Estimating the true arrival, balking, and reneging processes from censored transactional data: a simulation-based approach

The transactional data typically collected/available on queueing systems are often subject to censoring as unsuccessful arrivals due to balking and/or unserved entities due to reneging are not recorded. In fact, in many situations, the true arrival, balking, and reneging events are unobservable, making it virtually impossible to collect data on these stochastic processes—information that is crucial for capacity planning and process improvement decisions. The objective of this paper is to estimate the true (latent) external arrival, balking, and reneging processes in queueing systems from such censored transactional data. The estimation problem is formulated as an optimization model and an iterative simulation-based inference approach is proposed to find appropriate input models for these stochastic processes. The proposed method is applicable in any complex queueing situation as long as it can be simulated. The problem is investigated under both known and unknown reneging distribution. Through extensive simulation experiments, general guidelines are provided for specifying the parameters of the proposed approach, namely, sample size and number of replications. The proposed approach is also validated through a real-world application in a call center, where it successfully estimates the underlying arrival, balking, and reneging distributions. Finally, to enable reproducibility and technology transfer, a working example, including all codes and sample data, are made available in an open online data repository associated with this paper.