Analysis of two-level support systems with time-dependent overflow: a banking application

In this paper, we analyze the performance of call centers of financial service providers with two levels of support and a time-dependent overflow mechanism. Waiting calls from the front-office queue flow over to the back office, if a waiting-time limit is reached and at least one back-office agent is available. The analysis of such a system with time-dependent overflow is reduced to the analysis of a continuous-time Markov chain with state-dependent overflow probabilities. To approximate the system with time-dependent overflow, some waiting-based performance measures are modified. Numerical results demonstrate the reliability of this Markovian performance approximation for different parameter settings. A sensitivity analysis shows the impact of the waiting-time limit and the dependence of the performance measures on the arrival rate.