Queueing System with Heterogeneous Customers as a Model of a Call Center with a Call-Back for Lost Customers

摘要

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 lostcustomers is investigated. Type 1 customers arrive to the system according to aMarkovian 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 andserve 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 distributionwith different parameters. The steady-state distribution of the system is analyzed. Some key performance measures are calculated. The Laplace-Stieltjes transform ofthe sojourn time distribution of type 2 customers is derived. The problem of optimalchoice of the number of each type servers is solved numerically.