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

Erik A. van Doorn; Alexander I. Zeifman

doi:10.1007/s11134-009-9134-9

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

Erik A. van Doorn, Alexander I. Zeifman

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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.

Original language	Undefined
Article number	10.1007/s11134-009-9134-9
Pages (from-to)	241-252
Number of pages	12
Journal	Queueing systems
Volume	63
Issue number	1-4
DOIs	https://doi.org/10.1007/s11134-009-9134-9
Publication status	Published - Jul 2009

Keywords

EWI-17002
Rate of convergence
IR-68868
Charlier polynomials
METIS-264240
MSC-90B22
MSC-60K25
Total variation distance

Access to Document

10.1007/s11134-009-9134-9

Cite this

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title = "On the speed of convergence to stationarity of the Erlang loss system",

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 = "EWI-17002, Rate of convergence, IR-68868, Charlier polynomials, METIS-264240, MSC-90B22, MSC-60K25, Total variation distance",

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KW - Charlier polynomials

KW - METIS-264240

KW - MSC-90B22

KW - MSC-60K25

KW - Total variation distance

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DO - 10.1007/s11134-009-9134-9

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