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Search: authors:"M. R. H. Mandjes"

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Networks of \(\cdot /G/\infty \) queues with shot-noise-driven arrival intensities

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by a shot-noise process. A shot-noise rate emerges naturally in cases where the arrival rate tends to exhibit sudden increases (or shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential...

A tandem fluid network with Lévy input in heavy traffic

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of Lévy input, covering compound Poisson, \(\alpha \)-stable Lévy motion (with \(1<\alpha <2\)), and Brownian motion. In our analysis, we separately deal with Lévy input processes with increments that have finite and infinite variance. A distinguishing...

A large deviations principle for infinite-server queues in a random environment

This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general càdlàg stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large...

A stability conjecture on bandwidth sharing networks

We consider a queueing model where documents are simultaneously transferred over a communication network. The bandwidth allocated to each document transfer is assumed to be the solution of a utility optimization problem. Under a natural stability condition and under the assumption that document arrivals are Poisson and that document sizes are independent exponential distributions...

Sample-Path Large Deviations in Credit Risk

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail asymptotics of the probabilities involved. We first derive a sample-path large deviation principle (LDP) for the portfolio's loss process, which...

A feedback fluid queue with two congestion control thresholds

Netherlands 4 M. R. H. Mandjes EURANDOM, Eindhoven, The Netherlands Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and