Browsing by Subject "Naor’s model"

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Stability and pricing in Naor's model with arrival rate uncertainty
(2019-05-14) Liu, Chengcheng; Hasenbein, John J.; Bickel, James Eric; Hanasusanto, Grani A.; Cudina, Milica
Naor's observable queueing model describes an M/M/1 queue with strategic customers and a system manager who maximizes the long-run average revenue rate or social benefit rate. Customers have identical service values and waiting time costs, assuming the waiting cost is linear in time. A new customer chooses to either enter the system or balk after observing the queue length. The system manager decides on the admission fee, which is assumed to be a constant. The results of Naor's model are: the optimal policy for customers is a threshold policy, and customers enter if and only if the queue length is no larger than a threshold; the revenue-maximizing threshold is no larger than the socially optimal threshold, or equivalently, a revenue maximizer (RM) charges a fee no less than a social optimizer (SO). This research studies an observable queueing system in which the arrival rate is not known with certainty by either customers or the system manager. The customer population is modeled to be either homogeneous or heterogeneous. We present three different models: static pricing with uncertain arrival rate and heterogeneous customers; state dependent pricing with uncertain arrival rate and homogeneous customers; and state dependent pricing with uncertain arrival rate and heterogeneous customers. We study the system stability, the optimal behavior of customers and the optimal pricing policies of the system manager.