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Probl. Peredachi Inf., 2008, Volume 44, Issue 4, Pages 72–91 (Mi ppi1290)  

This article is cited in 9 scientific papers (total in 9 papers)

Communication Network Theory

Limit Theorems for Queueing Systems with Doubly Stochastic Poisson Arrivals (Heavy Traffic Conditions)

L. G. Afanas'eva, E. E. Bashtova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Probability Theory Chair

Abstract: We consider a single-server queueing system with a doubly stochastic Poisson arrival flow under heavy traffic conditions. We prove the convergence of the limiting stationary or periodic distribution to the exponential distribution. In a scheme of series, we consider the $C$-convergence of the waiting time process to a diffusion process with constant coefficients and reflection at the zero boundary. Examples of computation of the diffusion coefficient in terms of characteristics of the arrival flow and service time are given.

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English version:
Problems of Information Transmission, 2008, 44:4, 352–369

Bibliographic databases:

UDC: 621.394/395.74:519.2
Received: 18.01.2008
Revised: 05.06.2008

Citation: L. G. Afanas'eva, E. E. Bashtova, “Limit Theorems for Queueing Systems with Doubly Stochastic Poisson Arrivals (Heavy Traffic Conditions)”, Probl. Peredachi Inf., 44:4 (2008), 72–91; Problems Inform. Transmission, 44:4 (2008), 352–369

Citation in format AMSBIB
\by L.~G.~Afanas'eva, E.~E.~Bashtova
\paper Limit Theorems for Queueing Systems with Doubly Stochastic Poisson Arrivals (Heavy Traffic Conditions)
\jour Probl. Peredachi Inf.
\yr 2008
\vol 44
\issue 4
\pages 72--91
\jour Problems Inform. Transmission
\yr 2008
\vol 44
\issue 4
\pages 352--369

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    This publication is cited in the following articles:
    1. L. G. Afanasyeva, E. V. Bulinskaya, “Systems reliability in case of regenerative flow of elements failures”, Autom. Remote Control, 71:7 (2010), 1294–1307  mathnet  crossref  mathscinet  zmath  isi
    2. Al Ajarmeh I., Yu J., Amezziane M., “Framework of Applying a Non-Homogeneous Poisson Process to Model VoIP Traffic on Tandem Networks”, New Aspects of Applied Informatics, Biomedical Electronics and Informatics and Communication, International Conference on Applied Informatics and Communications-International Conference on Biomedical Electronics and Biomedical Informatics, 2010, 164–169  isi
    3. L. G. Afanas'eva, T. N. Belorusov, “Limit theorems for systems with impatient customers under high load”, Theory Probab. Appl., 56:4 (2011), 674–682  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Afanasyeva L., Bashtova E., Bulinskaya E., “Limit Theorems for Semi-Markov Queues and Their Applications”, Communications in Statistics-Simulation and Computation, 41:6, Part 1 Sp. Iss. SI (2012), 688–709  crossref  mathscinet  zmath  isi
    5. I. V. Rudenko, “Two-phase queueing system with unreliable servers under heavy load”, Moscow University Mathematics Bulletin, 68:1 (2013), 61–64  mathnet  crossref
    6. Afanasyeva L., Bulinskaya E., “Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption”, Methodol. Comput. Appl. Probab., 15:4 (2013), 935–950  crossref  mathscinet  zmath  isi  elib
    7. Afanasyeva L.G., Bashtova E.E., “Coupling Method for Asymptotic Analysis of Queues with Regenerative Input and Unreliable Server”, Queueing Syst., 76:2, SI (2014), 125–147  crossref  mathscinet  zmath  isi  elib
    8. S. Zh. Aibatov, L. G. Afanasyeva, “Subexponential asymptotics for steady state tail probabilities in a single-server queue with regenerative input flow”, Theory Probab. Appl., 62:3 (2018), 339–355  mathnet  crossref  crossref  zmath  isi  elib
    9. A. V. Lebedev, “Maximum remaining service time in infinite-server queues”, Problems Inform. Transmission, 54:2 (2018), 176–190  mathnet  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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