Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option

作者：Dudin Alexander; Kim Chesoong^*; Dudina Olga; Dudin Sergey

来源：Annals of Operations Research, 2016, 239(2): 401-428.

DOI：10.1007/s10479-014-1626-2

• Call center
• Call-back
• Generalized phase-type distribution
• Markovian arrival process
• Multi-server queueing system

A multi-server queueing system with a Markovian arrival process and finite and infinite buffers to model a call center with a call-back option is investigated. If all servers are busy during the 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, a real customer can be impatient and may leave the system without service or request for call-back (becomes a virtual customer). The service time of a customer and the dial time to a virtual customer for a server have a phase-type distribution. To simplify the investigation of the system we introduce the notion of a generalized phase-type service time distribution. We determine the stationary distribution of the system states and derive the Laplace-Stieltjes transforms of the sojourn and waiting time distributions for real and virtual customers. Some key performance measures are calculated and numerical results are presented.

• 出版日期2016-4