Balking and reneging in M/G/s systems exact analysis and approximations

We consider the virtual queueing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of im-patient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multi-server system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.