Pricing in Queues Without Demand Information

We consider revenue optimization in an M/M/1 queue with price and delay sensitive customers, and we study the performance of demand-independent pricing that does not require any arrival rate information. We formally characterize the optimal demand-independent price and its performance relative to pricing with precise arrival rate knowledge. We find that demand-independent pricing can perform remarkably well and its performance improves as customers become more delay sensitive. In particular, for uniformly distributed customer valuations, under a large set of parameters, we find that demand-independent prices can capture more than 99% of the optimal revenue. We also study social optimization and find that demand-independent pricing can perform quite well; however, the performance is better under revenue optimization.