Regulating an M/G/1 queue when customers know their demand

Customers do not necessarily join a queue at a socially optimal rate. Hence, queueing systems may call for regulation. For customers in an M/G/1 unobservable (not necessarily FCFS) queue and homogeneous with respect to waiting costs and service rewards, we show how queueing systems can be regulated by imposing an entry fee, a holding fee (based on time in the system), or a service fee (based on the required service time) when customers know their service requirements. We start with a unified approach and state the socially optimal fees. We show that customers are always worse off under a flat entry fee in comparison with holding and service fees. As for holding vs. service fees, the answer depends on the queueing regime and/or the service length itself. For example, under FCFS, service fees are preferred by all. Details are given on some common service regimes. We also review the case where customers know only the common distribution of service times, but not their actual requirements.