Rate of convergence to stationarity of the system $M/M/N/N+R$

Erik A. van Doorn

Rate of convergence to stationarity of the system $M/M/N/N+R$

Erik A. van Doorn

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Abstract

We consider the $M/M/N/N+R$ service system, characterized by $N$ servers, $R$ waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of $R$, $N$ and the arrival rate $\lambda$, allowing $\lambda$ to be a function of $N.$

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente
Number of pages	18
Publication status	Published - Jul 2010

Publication series

Name	Memorandum / Department of Applied Mathematics
Publisher	University of Twente, Department of Applied Mathematics
No.	1923
ISSN (Print)	1874-4850
ISSN (Electronic)	1874-4850

Keywords

EWI-18166
MSC-90B22
METIS-270921
MSC-60K25
IR-72428

Access to Document

http://www.math.utwente.nl/publications

Cite this

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title = "Rate of convergence to stationarity of the system \$M/M/N/N+R\$",

abstract = "We consider the \$M/M/N/N+R\$ service system, characterized by \$N\$ servers, \$R\$ waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of \$R\$, \$N\$ and the arrival rate \$\textbackslash{}lambda\$, allowing \$\textbackslash{}lambda\$ to be a function of \$N.\$",

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AB - We consider the $M/M/N/N+R$ service system, characterized by $N$ servers, $R$ waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of $R$, $N$ and the arrival rate $\lambda$, allowing $\lambda$ to be a function of $N.$

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KW - METIS-270921

KW - MSC-60K25

KW - IR-72428

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BT - Rate of convergence to stationarity of the system $M/M/N/N+R$

PB - University of Twente

CY - Enschede

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