342 research outputs found
On a queueing model with service interruptions
No full textSingle-server queues in which the server takes vacations arise naturally as models for a wide
range of computer-, communication- and production systems. In almost all studies on vacation
models, the vacation lengths are assumed to be independent of the arrival, service, workload
and queue length processes. In the present study we allow the length of a vacation to depend
on the length of the previous active period, viz., the period since the previous vacation. Under
rather general assumptions regarding the offered work during active periods and vacations, we
determine the steady-state workload distribution. We conclude by discussing several special
cases including polling models, and relate our findings to results obtained earlier
Sample-Path Large Deviations for Generalized Processor Sharing Queues with Gaussian Inputs
No full textSample-path large deviations for generalized processor sharing queues with Gaussian inputs M.R.H. Mandjes, M.J.G. van Uiter
A versatile model for TCP bandwidth sharing in networks with user heterogeneity
No full textABSTRACTEnabled by the emergence of various access technologies (such as ADSL and wireless LAN),the number of users with high-speed access to the Internet is growing rapidly, and theirexpectation with respect to the quality-of-service of the applications has been increasingaccordingly. With TCP being the ubiquitous underlying end-to-end control, this motivates theinterest in easy-to-evaluate, yet accurate, performance models for a TCP-based network shared by multiple classes of users. Building on the vast body of existing models, we develop a novelversatile model that explicitly captures user heterogeneity, and takes into considerationdynamics at both the packet level and the flow level. It is described how the resulting multipletime-scale model can be numerically evaluated. Validation is done by using NS2 simulations as a benchmark. In extensive numerical experiments, we study the impact of heterogeneity in theround-trip times on user-level characteristics such as throughputs and flow transmission times, thus quantifying the resulting bias. We also investigate to what extent this bias is affected by the networks' 'packet-level parameters', such as buffer sizes. We conclude by extending the singlelink model in a straightforward way to a general network setting. Also in this network setting the impact of heterogeneity in round-trip times is numerically assessed.2000 Mathematics Subject Classification: 60K25, 68M20Keywords and Phrases: TCP; user heterogeneity; performance; throughput; round-trip times; packet level; flow level; acyclic networksNote: The work of H. van den Berg and M. Mandjes was partially funded by the Dutch Ministry of Economic Affairs (through its agency SENTER/NOVEM) under the programme `Technologische Samenwerking ICT Doorbraakprojecten', project TSIT 2031 EQUANET. M. Mandjes is also with Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, the Netherlands, and EURANDOM, Eindhoven, the Netherlands. D. Abendroth is currently with Bayerische Motor Werke, München, Germany
Performance analysis of stochastic networks
No full textQueues are everywhere, and have significant impact on how we experience everyday’s life. The mathematical analysis of queueing, rooted in the interface of probability theory and operations research, is a strongly developed branch of research. Onno Boxma, Stella Kapodistria, Michel Mandjes give an overview
Convexity properties of loss and overflow functions
No full textWe show that the fluid loss ratio in a fluid queue with finite buffer b and constant link capacity c is always a jointly convex function of b and c. This generalizes prior work by Kumaran and Mandjes (Queueing Systems 38 (2001) 471), which shows convexity of the (b,c) trade-off for large number of i.i.d. multiplexed sources, using the large deviations rate function as approximation for fluid loss. Our approach also leads to a simpler proof of the prior result, and provides a stronger basis for optimal measurement-based control of resource allocation in shared resource systems
NETWORKS
No full textNETWORKS is een tien jaar lopend (2014-2023) Zwaartekrachtproject waarin, met de steun van het Ministerie van Onderwijs, Cultuur en Wetenschap, fundamenteel onderzoek gedaan wordt naar de eigenschappen van netwerken. Het project zal bruggen slaan tussen wiskunde en informatica, theorie en praktijk, en wetenschap en maatschappij. En bovenal zal NETWORKS veel jonge talenten opleiden die deze bruggen gaan bewandelen. Johan van Leeuwaarden en Michel Mandjes zijn lid van het projectteam
A versatile model for TCP bandwidth sharing in networks with user heterogeneity.
No full textABSTRACT Enabled by the emergence of various access technologies (such as ADSL and wireless LAN), the number of users with high-speed access to the Internet is growing rapidly, and their expectation with respect to the quality-of-service of the applications has been increasing accordingly. With TCP being the ubiquitous underlying end-to-end control, this motivates the interest in easy-to-evaluate, yet accurate, performance models for a TCP-based network shared by multiple classes of users. Building on the vast body of existing models, we develop a novel versatile model that explicitly captures user heterogeneity, and takes into consideration dynamics at both the packet level and the flow level. It is described how the resulting multiple time-scale model can be numerically evaluated. Validation is done by using NS2 simulations as a benchmark. In extensive numerical experiments, we study the impact of heterogeneity in the round-trip times on user-level characteristics such as throughputs and flow transmission times, thus quantifying the resulting bias. We also investigate to what extent this bias is affected by the networks' 'packet-level parameters', such as buffer sizes. We conclude by extending the singlelink model in a straightforward way to a general network setting. Also in this network setting the impact of heterogeneity in round-trip times is numerically assessed. 2000 Mathematics Subject Classification: 60K25, 68M20 Keywords and Phrases: TCP; user heterogeneity; performance; throughput; round-trip times; packet level; flow level; acyclic networks Note: The work of H. van den Berg and M. Mandjes was partially funded by the Dutch Ministry of Economic Affairs (through its agency SENTER/NOVEM) under the programme `Technologische Samenwerking ICT Doorbraakprojecten', project TSIT 2031 EQUANET. M. Mandjes is also with Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, the Netherlands, and EURANDOM, Eindhoven, the Netherlands. D. Abendroth is currently with Bayerische Motor Werke, München, Germany
Communication Networks - Analysis of jitter due to call-level fluctuations
No full textAbstract In communication networks used by constant bit rate applications, call-level dynamics (i.e. entering and leaving calls) lead to fluctuations in the load, and therefore also fluctuations in the delay (jitter). By intentionally delaying the packets at the destination, one can transform the perturbed packet stream back into the original periodic stream; in other words: there is a trade off between jitter and delay, in that jitter can be removed at the expense of delay. As a consequence, for streaming applications for which the packet delay should remain below some predefined threshold, it is desirable that the jitter remains small. This paper presents a set of procedures to compute the jitter due to call-level variations. We consider a network resource shared by a fluctuating set of constant bit rate applications (modelled as periodic sources). As a first step, we study the call-level dynamics: supposing that a tagged call sees n0 calls when entering the system, then we compute the probability that at the end of its duration (consisting of, say, i packets) ni calls are present, of which n0,i stem from the original n0 calls. As a second step, we show how to compute the jitter, for given n0, ni, and n0,i; in this analysis generalised Ballot-problems have to be solved. We find an iterative exact solution to these, and explicit approximations and bounds. Then, as a final step, the (packet-level) results of the second step are weighed with the (call-level) probabilities of the first step, thus resulting in the probability distribution of the jitter experienced within the call duration. An explicit Gaussian approximation is proposed. Extensive numerical experiments validate the accuracy of the approximations and bounds. Copyright © 2006 AEI
Large Deviations for Gaussian Queues (Modelling Communication Networks)
No full textIn recent years the significance of Gaussian processes to communication networks has grown considerably. The inherent flexibility of the Gaussian traffic model enables the analysis, in a single mathematical framework, of systems with both long-range and short-range dependent input streams. Large Deviations for Gaussian Queues demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. The text provides a general introduction to Gaussian queues, and surveys recent research into the modelling of communications networks. Coverage includes: * Discussion of the theoretical concepts and practical aspects related to Gaussian traffic models. * Analysis of recent research asymptotic results for Gaussian queues, both in the large-buffer and many-sources regime. * An emphasis on rare-event analysis, relying on a variety of asymptotic techniques. * Examination of single-node FIFO queuing systems, as well as queues operating under more complex scheduling disciplines, and queuing networks. * A set of illustrative examples that directly relate to important practical problems in communication networking. * A large collection of instructive exercises and accompanying solutions. Large Deviations for Gaussian Queues assumes minimal prior knowledge. It is ideally suited for postgraduate students in applied probability, operations research, computer science and electrical engineering. The book’s self-contained style makes it perfect for practitioners in the communications networking industry and for researchers in related areas
A note on the benefits of buffering
No full textGaussian traffic models are capable of representing a broad variety of correlation structures, ranging from short-range dependent (e.g. Ornstein-Uhlenbeck type) to long-range dependent (e.g. fractional Brownian motion, with Hurst parameter H exceeding 1/2). This note focuses on queues fed by a large number (n) of Gaussian sources, emptied at constant service rate nc. In particular, we consider the probability of exceeding buffer level nb, as a function of b. This probability decaying (asymptotically) exponentially in n, the essential information is contained in the exponential decay rate I(b). The main result of this note describes the duality relation between the shape of I(.) and the correlation structure. More specifically, it is shown that the curve I(cdot) is convex at some buffer size b if and only if there are negative correlations on the time scale at which the overflow takes place
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