A Lévy input fluid queue with input and workload regulation

Abstract

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers {e (i) q } i=1,2,... according to a spectrally positive Lévy process Y i (t) that is reflected at zero, and where the environment i equals 0 or 1. When the exponential clock e (i) q ends, the workload, as well as the Lévy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment i of the Lévy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of Lévy processes, to workload and queuing models.

A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

“…Dȩbicki et al [15] focused on transient analysis of Lévy-driven tandem queues. Palmowski et al [16] considered a controlled fluid queuing model with Lévy input. Boxma and Kella [17] generalized known workload decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions.…”

Lévy-driven Fluid Queue with Server Breakdowns and Vacations

“…Dȩbicki et al [8] focused on transient analysis of Lévy-driven tandem queues. Palmowski et al [21] considered a controlled fluid queuing model with Lévy input. Boxma and Kella [6] generalized known workload decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions.…”