, Volume 19, Issue 2, pp 336–350 | Cite as

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

  • Erik A. van Doorn
Original Paper


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 RN and the arrival rate λ, allowing λ to be a function of N.


Decay rate Delay and loss system Many-server queue Orthogonal polynomials 

Mathematics Subject Classification (2000)

60K25 90B22 


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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