The impact of a waiting-time threshold in overflow systems with impatient customers

This paper analyzes the performance of call centers with impatient customers, two levels of support, and an overflow mechanism. Waiting calls from the front-office queue – if not reneging – are sent to the back office if at least one back-office agent is available and if a certain threshold t on the waiting time is reached. We approximate such systems via a continuous-time Markov chain that allows for overflow immediately upon arrival. Two different approaches for the derivation of the respective probability of an overflow are developed. Numerical results compare the reliability of these Markovian performance approximations for different parameter settings. The impact of the threshold t on different performance measures is shown dependent on the impatience of customers.