Sensitivity of optimal prices to system parameters in a steady-state service facility

We consider the problem of maximizing the long-run average reward in a service facility with dynamic pricing. We investigate sensitivity of optimal pricing policies to the parameters of the service facility which is modelled as an M/M/s/KM/M/s/K queueing system. Arrival process to the facility is Poisson with arrival rate a decreasing function of the price currently being charged by the facility. We prove structural results on the optimal pricing policies when the parameters in the facility change. Namely, we show that optimal prices decrease when the capacity of the facility or the number of servers in the facility increase. Under a reasonable assumption, we also show that optimal prices increase as the overall demand for the service provided by the facility increases or when the service rate of the facility decreases. We illustrate how these structural results simplify the required computational effort while finding the optimal policy.