Call centres with balking and abandonment: from queueing to queueing network models

The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints. The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model. We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available