An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals

Sevast'yanov, Boris Alexandrovich

doi:10.1137/1102005

Cited by 188 publications

(96 citation statements)

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“…Thus, in this case, as shown in [4], stationary probabilities , 0, 2 i P i = are invariant under the laws of distribution of service time.…”

Section: T F Y X T H Y Y X F X T H T T X Y Y F Y T H T T Xmentioning

confidence: 87%

Semi-Markovian Model of Two-Line Queuing System with Losses

Obzherin¹

2016

IIM

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In the present paper, to build model of two-line queuing system with losses GI/G/2/0, the approach introduced by V.S. Korolyuk and A.F. Turbin, is used. It is based on application of the theory of semi-Markov processes with arbitrary phase space of states. This approach allows us to omit some restrictions. The stationary characteristics of the system have been defined, assuming that the incoming flow of requests and their service times have distributions of general form. The particular cases of the system were considered. The used approach can be useful for modeling systems of various purposes.

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“…Thus, in this case, as shown in [4], stationary probabilities , 0, 2 i P i = are invariant under the laws of distribution of service time.…”

Section: T F Y X T H Y Y X F X T H T T X Y Y F Y T H T T Xmentioning

confidence: 87%

Semi-Markovian Model of Two-Line Queuing System with Losses

Obzherin¹

2016

IIM

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“…A remarkable paper is Sevastyanov [12], who applied the method to M/G I /s loss systems to prove that Erlang's formula holds for arbitrary service time distributions, a famous example of insensitivity. Other uses of supplementary variables are in Gnedenko and Kovalenko [5], Cohen [1], Gupur [6] and their references.…”

Section: Q(t)}mentioning

confidence: 99%

Service-time ages, residuals, and lengths in an $$M/GI/\infty $$ M / G I / ∞ service system

2014

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Important supplementary variables of a stationary M/G I /∞ service system are the service-time ages, residuals, and lengths of the customers present in the system at time 0. Our main result for a stationary system is that these times form a Poisson processes on R 3 + . Thus, by the order statistic property of Poisson processes, the three-dimensional vectors of the service-time ages, residuals, and lengths are independent and identically distributed. The joint distribution function of these three times is the same as the respective joint limiting distribution function of an inter-renewal time's age, residual, and length in a renewal process. The proof is based on a spacetime Poisson representation of the M/G I /∞ system. A similar result is presented for a non-stationary system. Included is an ecological application concerning ages of trees in a forest.

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“…Our experimental prediction is that there will not be a significant difference between the throughputs for the two (different) distributions of message duration. In effect, we are testing whether or not the insensitivity property that is well established for Erlang-loss systems [17] holds here.…”

Section: Experimental Predictionsmentioning

confidence: 99%

Assessing the appropriateness of using markov decision processes for RF spectrum management

Meier

Karaus

Sistla

et al. 2013

Proceedings of the 16th ACM International Conference on Modeling, Analysis &Amp; Simulation of Wireless and Mobile Systems

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The stochastic nature of wireless communication suggests a Markov Decision Process (MDP) as a formalism for identifying and evaluating spectrum control policies. However, in practice numerous factors influence the success or failure of a transmission, so that the applicability of particular MDP models to real spectrum management problems must itself be examined. This paper presents a series of model validation studies in which correspondence between an MDP model and a discrete-event simulation (DES) model is evaluated. We test several hypotheses that together provide a foundation and an exemplar for the idea of using MDPs to guide management of shared spectrum. We conclude that there is sufficient similarity between the performance predictions made by the MDP model and the DES model that MDPs can be used effectively to determine spectrum control policies.

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An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals

Cited by 188 publications

References 0 publications

Semi-Markovian Model of Two-Line Queuing System with Losses

Semi-Markovian Model of Two-Line Queuing System with Losses

Service-time ages, residuals, and lengths in an $$M/GI/\infty $$ M / G I / ∞ service system

Assessing the appropriateness of using markov decision processes for RF spectrum management

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