Mrh Michel Mandjes

Large deviations of sojourn times in processor sharing queues

This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting. Our proof gives insight into the way a large sojourn time occurs, enabling the construction of an (asymptotically efficient) importance sampling algorithm. Finally our results for PS are compared to a number of other service disciplines, such as FCFS, LCFS, and SRPT.

On a queuing model with service interruptions

htmlabstractSingle-server queues in which the server takes vacations arise naturally as models for a wide range of computer-, communication- and production systems. In almost all studies on vacation models, the vacation lengths are assumed to be independent of the arrival, service, workload and queue length processes. In the present study we allow the length of a vacation to depend on the length of the previous active period, viz., the period since the previous vacation. Under rather general assumptions regarding the offered work during active periods and vacations, we determine the steady-state workload distribution. We conclude by discussing several special cases including polling models, and relate our findings to results obtained earlier.

Asymptotic analysis of Lévy-driven tandem queues

We analyze tail asymptotics of a two-node tandem queue with spectrally-positive Lévy input. A first focus lies in the tail probabilities of the type ℙ(Q1>αx,Q2>(1−α)x), for α∈(0,1) and x large, and Qi denoting the steady-state workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Lévy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.

Analysis of Markov-modulated infinite-server queues in the central-limit regime

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix

A large-deviations analysis of Markov-modulated infinite-server queues

Q\equiv(q_{ij})_{i,j=1}^d

Lévy-driven polling systems and continuous-state branching processes

. {Both arrival rates and service rates are depending on the state of the background process.} The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time

Generalized processor sharing: Characterization of the admissible region and selection of optimal weights

t\ge 0

First passage of time-reversible spectrally negative Markov additive processes

, in the asymptotic regime in which the arrival rates

Sojourn time asymptotics in Processor Sharing queues with varying service rate

\lambda_i

Networks of ·/G/∞ queues with shot-noise-driven arrival intensities

are scaled by a factor