Optimal Pricing in Multi Server Systems

We study optimal service pricing in server farms where customers arrive according to a renewal process and have independent and identical ($i.i.d.$) exponential service times and $i.i.d.$ valuations of the service. The service provider charges a time varying service fee aiming at maximizing its revenue rate. The customers that find free servers and service fees lesser than their valuation join for the service else they leave without waiting. We consider both finite server and infinite server farms. We solve the optimal pricing problems using the framework of Markov decision problems. We show that the optimal prices depend on the number of free servers. We propose algorithms to compute the optimal prices. We also establish several properties of the optimal prices and the corresponding revenue rates in the case of Poisson customer arrivals. We illustrate all our findings via numerical results.