Queues with non-stationary input stream

Stability and Non-Stationary Characteristics of Queues

stationary single-server queues

This paper complements two previous studies (Daley and Rolski, 1984, 199 1) by indicating the extent to which characteristics of a general stationary point process taken as the arrival process of a single-server queue influence light traffic limit theorems for the two essentially distinct schemes of dilation and thinning as routes to the limit. Properties of both the work-load and the waiting-t...

Patterns of Buffer Overflow in a Class of Queues with Long Memory in the Input Stream

We study the time it takes until a a uid queue with a nite, but large, holding capacity reaches the overrow point. The queue is fed by an on/oo process, with a heavy tailed on distribution, which is known to have long memory. It turns out that the expected time until overrow, as a function of capacity L, increases only polynomially fast, and so overrows happen much more often than in the \class...

Device Queues Input

Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steadystate performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature focusin...