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Queueing Systems

, 63:241 | Cite as

On the speed of convergence to stationarity of the Erlang loss system

  • Erik A. van Doorn
  • Alexander I. Zeifman
Open Access
Article

Abstract

We consider the Erlang loss system, characterized by N servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of N. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates.

Keywords

Charlier polynomials Rate of convergence Total variation distance 

Mathematics Subject Classification (2000)

60K25 90B22 

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Institute of Informatics Problems RAS, VSCC CEMI RASand Vologda State Pedagogical UniversityVologdaRussia

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