Sample-Path Analysis of Queueing Systems

Koole, Ger; El-Taha, Muhammad; Stidham, Shaler

doi:10.1007/978-1-4615-5721-0

Cited by 95 publications

(39 citation statements)

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“…All the processes introduced below are assumed to be defined on a common probability space, on which a probability measure P is defined. Let N i [a, b] be the 2 Examples have been obtained in [6] for the single class case number of class i arrivals in the interval [a, b]. We assume that the limits…”

Section: Discriminatory Processor Sharing: Model and Analysissupporting

confidence: 41%

DPS queues with stationary ergodic service times and the performance of TCP in overload

Altman

Jiménez

Kofman³

Ieee Infocom 2004

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Abstract-In a recent paper, Bonald and Roberts [1] studied non-persistent TCP connections in transient overload conditions, under the assumption that all connections have the same round-trip times. In this paper our goal is to develop theoretical tools that will enable us to relax this assumption and obtain explicit expressions for the rate of growth of the number of connections at the system, the rate at which TCP connections leave the system, as well as the time needed for the completion of a connection. To that end, we model the system as a DPS (Discriminatory Processor Sharing) system which we analyze under very mild assumptions on the probability distributions related to different classes of arrivals: we only assume that the arrival rates of connections exist, and that the amount of information transmitted during a connection of a given type forms a stationary ergodic sequence. We then proceed to obtain explicit expressions for the growth rate of the number of connections at the DPS system for several specific probability distributions. We check through simulations the applicability of our queueing results for modeling TCP connections sharing a bottleneck.

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Section: Discriminatory Processor Sharing: Model and Analysissupporting

confidence: 41%

DPS queues with stationary ergodic service times and the performance of TCP in overload

Altman

Jiménez

Kofman³

Ieee Infocom 2004

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“…Equivalently, the output rate should equal the input rate at each facility. This is called rate stability and, because it deals in long-run averages, can be analyzed on a pathwise basis (i.e., deterministically)-see El-Taha and Stidham (1999). For systems with sufficient probabilistic structure, "stable" can be strengthened to mean that there exists a proper limiting or at least stationary distribution for the system state (e.g., the vector of contents at each facility).…”

Section: Stability and Fluid Modelscontrasting

confidence: 37%

“…Later work by Stidham, El-Taha, and others showed that the same was true with relations between time-stationary and Palm distributions and (to a lesser extent) insensitivity. The book by El-Taha and Stidham (1999) offers a compendium of results like these (as well as other results) achievable by samplepath analysis. See also Sigman (1995), Serfozo (1999).…”

Section: / Stidhammentioning

confidence: 41%

Analysis, Design, and Control of Queueing Systems

Stidham

2002

Operations Research

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105

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“…Since, for spatially constant ρ, the value of ρ coincides with the WIP W (t), and since in the time-independent case C = 1 T1 holds, we obtain the relation W = λT 1 . Thus we recover, up to a scaling factor introduced by using arrival probabilities instead of the arrival density, the well-known Little's law W = λτ [12], [7] for the steady-state situation.…”

Section: = T (R) ω(R T)r T (R ) Dr − ω(R T)rt (R) Which Implies ωmentioning

confidence: 48%

Thermalized Kinetic and Fluid Models for Reentrant Supply Chains

Armbruster

Ringhofer

2005

Multiscale Model. Simul.

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Abstract. Standard stochastic models for supply chains predict the throughput time (TPT) of a part from a statistical distribution, which is dependent on the work in progress at the time the part enters the system. So they try to predict a transient response from data which are sampled in a quasi-steady-state situation. For reentrant supply chains this prediction is based on insufficient information, since subsequent arrivals can dramatically change the TPT. This paper extends these standard models by introducing the concept of a stochastic phase velocity which dynamically updates the TPT estimate. This leads to the concepts of temperature and diffusion in the corresponding kinetic and fluid models for supply chains.

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Sample-Path Analysis of Queueing Systems

Cited by 95 publications

References 0 publications

DPS queues with stationary ergodic service times and the performance of TCP in overload

DPS queues with stationary ergodic service times and the performance of TCP in overload

Analysis, Design, and Control of Queueing Systems

Thermalized Kinetic and Fluid Models for Reentrant Supply Chains

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