanisms and buffer overflows. First, we derive the formula for the burst ratio in the case of compound Poisson arrivals, general distribution of the service time and general distribution of the batch size. Then, we study its asymptotic behavior, as the buffer size grows to infinity. Using the obtained analytical solutions, we present several numerical examples with various batch size distributions, service time distributions, buffer sizes and system loads. Finally, we compare the computed burst ratios with values obtained in simulations.