Queueing models for call centres
This research develops and evaluates queueing models that can be used to model characteristics of basic call centres, i.e. multi-server systems with time-dependent arrival rates, general service time distribution and state-dependent abandonments on arrival (balking). The discrete-time modelling approach which has previously been used for modelling the time-dependent behaviour of multi-server queues is extended to incorporate state-dependent balking. Pure birth state-dependent arrival processes are studied for different arrival rates and are extended for the case of a recurrent arrival rate. Two approximations are introduced to model time-dependent systems with state-dependent balking. These approximations are proved to bound the actual solution for M(t,n)/D/s systems. A simulation model for systems with state-dependent balking is developed. Empirical tests versus this model show that the two approximations provide bounds of controllable accuracy. The performance of systems with balking is studied. Results show insensitivity to the service time distribution. The pointwise stationary approximation (PSA) generally performs well for these systems. A simple formula to estimate the mean number in the system is derived for busy systems with balking. Insights potentially useful to call centre management are reported.