Abordagens de modelos de filas com abandono para análise de congestão em Call Centers

Abstract

This work deals with the analysis of queueing systems for Call Centers regarding the possibility of the customer abandon the system before being served, due to his/her impatience. The Call Centers are service organizations that predominantly serve customers by phone calls and are considered a particular kind of Contact Centers that serve their costumers through phone, fax, e-mail, chat, mobile devices and other communication channels. From a business point of view, the main concern on the management of the Call Center is the offer quality service with minimum cost. The perception of the quality of services offered is expressed, by customer, for example, through the abandonment of queue, which is considered one of the most important operational measures to evaluate the performance of a Call Center. This work aims to present and apply analytical queueing models with abandonment, represented by generic probability distributions (particularly mixed distributions), as an effective analysis approach to represent the problem of congestion in Call Center systems and support decisions of dimensioning and operations on these systems. Two studies were conducted with Call Center extracted data of a company located in the countryside of São Paulo State, Brazil and another located overseas, in Israel. The parameters (e.g, arrival rate, service rate, abandonment rate) and some measures of performance (e.g, average waiting time, waiting probability, abandonment probability and traffic intensity) were established based on these data. These sampling measures were equated with the same measures achieved by the analytical queueing models M/M/c+G, M/Gc/1+G and M/G/c+G considered in this research, using the parameters obtained empirically and mixed, Exponential, Fatigue Life, Normal and Lognormal distributions to represent the abandonment (patience) of users. It was observed that in some cases, depending on the considered performance measure, the queueing models with mixed distributions for the abandonment have better results (minor deviations, compared to the real data) than their corresponding with nonmixed distributions. It was observed, also, that independently of the analyzed performance measures, the Call Centers may be represented by a analytical queueing model with a mixed distribution for abandonment times, which behaves better than the others. There were no evidences that the mixed distributions to represent the abandonment times were the best in all analyzed performance measures, but they were always competitive. It was used, also, an experimental model of discrete simulation that properly represents the Call Center in order to check the results of the analytical models and explore alternative scenarios. The same scenarios were considered with the theoretical model and the performance measures achieved by the simulation and by the theoretical models were compared, showing the potential of the use of the approaches based on analytical models with abandonment for the Call Centers analysis.