Performance analysis of buffers with train arrivals and correlated output interruptions

Abstract

In this paper, we study a discrete-time buffer system with a timecorrelated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying J-state Markov process during that slot.First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a 2-state Markov process. Some numerical examples help to visualise the influence of the various model parameters.

Analysis of a 2-state discrete-time queue with stochastic state-period lengths and state-dependent server availability and arrivals

“…Most of the available research with respect to server interruptions, however, concerns the single-server case, see e.g. [2,3,4,5,6] for some related results.…”

“…The simultaneous presence of time-correlation in both the arrival process and the server availability has to the best of our knowledge only been considered in the single-server case, see e.g. [4,5,6]. Even for discrete-time queues without server interruptions, the effect of time-correlated arrivals has mainly been studied for single-server queues, see e.g.…”