4,739 research outputs found
Continuous feedback fluid queues
We investigate a fluid buffer which is modulated by a stochastic background process, while the momentary behavior of the background process depends on the current buffer level in a continuous way. Loosely speaking the feedback is such that the background process behaves `as a Markov process' with generator at times when the buffer level is , where the entries of are continuous functions of . Moreover, the flow rates for the buffer may also depend continuously on the current buffer level. Such models are interesting in the context of closed-loop telecommunication networks, in which sources interact with network buffers, but may also be deployed in the study of certain production systems. \u
Shot-noise queueing models
We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process
On level crossings for a general class of piecewise-deterministic Markov processes
We consider a piecewise-deterministic Markov process governed by a jump
intensity function, a rate function that determines the behaviour between
jumps, and a stochastic kernel describing the conditional distribution of jump
sizes. We study the point process of upcrossings of a level by the Markov
process. Our main result shows that, under a suitable scaling , the
point process converges, as tends to infinity, weakly to a geometrically
compound Poisson process. We also prove a version of Rice's formula relating
the stationary density of the process to level crossing intensities. This
formula provides an interpretation of the scaling factor . While our
proof of the limit theorem requires additional assumptions, Rice's formula
holds whenever the (stationary) overall intensity of jumps is finite.Comment: 25 page
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 steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009
Sojourn time in a single server queue with threshold service rate control
We study the sojourn time in a queueing system with a single exponential
server, serving a Poisson stream of customers in order of arrival. Service is
provided at low or high rate, which can be adapted at exponential inspection
times. When the number of customers in the system is above a given threshold,
the service rate is upgraded to the high rate, and otherwise, it is downgraded
to the low rate. The state dependent changes in the service rate make the
analysis of the sojourn time a challenging problem, since the sojourn time now
also depends on future arrivals. We determine the Laplace transform of the
stationary sojourn time and describe a procedure to compute all moments as
well. First we analyze the special case of continuous inspection, where the
service rate immediately changes once the threshold is crossed. Then we extend
the analysis to random inspection times. This extension requires the
development of a new methodological tool, that is "matrix generating
functions". The power of this tool is that it can also be used to analyze
generalizations to phase-type services and inspection times.Comment: 16 pages, 13 figure
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