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On/off storage systems with state dependent input, output and switching rates
 Probability in the Engineering and Informational Sciences
, 2004
"... We consider a storage model which can be on or off. When on, the content increases at some statedependent rate and the system can switch to the off state at a statedependent rate as well. When off, the content decreases at some statedependent rate (unless it is at zero) and the system can switch ..."
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We consider a storage model which can be on or off. When on, the content increases at some statedependent rate and the system can switch to the off state at a statedependent rate as well. When off, the content decreases at some statedependent rate (unless it is at zero) and the system can switch to the on position at a statedependent rate. This process is a special case of a piecewise deterministic Markov process. We identify the stationary distribution and conditions for its existence and uniqueness.
Simple models of network access using feedback fluid queues. See: http://cm.belllabs.com/cm/ms/who/michel/pub.html
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MarkovModulated Feedforward FluidNetworks
, 1999
"... With the aim of studying a multistation feedforward fluid network with Markov modulated input and output rates we first study a two dimensional parallel network having the property that the second station cannot be empty unless the first station is. A method for computing the steady state character ..."
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With the aim of studying a multistation feedforward fluid network with Markov modulated input and output rates we first study a two dimensional parallel network having the property that the second station cannot be empty unless the first station is. A method for computing the steady state characteristics of such a process is given and it is shown that this can be used to determine the steady state characteristics of two dimensional tandem fluid networks and more general networks. Finally a multistation feedforward network is considered. Under appropriate conditions, it is explained how to determine the joint steady state LaplaceStieltjes transform (LST) and it turns out that in order to compute conditional means and the covariance structure (given the state of the underlying Markov chain) all that is needed is the methods developed for the two dimensional parallel model together with some trivial linear algebra. Keywords: fluid network, Markov modulated, exponential martingale, tand...
Simple Models of Network Access, with Applications to the Design of Joint Rate and Admission Control
 in IEEE Infocom
, 2002
"... At the access to networks, in contrast to the core, distances and feedback delays, as well as link capacities are small, which has network engineering implications that are investigated in this paper. We consider a single point in the access network which multiplexes several bursty users. The users ..."
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At the access to networks, in contrast to the core, distances and feedback delays, as well as link capacities are small, which has network engineering implications that are investigated in this paper. We consider a single point in the access network which multiplexes several bursty users. The users adapt their sending rates based on feedback from the access multiplexer. Important parameters are the user's peak transmission rate p, which is the access line speed, the user's guaranteed minimum rate r, and the bound # on the fraction of lost data.
Asymptotic analysis by the saddle point method of a datahandling system with many sources. The Journal of Applied Mathematics and Stochastic Analysis
"... We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first formulated and analyzed by Anick, Mitra and Sondhi in [3]. ..."
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We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first formulated and analyzed by Anick, Mitra and Sondhi in [3]. We obtain an alternate representation of the joint steady state distribution of the buffer content and the number of on sources. This is given as a contour integral that we then analyze in the limit N → ∞. We give detailed asymptotic results for the joint distribution, as well as the associated marginal and conditional distributions. In particular, simple conditional limits laws are obtained. These shows how the buffer content behaves conditioned on the number of active sources and vice versa. Numerical comparisons show that our asymptotic results are very accurate even for N = 20. 1
FOR MATHEMATICSAnalysis of Dependence Metrics for Queueing Processes
"... Met literatuur opgave en samenvatting in het Nederlands ..."
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"... mit Hilfe verkehrstheoretischer FlußModelle 2 The fluid flow model is used to model variable server and link rates, as they appear in mobile channels due to fading, bit error recovery and failed channel reservations. Assuming a GilbertElliott model for the channel, the influence of transmission qu ..."
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mit Hilfe verkehrstheoretischer FlußModelle 2 The fluid flow model is used to model variable server and link rates, as they appear in mobile channels due to fading, bit error recovery and failed channel reservations. Assuming a GilbertElliott model for the channel, the influence of transmission quality on network Quality of Service (QoS) might be studied. Thus, the fluid flow model assumes the role of a model that might be used for dimensioning and performance evaluation both at the edge and inside a network. We present a userfriendly, contemporary, flexible, fast and numerically stabilized computing environment for the fluid flow model with a wellknown user interface that is able to handle multiple users and that might be used as well for batch processing. We discuss two case studies that emphasize the crucial impact of the relationship between server and source dynamics on QoS. Keywords: Fluid flow model, variable server capacity, GilbertElliott model, performance analysis,
Probability, Networks and Algorithms PNA Probability, Networks and Algorithms
, 2006
"... A fluid system with coupled input and output, and its application to bottlenecks in ad hoc networks ..."
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A fluid system with coupled input and output, and its application to bottlenecks in ad hoc networks
Modelling bursty flows with fluid queues
, 2014
"... Many modern systems must deal with bursty traffic, from computer systems subject to jobs arriving in clusters to devices with an intermittent energy supply such as those powered by renewable sources. As computer systems become ever more commonplace, and renewable energy targets make unreliable powe ..."
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Many modern systems must deal with bursty traffic, from computer systems subject to jobs arriving in clusters to devices with an intermittent energy supply such as those powered by renewable sources. As computer systems become ever more commonplace, and renewable energy targets make unreliable power ubiquitous, an important part of system design will be ensuring system performance under bursty demand. We seek to understand the impact of bursty arrivals and show how system parameters can be chosen to meet service requirements in these situations. In this thesis, we will be concerned with the fluid queue, a modelling paradigm for systems subject to bursty arrivals. Fluid queues describe the evolution of a stochastic buffer fed by a source which changes rate according to a background process, typically a continuoustime Markov chain. We choose this model as it captures the key behaviour we wish to model and the characteristics we seek to compute are amenable to efficient solution. In this thesis we make three contributions to the theory of fluid queues, significantly increasing the class of systems which can be modelled without resorting to experiments or simulations. Firstly, we derive hitting times in models with multiregime (leveldependent) behaviour, then busy periods in models where the environment process has an infinite (but countable) state space such as the M/M/c queue, and finally performance metrics in networks of fluid queues. We apply such models to give insights into mobile phone battery life, the temperature of a computer system and reserve levels in energy storage reservoirs, all systems subject to bursty arrivals. 3 4