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

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

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Article ID: iaor201111380
Volume: 19
Issue: 2
Start Page Number: 336
End Page Number: 350
Publication Date: Dec 2011
Journal: TOP
Authors:
Keywords: M/M/c queues, Poisson process
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 λ, allowing λ to be a function of N.

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