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