Statistical distributions for service times

Abstract

Queueing models have been used extensively in the design of call centres. In particular, a queueing model will be used to describe a help desk which is a form of a call centre. The design of the queueing model involves modelling the arrival an service processes of the system.Conventionally, the arrival process is assumed to be Poisson and service times are assumed to be exponentially distributed. But it has been proposed that practically these are seldom the case. Past research reveals that the log-normal distribution can be used to model the service times in call centres. Also, services may involve stages/tasks before completion. This motivates the use of a phase-type distribution to model the underlying stages of service.This research work focuses on developing statistical models for the overall service times and the service times by job types in a particular help desk. The assumption of exponential service times was investigated and a log-normal distribution was fitted to service times of this help desk. Each stage of the service in this help desk was modelled as a phase in the phase-type distribution.Results from the analysis carried out in this work confirmed the irrelevance of the assumption of exponential service times to this help desk and it was apparent that log-normal distributions provided a reasonable fit to the service times. A phase-type distribution with three phases fitted the overall service times and the service times of administrative and miscellaneous jobs very well. For the service times of e-mail and network jobs, a phase-type distribution with two phases served as a good model.Finally, log-normal models of service times in this help desk were approximated using an order three phase-type distribution.