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

Erik A. van Doorn

doi:10.1007/s11750-011-0173-0

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

Erik A. van Doorn

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

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
Pages (from-to)	336-350
Number of pages	15
Journal	Top
Volume	19
Issue number	2
DOIs	https://doi.org/10.1007/s11750-011-0173-0
Publication status	Published - Dec 2011

Keywords

MSC-60K25
MSC-90B22
Orthogonal polynomials
EWI-20787
IR-78448
Decay rate
Delay and loss system
METIS-279694
Many-server queue

Access to Document

10.1007/s11750-011-0173-0

http://eprints.eemcs.utwente.nl/secure2/20787/01/fulltext.pdf

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 $\lambda$, allowing $\lambda$ to be a function of $N.$",

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author = "{van Doorn}, {Erik A.}",

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Y1 - 2011/12

N2 - 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 $N.$

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 $N.$

KW - MSC-60K25

KW - MSC-90B22

KW - Orthogonal polynomials

KW - EWI-20787

KW - IR-78448

KW - Decay rate

KW - Delay and loss system

KW - METIS-279694

KW - Many-server queue

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DO - 10.1007/s11750-011-0173-0

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JO - Top

JF - Top

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ER -