Admission control and pricing in a queue with batch arrivals

We investigate a problem of admission control and pricing in a firm which dominates the market. In the model, there is a single server with exponential service times and arrivals follow a compound Poisson process where the number of customers in a group is an arbitrary discrete random variable. Each arriving group calculates the expected return for the whole group using the waiting cost per unit time, the current queue length, the price provided by the firm and the substitute product reward. It is assumed the firm is a monopoly and price maker per se. The firm’s problem is to set state dependent prices for arriving batches. Once the prices have been set we formulate the admission control problem for the firm, which is a Markov decision process. Properties of the pricing and value functions are characterized, as are the optimal admission policies for a revenue maximizing firm and a social optimizer.