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Sensitivity of Performance in the Erlang-A Queueing Model to Changes in the Model Parameters

Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027-6699
ww2040{at}columbia.edu

This paper studies the M/M/s+M queue, i.e., the M/M/s queue with customer abandonment, also called the Erlang-A model, having independent and identically distributed customer abandon times with an exponential distribution (the +M), focusing on the case in which the arrival rate and the number of servers are large. The goal is to better understand the sensitivity of performance to changes in the model parameters: the arrival rate, the service rate, the number of servers, and the abandonment rate. Elasticities are used to show the percentage change of a performance measure caused by a small percentage change in a parameter. Elasticities are calculated using an exact numerical algorithm and simple finite-difference approximations. Insight is gained by applying fluid and diffusion approximations. The analysis shows that performance is quite sensitive to small percentage changes in the arrival rate or the service rate, but relatively insensitive to small percentage changes in the abandonment rate.

Subject classifications: queues; multichannel; sensitivity analysis; queues; balking and reneging; sensitivity to changes in model parameters.
History: Received July 2004; revision received January 2005; accepted February 2005.

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