Descripción de procesos del negocio

6.1 INTRODUCTION

This chapter gives the summary of this present work, conclusion based on the analysis and findings of this work as well as recommendations for future work.

6.2 SUMMARY

The help desk analyzed in this work is a form of a contact centre for technical support for hardware or software. It is staffed by people who can either solve the problem directly or forward the job to someone else who can handle it. One of the goals of the design of this help desk is to establish the right number of staff to be employed as well as number of trunk lines to be provided in order to maintain a target service level. In order to achieve this goal, statistical model has to be developed to design this help desk.

Queueing models have been used extensively in designing call centres. In this research work, a simple queueing model G|G|N|S was used in designing and analyzing this help desk. Major inputs to the building of this model are the description of the arrival process and the service process. This research work focused on describing service process in this help desk.

From the literature, service times are assumed to be exponentially distributed.

Mandelbaum [23] proposed that at least for one call centre, exponential distribution does not describe the service times and suggested a log-normal distribution as an option to model the service times in call centres. Since queues with log-normal service times are difficult to analyze, phase-type distributions that can model several stages of the service process were investigated as possible models of the service times.

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This research work confirms the irrelevance of assumption of exponential dis-tribution to this help desk. It also modelled service times in this help desk with log-normal distribution as suggested by Mandelbaum. Phase-type distributions with phases p = 2, 3, 4 were fitted to service times of this help desk. Finally, the log-normal models of this help desk were approximated using phase-type distribution of order p = 3. Parameters of log-normal models were estimated using the maxi-mum likelihood parameter estimation. Due to the complexity in the derivation of maximum likelihood parameter estimates of the phase-type distribution, the expec-tation - maximization (EM) algorithm was used in estimating the parameters of the phase-type distribution. This was implemented using the EMpht program. The two famous goodness of fit tests, Kolmogorov-Smirnov and Anderson-Darling tests were implemented to assess the models and for model selection.

6.3 CONCLUSION

Based on the analysis of the data from this particular help desk, it was found that service times in this help desk are not exponentially distributed. Log-normal distributions gave appropriate description of the overall service times and the service times of administrative, e-mail, miscellaneous and network jobs. A phase-type dis-tribution with three phases (PH(3)) provided a reasonable fit to the overall service times and the service times of administrative jobs and miscellaneous jobs. Whereas a phase-type distribution with two phases (PH(2)) provided a suitable model for the service times of e-mail and network jobs. Finally, a phase-type distribution with three phases (PH(3)) was used to approximate the log-normal model for the overall service times and the service times by job types.

6.4 RECOMMENDATION FOR FUTURE RESEARCH

The arrival process in this help desk should be investigated, so as to be able to analyze the model G|G|N|S used in modelling this help desk. Further work is necessary on practical interpretation of the phases in the phase-type model. Analyzing other call centre data should also provide more insights into modelling service times by other non-exponential distributions.

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