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Fluid queue driven by aGI/GI/1 queue
Journal of Mathematical Sciences, 1998The Laplace-Stieltjes transform of the stationary distribution of the buffer content in the case of M/GI/1 queue is the first phase. The author shows that this distribution depends on the form of the service-time distribution which entails that the change of GI/GI/1 by M/M/1 is not correct, in general.
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Fluid limits of queueing networks with batches
Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering, 2012This paper presents an analytical model for the performance prediction of queueing networks with batch services and batch arrivals, related to the fluid limit of a suitable single-parameter sequence of continuous-time Markov chains and interpreted as the deterministic approximation of the average behaviour of the stochastic process.
Luca Bortolussi, Mirco Tribastone
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Approximate analysis of a network of fluid queues
ACM SIGMETRICS Performance Evaluation Review, 2007Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional 'heavy traffic' approximations to the recent advances in bio-chemical system models. Here we use an approximate compositional method to analyse a simple feedforward network of fluid queues which comprises both probabilistic ...
Tony Field, Peter G. Harrison
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A TANDEM FLUID QUEUE WITH GRADUAL INPUT
Probability in the Engineering and Informational Sciences, 2002For a two-node tandem fluid model with gradual input, we compute the joint steady-state buffer-content distribution. Our proof exploits martingale methods developed by Kella and Whitt. For the case of finite buffers, we use an insightful sample-path argument to extend an earlier proportionality result of Zwart to the network case.
Scheinhardt, Werner R.W., Zwart, Bert
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Risk processes analyzed as fluid queues
Scandinavian Actuarial Journal, 2005This paper presents the Laplace transform of the time until ruin for a fairly general risk model. The model includes both the classical and most Sparre-Andersen risk models with phase-distributed claim amounts as special cases. It also allows for correlated arrival processes, and claim sizes that depend upon environmental factors such as periods of ...
Badescu, Andrei +5 more
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ON THE COMPARISON OF QUEUEING SYSTEMS WITH THEIR FLUID LIMITS
Probability in the Engineering and Informational Sciences, 2001A tandem of multiserver queues is compared with an associated fluid limit. It is shown that, for a certain class of cost functions, the expected cost incurred by the workload processes of the two models is lower for the fluid limit at all times. The analysis uses dynamic programming and phase-type distributions and extends to some other types of ...
Altman, Eitan +2 more
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Fluid Models for Multiserver Queues with Abandonments
Operations Research, 2006Deterministic fluid models are developed to provide simple first-order performance descriptions for multiserver queues with abandonment under heavy loads. Motivated by telephone call centers, the focus is on multiserver queues with a large number of servers and nonexponential service-time and time-to-abandon distributions. The first fluid model serves
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Sojourn Time Distribution in Fluid Queues
2019We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time
Eleonora Deiana +2 more
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A Fluid Flow Model of Networks of Queues
Management Science, 1983This paper describes a new technique for modeling flow through a network of queues. The advantages of this method over many discrete event simulations or queueing theory techniques include simplicity, low cost and portability. The paper describes the kinds of processes to which the technique can be applied, and the characteristics of the process that ...
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A fluid model for layered queueing networks
IEEE Transactions on Software Engineering, 2013Layered queueing networks are a useful tool for the performance modeling and prediction of software systems that exhibit complex characteristics such as multiple tiers of service, fork/join interactions, and asynchronous communication. These features generally result in nonproduct form behavior for which particularly efficient approximations based on ...
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