Queueing System MAP/M/N as a Model of Call Center with Call-Back Option

摘要

A multi-server queueing system with a Markovian Arrival Process (MAP), an infinite buffer and impatient customers useful in modeling a call center with a call-back option is investigated. The service time of a customer by a server has an exponential distribution. If all servers are busy at a customer arrival epoch, the customer may leave the system forever or move to the buffer (such a customer is referred to as a real customer), or, alternatively, request for call-back (such a customer is referred to as a virtual customer). During a waiting period, the real customer can be impatient and can leave the system without the service or request for call-back (becomes a virtual customer). An efficient algorithm for calculating the stationary probabilities of system states is proposed. Some key performance measures are calculated. The Laplace-Stieltjes transform of the sojourn time distribution for virtual customers is derived. Some numerical results are presented.