Performance analysis of call centers based on M/M/S/K+M queue in changeable service rate with server breakdowns

In order to analyze performance qualities of a call center quantitatively, as such characters that a customer's waiting queue will probably be abandoned due to impatience when all the servers are busy, agents change service rate according to the length of waiting queue and the servers can break down at any time. An M/M/S/K+M queueing model in the changeable service rate with impatience and server breakdowns is studied. An analytic solution and some system measures in stability of the model are given. It is pointed out that optimal number of servers can be derived if interrelated parameters are given, customers will be more satisfied if agents or trunks are increased, and the system performance can be improved by using quicker service rate when the length of waiting queue is greater than zero. In addition the spare servers can be provided according the measure of expected value of server breakdowns.