Article

Queueing Systems

, Volume 63, Issue 1, pp 241-252

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Erik A. van DoornAffiliated withDepartment of Applied Mathematics, University of Twente Email author 
  • , Alexander I. ZeifmanAffiliated withInstitute of Informatics Problems RAS, VSCC CEMI RAS, and Vologda State Pedagogical University

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