, Volume 12, Issue 1, pp 91–110

Performance analysis of a call center with interactive voice response units

  • Raj Srinivasan
  • Jérome Talim
  • Jinting Wang


A Call center may be defined as a service unit where a group of agents handle a large volume of incoming telephone calls for the purpose of sales, service, or other specialized transactions. Typically a call center consists of telephone trunk lines, a switching machine known as the automatic call distributor (ACD) together with a voice response unit (VRU), and telephone sales agents. Customers usually dial a special number provided by the call center; if a trunk line is free, the customer seizes it, otherwise the call is lost. Once the trunk line is seized, the caller is instructed to choose among several options provided by the call center via VRU. After completing the instructions at the VRU, the call is routed to an available agent. If all agents are busy, the call is queued at the ACD until one is free. One of the challenging issues in the design of a call center is the determination of the number of trunk lines and agents required for a given call load and a given service level. Call center industries use the Erlang-C and the Erlang-B formulae in isolation to determine the number of agents and the number of trunk lines needed respectively.

In this paper we propose and analyze a flow controlled network model to capture the role of the VRU as well as the agents. Initially, we assume Poisson arrivals, exponential processing time at the VRU and exponential talk time. This model provides a way to determine the number of trunk lines and agents required simultaneously. An alternative simplified model (that ignores the role of the VRU) will be to use anM|M|S|N queueing model (whereS is the number of agents andN is the number of trunk lines) to determine the optimalS andN subject to service level constraints. We will compare the effectiveness of this simplified model and other approximate methods with our model. We will also point out the drawbacks of using Erlang-C and Erlang-B formulae in isolation.

Key Words

Call center flow controlled Jackson networks Erlang formulae 

AMS subject classification



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Copyright information

© Sociedad de Estadística e Investigación Operativa 2004

Authors and Affiliations

  • Raj Srinivasan
    • 1
  • Jérome Talim
    • 1
  • Jinting Wang
    • 2
  1. 1.Mathematical Sciences GroupUniversity of SaskatchewanSaskatoonCanada
  2. 2.Department of MathematicsBeijing Jiaotong UniversityBeijingP.R. China

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