Abstract
A multiserver queueing system with infinite and finite buffers, two types of customers, and two types of servers as a model of a call center with a call-back for lost customers is investigated. Type 1 customers arrive to the system according to a Markovian arrival process. All rejected type 1 customers become type 2 customers. Typer,r=1,2, servers serve typercustomers if there are any in the system and serve typer′,r′=1,2, r′≠r,customers if there are no typercustomers in the system. The service times of different types of customers have an exponential distribution with different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution of type 2 customers is derived. The problem of optimal choice of the number of each type servers is solved numerically.
Highlights
A call center is a specialized unit of companies that handles voice requests from clients
To achieve the call center performance without losses is very difficult because (i) the arrival flow of customers can be correlated; (ii) it is too expensive to have a large number of operators
Real customers arrive at the system according to a Markovian arrival process (MAP)
Summary
A call center is a specialized unit of companies that handles voice requests from clients. Loss of customers or potential customers may cause damage or loss of profit This is especially important for such organizations as banks, Internet shops, telemarkets, and other organizations that deal with selling and providing the paid services. For the first group of operators (type 1), processing of real customers has a priority, while the operators from the second group (type 2) firstly provide service to virtual customers, if there are any in the system This approach allows us to solve the issue of determination of the number of different types of operators under constraints on the waiting time of an arbitrary virtual customer but complicates the investigation of the system. We consider the model of a call center in which a call-back is not proposed to the customers but operators who call back all customers leaving the system without service.
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