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 $Q(y)$ at times when the buffer level is $y$, where the entries of $Q(y)$ are continuous functions of $y$. 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

Fluid flow models in performance analysis

We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions

A make-to-stock mountain-type inventory model

We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate a(x) that is a function of the current buffer level x; in states 1 and 2 it decreases linearly, with different speeds. We study the steady-state buffer content, by using level crossing theory and by exploiting relations between the fluid queue and queues with instantaneous input and/or output

Design issues of a back-pressure-based congestion control mechanism

Congestion control in packet-based networks is often realized by feedback protocols -- in this paper we assess the performance under a back-pressure mechanism that has been proposed and standardized for Ethernet metropolitan networks. Relying on our earlier results for feedback fluid queues, we derive explicit expressions for the key perfomance metrics, in terms of the model parameters, as well as the parameters agreed upon in the service level agreement. Numerical experiments are performed to evaluate the main trade-offs of this model (for instance the trade-off between the signaling frequency and the throughput). These can be used to generate design guidelines. The paper is concluded by an elementary, yet powerful, Markovian model that can be used as an approximative model in situations of large traffic aggregates feeding into the system; the trade-offs and guidelines identified for the feedback fluid model turn out to carry over to this more stylized model

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

Solving multi-regime feedback fluid queues

In this paper, we study Markov fluid queues with multiple thresholds, or the so-called multi-regime feedback fluid queues. The boundary conditions are derived in terms of joint densities and for a relatively wide range of state types including repulsive and zero drift states. The ordered Schur factorization is used as a numerical engine to find the steady-state distribution of the system. The proposed method is numerically stable and accurate solution for problems with two regimes and 210 states is possible using this approach. We present numerical examples to justify the stability and validate the effectiveness of the proposed approach

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008