A tandem queue with server slow-down and blocking

We consider two variants of a two-station tandem network with blocking. In both variants the first server ceases to work when the queue length at the second station hits a `blocking threshold'. In addition, in variant $2$ the first server decreases its service rate when the second queue exceeds a `slow-down threshold', which is smaller than the blocking level. In both variants the arrival process is Poisson and the service times at both stations are exponentially distributed. Note, however, that in case of slow-downs, server $1$ works at a high rate, a slow rate, or not at all, depending on whether the second queue is below or above the slow-down threshold or at the blocking threshold, respectively. For variant $1$, i.e., only blocking, we concentrate on the geometric decay rate of the number of jobs in the first buffer and prove that for increasing blocking thresholds the sequence of decay rates decreases monotonically and at least geometrically fast to $\max\{\rho_1,\rho_2\}$, where $\rho_i$ is the load at server $i$. The methods used in the proof also allow us to clarify the asymptotic queue length distribution at the second station. Then we generalize the analysis to variant $2$, i.e., slow-down and blocking, and establish analogous results. \u

Markovian arrivals in stochastic modelling: a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.Peer Reviewe

Queues with Congestion-dependent Feedback

This dissertation expands the theory of feedback queueing systems and applies a number of these models to a performance analysis of the Transmission Control Protocol, a flow control protocol commonly used in the Internet

Queueing models for cable access networks

abstract in thesi