Effective bandwidth and fast simulation of ATM intree networks

Chang, Cheng-Shang; Heidelberger, Philip; Juneja, Sandeep; Shahabuddin, Perwez

doi:10.1016/0166-5316(94)90005-1

Cited by 121 publications

(117 citation statements)

References 23 publications

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“…For c 1 < −κ (t) the first queue plays a more explicit role in delaying and reshaping the traffic before entering the second queue. This sharp dichotomy is in line with those in, e.g., [15,33].…”

Section: Lemma 41 For Allsupporting

confidence: 65%

“…[26] considers a series of queues with exponential service times, and uses sample-path large deviations to characterize the queueing asymptotics. An early reference on the concept of effective bandwidths, and particularly those of departure processes, is [15]; related results are presented in [9,10,19]. Results for sojourn times in the heavy-tailed case are given in [6], and see also [23] for recent results on a specific class of light-tailed distributions.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic analysis of Lévy-driven tandem queues

Lieshout

Mandjes

2008

Queueing Syst

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We analyze tail asymptotics of a two-node tandem queue with spectrallypositive Lévy input. A first focus lies in the tail probabilities of the type, for α ∈ (0, 1) and x large, and Q i denoting the steadystate workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Lévy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.

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Section: Lemma 41 For Allsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of Lévy-driven tandem queues

Lieshout

Mandjes

2008

Queueing Syst

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show abstract

“…To improve the simulation accuracy, we use importance-sampling (IS) [16] whenever applicable. The rate matrices of the on-off Markov fluid sources are adjusted according to the techniques presented in [17] to speed up the simulation.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…One thing to note is that in each run of the iterative root-finding algorithm to check a candidate solution point , the calculation of and its inclusion in the sum in the left side of (17) need to be done only for those regions with overload states. With the value, can be easily solved from (16). If the input peak rate decreases below the channel capacity when buffer content exceeds , the algorithm gives , and there is no packet loss for the traffic of classes .…”

Section: ) Wherementioning

confidence: 99%

“…Substituting and into (13) and simplifying the expression, we have (16) where , , and for convenience. After a simple manipulation to (16), the following equation of can be obtained: (17) Again due to the monotonicity of the dominant eigenvalue , the left side of (17) is a strictly decreasing function of . We can solve (17) for by using a standard iterative root-finding technique (such as Newton's method).…”

Section: ) Wherementioning

confidence: 99%

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Effective bandwidth of multiclass Markovian traffic sources and admission control with dynamic buffer partitioning

Cheng

Zhuang

Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE

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Abstract-We investigate the statistical multiplexing and admission control for a partitioned buffer, where the traffic is generated by multiclass Markov-modulated fluid sources. Each of the sources has ( 1) classes at each state. The quality of service (QoS) is described by the packet loss probability for each class. The buffer is partitioned with 1 thresholds to provide the loss priorities. Extending the effective bandwidth concept to such a buffer system is a challenging topic. In this paper, we find the minimal effective bandwidth in the asymptotic regime of large buffers and small loss probabilities by optimally setting the partition thresholds. The minimal effective bandwidth achieves efficient resource utilization and can be used to do admission control for heterogeneous multiclass Markovian sources in an additive way. The buffer partition thresholds are dynamically adjusted according to the input traffic load to guarantee QoS. Numerical analysis and simulation results verify the QoS satisfaction and the obvious improvement of resource utilization compared with previously published results, when the minimal effective bandwidth is used for resource allocation with the proposed dynamic buffer partitioning techniques.Index Terms-Differentiated services (DiffServ), dynamic buffer partitioning, effective bandwidth, loss priorities, multiclass Markovian traffic sources.

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An importance sampling algorithm for the simulation of a GPS scheduler

Giordano

Pagano

Tartarelli³

2002

Trans Emerging Tel Tech

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A key requirement of modem telecommunications networks is the capability of providing a variety of Quality of Service (QoS) guarantees to different classes of users. In this scenario scheduling systems play a major role, thanks totheir ability of offering different levels of service, while preventing some "greedy users" from degrading the QoS of other classes. A primary QoS parameter is the Cell Loss Probability (CLP), whose typical values are very small and therefore difficult to estimate through standard Monte Carlo (MC) simulation. since long run times are required to achieve accurate results. Under proper conditions, Imponance Sampling (IS) techniques can speed up simulations involving rare events. In this paper we propose an application of IS to the simulation of a Generalized Processor Sharing (GPS) scheduler, fed by Markov Amval Processes (MAP). The algorithms we propose are based on large deviations principles, which provide asymptotic results on the decay rate of per-session queue length tail distributions in an idealized GPS discipline. In particular, we first present a scheme for the simulation of a two-buffer system, then we extend the technique to the general case of a multi-buffer scheduler. We subsequently employ our algorithms to simulate a packetized realistic system, namely the Packet-by-packet Generalized Processor Sharing.

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Effective bandwidth and fast simulation of ATM intree networks

Cited by 121 publications

References 23 publications

Asymptotic analysis of Lévy-driven tandem queues

Asymptotic analysis of Lévy-driven tandem queues

Effective bandwidth of multiclass Markovian traffic sources and admission control with dynamic buffer partitioning

An importance sampling algorithm for the simulation of a GPS scheduler

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