New constant service time Polya/D/n traffic model with peaked input stream

Mirtchev, S. T.; Goleva, Rossitza

doi:10.1016/j.simpat.2012.08.004

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…The family of generalised Pareto distribution (GPD) has three parameters: the location parameter , the scale parameter and the shape parameter . In the last decade, the Pareto distribution was widely applied for IP traffic descriptions [33,[37][38][39] and Polya arrival process or renewal process in many cases of distribution parameters. The cumulative distribution function of the GPD is…”

Section: Pareto and Gamma Arrival Processmentioning

confidence: 99%

3G network traffic sources measurement and analysis

Goleva

Atamian

Mirtchev

et al. 2013

Trans. Emerging Tel. Tech.

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In this paper, we show statistical analyses of several types of traffic sources in a 3G network, namely voice, video and data sources. For each traffic source type, measurements were collected in order to, on the one hand, gain better understanding of the statistical characteristics of the sources and, on the other hand, enable forecasting traffic behaviour in the network. The latter can be used to estimate service times and quality of service parameters. The probability density function, mean, variance, mean square deviation, skewness and kurtosis of the interarrival times are estimated by Wolfram Mathematica and Crystal Ball statistical tools. Based on evaluation of packet interarrival times, we show how the gamma distribution can be used in network simulations and in evaluation of available capacity in opportunistic systems. As a result, from our analyses, shape and scale parameters of gamma distribution are generated. Data can be applied also in dynamic network configuration in order to avoid potential network congestions or overflows.

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Section: Pareto and Gamma Arrival Processmentioning

confidence: 99%

3G network traffic sources measurement and analysis

Goleva

Atamian

Mirtchev

et al. 2013

Trans. Emerging Tel. Tech.

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“…with state‐dependent rates [6], with a processor sharing discipline [7], with rest periods [8], and so on. A new traffic model of a multi‐server delay system with a Polya peaked input stream and a constant service time is studied in [9]. These models make it possible to describe the traffic flow burstiness in Internet protocol networks, for instance.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical results: The mean waiting time (experienced by the customers in the system), for different values of the coefficient of peakedness z of the number of arrivals and of the coefficient of variation C t of the service-time distribution, could be obtained by the suggested generalised Pollaczek-Khinchin formula (9). Fig.…”

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confidence: 99%

Generalised Pollaczek–Khinchin formula for the Polya/G/1 queue

Mirtchev¹,

Ганчев

2017

Electron. lett.

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Queues with path-dependent arrival processes

Fendick

Whitt

2021

J. Appl. Probab.

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We study the transient and limiting behavior of a queue with a Pólya arrival process. The Pólya process is interesting because it exhibits path-dependent behavior, e.g. it satisfies a non-ergodic law of large numbers: the average number of arrivals over time [0, t] converges almost surely to a nondegenerate limit as $t \rightarrow \infty$. We establish a heavy-traffic diffusion limit for the $\sum_{i=1}^{n} P_i/GI/1$ queue, with arrivals occurring exogenously according to the superposition of n independent and identically distributed Pólya point processes. That limit yields a tractable approximation for the transient queue-length distribution, because the limiting net input process is a Gaussian Markov process with stationary increments. We also provide insight into the long-run performance of queues with path-dependent arrival processes. We show how Little’s law can be stated in this context, and we provide conditions under which there is stability for a queue with a Pólya arrival process.

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New constant service time Polya/D/n traffic model with peaked input stream

Cited by 4 publications

References 10 publications

3G network traffic sources measurement and analysis

3G network traffic sources measurement and analysis

Generalised Pollaczek–Khinchin formula for the Polya/G/1 queue

Queues with path-dependent arrival processes

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