Personalized queues: the customer view, via a fluid model of serving least-patient first

In personalized queues, information at the level of individuals – customers or servers – is affecting system dynamics. Such information is becoming increasingly accessible, directly or statistically, as exemplified by personalized/precision medicine (customers) or call-center workforce management (servers). In the present work, we take advantage of personalized information about customers, specifically knowledge of their actual (im)patience while waiting to be served. This waiting takes place in a many-server queue that alternates between overand under-loaded periods, hence a fluid view provides a natural modeling framework. The parsimonious fluid view enables us to parameterize and analyze partial information, and consequently calculate and understand the benefits from personalized customer information. We do this by comparing Least-Patience First (LPF) routing (personalized) against FCFS (relatively info-ignorant). An example of a resulting insight is that LPF can provide significant advantages over FCFS when the durations of overloaded periods are comparable to (im)patience times.