Queueing Systems

, Volume 58, Issue 2, pp 137–153 | Cite as

Approximations for the M/GI/N+GI type call center

  • Foad Iravani
  • Barış Balcıog̃luEmail author


In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions. Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.


Call centers The M/GI/N+GI queue Impatient customers Level-crossing method Volterra integral equation 

Mathematics Subject Classification (2000)

60K25 68M20 90B22 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.UCLA Anderson School of ManagementLos AngelesUSA
  2. 2.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

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