A Hybrid Approximation Method for Time-Dependent Queues in Service Systems

Many service systems have time-dependent parameters e.g. queues in healthcare facilities and call centers. For this reason, analysis of time-dependent queues is of great interest. Among the various available approximation methods for time-dependent queues, the fluid/diffusion-based methods, and the stationary-backlog-carryover (SBC) method are efficient and accurate. However, the fluid/diffusion based models do not perform well for under-loaded periods and the SBC method’s performance is negatively affected by the over-loaded periods. To remedy these drawbacks, we develop a hybrid method that alternates between the two methods aiming to apply each one when they perform best. Finally using numerical experiments, we show the accuracy and the efficiency of the hybrid method.