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

Erik A. van Doorn

Research output: Book/ReportReportProfessional

### 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 Enschede University of Twente, Department of Applied Mathematics 18 Published - Jul 2010

### Publication series

Name Memorandum / Department of Applied Mathematics University of Twente, Department of Applied Mathematics 1923 1874-4850 1874-4850

### Keywords

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

## Cite this

van Doorn, E. A. (2010). Rate of convergence to stationarity of the system $M/M/N/N+R$. (Memorandum / Department of Applied Mathematics; No. 1923). Enschede: University of Twente, Department of Applied Mathematics.