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

الملخص EN

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.

Type r, r=1,2, servers serve type r customers if there are any in the system andserve type r′, r′=1,2, r′≠r, customers if there are no type r customers 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.