Control of arrivals and departures in a state-dependent input-output system

At each decision epoch, an offer for a unit to either enter or leave a system is received. These offers arrive according to a Poisson process. With each offer is associated a value revealed upon the arrival of the offer. The distribution of the value of the offer is given and is a function of what kind of offer is received (enter or leave). The decision to accept or reject and offer is allowed to depend on the current state and the current value received. The objective is to maximize the expected discounted difference between the sum of the accepted output offers and the sum of the accepted input offers. The key result of the paper that under various conditions, the decision to accept or reject an offer depends on whether or not its value is above or below, respectively, a critical value that depends on the state of the system.