Admission Control and Pricing in a Queue with Batch Arrivals
Utku Yildirim and J. J. Hasenbein
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.