Fluid Models of Parallel Service Systems Under FCFS

In parallel service systems, customers of various types are served simultaneously by several servers that have some dierent and some overlapping skills or capacities. Examples include customer routing in call centers, scheduling of hospital operating rooms, and driver assignment in ride-hailing services. First come first served (FCFS) is a natural and widespread resource allocation policy, yet its performance both during the transient stage and in the long run is often difficult to analyze. In particular, matching rates, which indicate what fraction from all services are of a specific server customer type, are difficult to evaluate under FCFS. In Fluid Models of Parallel Service Systems under FCFS, Yuval Nov, Gideon Weiss, and Hanqin Zhang formulate a stochastic queueing model for such systems and study its fluid approximation. The paper demonstrates the usefulness and the limitations of exploring fluid performance in evaluating system behavior in terms of stability, responsiveness, and utilization.