A call center is a service unit where a group of agents handle a large volume of incoming telephone calls for the purpose of sales, service or specialized transactions. A challenging issue 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 service level. Service level is defined as X% of the calls answered in Y seconds. Call center industries use the Erlang-C and Erlang-B formulae in isolation to determine the numbers of agents and trunk lines needed. To use the Erlang-B formula determine the number of trunk lines needed, one has to know the total holding time of the calls, which is a function of the number of agents available. Without knowing the number of agents required one cannot determine the number of trunk lines needed. Also, the use of Erlang-C and the Erlang-B formulae in isolation ignores the time spent by the calls interacting with the VRU. We have developed a semi-open queuing network model, which captures simultaneously the role of the trunk lines and agents, that provides a way to determine the optimal number of trunk lines and agents needed, subject to specified service level constraints.
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