Charging more for priority via two-part tariff for accumulating priorities

We consider an unobservable M/G/1 queue with accumulating priorities and strategic customers who pay for priority accumulation rates. We show that when affine pricing is introduced, multiple equilibria may exist. This is in contrast to the standard linear pricing case where the equilibrium strategy is unique. Furthermore, a revenue-maximizing operator may generate more revenue under the optimal affine pricing than under linear pricing. In particular, we show that if the utilization level is not too high, no other combination of a priority scheme and pricing generates more revenue than the optimal affine pricing of accumulating priorities.