Stochastic Theory of a Data-Handling System with Multiple Sources

Anick, David J.; Mitra, Debasis; Sondhi, M. M.

doi:10.1002/j.1538-7305.1982.tb03089.x

Cited by 1,177 publications

(717 citation statements)

References 2 publications

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“…Post-and pre-multiplying (39) by I −ΨΨ and substituting the definitions of matricesK and U based on (10) and (17) gives…”

Section: Important Relationsmentioning

confidence: 99%

“…With the evolution of fluid queueing models [6,7,8,9] and their use in applied modeling [10] the question of the fluid counterpart of vacation and polling models has arisen. A first step toward this direction is by Czerniak and Yechiali [11] whose model is rather limited with respect to the stochastic evolution of the considered process: the load and the fluid service rate of stations are constant and the only stochastic ingredient of the model is the switchover time.…”

Section: Introductionmentioning

confidence: 99%

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Exhaustive fluid vacation model with positive fluid rate during service

Horvth

Telek

2015

Performance Evaluation

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Using an elegant transform domain iterative operator approach exhaustive fluid vacation models with strictly negative fluid rate during service has been analyzed, recently. Unfortunately, the potential presence of positive fluid rate during service (when the fluid input rate is larger than the fluid service rate) inhibits the use of all previously applied methodologies and makes the extension of the analysis approaches of discrete vacation and polling models toward fluid vacation and polling models rather difficult.Based on the level crossing analysis of Markov fluid models the paper introduces an analysis approach which is applicable for the stationary analysis of the fluid level distribution and its moments. In the course of the analysis compact new matrix exponential expressions are obtained for the distribution of fluid level during a busy period starting from a given positive fluid level and by exploiting the relations of upward and downward measures of fluid processes several matrix transformations are applied to avoid Kronecker expansion matrix multiplications. Finally, the obtained fluid level distribution is related with previous results of fluid vacation models.

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“…Post-and pre-multiplying (39) by I −ΨΨ and substituting the definitions of matricesK and U based on (10) and (17) gives…”

Section: Important Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exhaustive fluid vacation model with positive fluid rate during service

Horvth

Telek

2015

Performance Evaluation

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“…A single-regime Markov fluid queue is defined through a finite state-space continuous-time Markov chain {Z(t) : t ≥ 0} that modulates the buffer through a drift function r(Z (t)) [14,20]. Let X (t) be the buffer level at time t. Let Z (t) have the state space S = {1, .…”

Section: Single-regime Markov Fluid Queuesmentioning

confidence: 99%

“…Ref. [14] studies MFQs with infinite queue sizes using a spectral expansion approach, whereas [15] extends this analysis to finite queue sizes. In MRMFQs, which are also called ''level-dependent'' [16], ''multi-layer'' [17,18] or ''multi-threshold'' [19] fluid queues, the buffer space is partitioned into a finite number of non-overlapping intervals which are called the regimes of the MRMFQ.…”

Section: Introductionmentioning

confidence: 99%

The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity

Yazıcı

Akar

2013

Performance Evaluation

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a b s t r a c tWe propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.

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“…In order for the buffer to exceed level Nx, where x exceeds b * , four events have to occur in order: (1) The buffer must become non-empty, i.e., the number of sources in the on-state must exceed N c/p. (2) Given that the buffer content is at the point of becoming positive, an amount of Nb * of fluid has to accumulate. At the epoch the buffer content reaches Nb * , let the number of sources transmitting be Nα.…”

Section: B Feedback Model With Thresholdmentioning

confidence: 99%

Simple models of network access, with applications to the design of joint rate and admission control

Mandjes

Mitra²,

Scheinhardt

2003

Computer Networks

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Abstract-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. Two feedback schemes are proposed. In both schemes the users are allowed to send at rate p if the system is relatively lightly loaded, at rate r during periods of congestion, and at a rate between r and p, in an intermediate region. For both feedback schemes we present an exact analysis, under the assumption that the users' job sizes and think times have exponential distributions. We use our techniques to design the schemes jointly with admission control, i.e., the selection of the number of admissible users, to maximize throughput for given p, r, and . Next we consider the case in which the number of users is large. Under a specific scaling, we derive explicit large deviations asymptotics for both models. We discuss the extension to general distributions of user data and think times. I. IntroductionIn today's communication networks, design and control of the network core and access are different, primarily because of the differences in scale in bandwidth and distance. Quite often the bottleneck is the access, rather than the core. This may happen because the access network is characterized by relatively low line speeds and the limited ability of users to buffer and shape traffic (think of the extreme case of a user with a wireless handset). Access control, supported by the use of feedback, is an important mechanism to address this problem. Since distances between users/clients and network access points are relatively short, feedback delay due to propagation is negligible, which contributes to the efficacy of feedback control. In this paper we investigate the problems of access control by introducing simple models and techniques for their evaluation, design and performance optimization. We make three main contributions. First, we present two simple models of network access. The models provide a framework for the joint design of feedback-based schemes for the adaptation of source rates and admission control. Second, we show how to compute the stationary behavior of the aforementioned feedback queues. We illustrate the use of these

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Stochastic Theory of a Data-Handling System with Multiple Sources

Cited by 1,177 publications

References 2 publications

Exhaustive fluid vacation model with positive fluid rate during service

Exhaustive fluid vacation model with positive fluid rate during service

The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity

Simple models of network access, with applications to the design of joint rate and admission control

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