Equilibrium customer strategies in a single server Markovian queue with setup times

We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off. Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine customer behavior under various levels of information regarding the system state. Specifically, before making the decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium strategies for the customers under the various levels of information and analyze the stationary behavior of the system under these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments. © 2007 Springer Science+Business Media, LLC

The effect of discounts on optimal pricing under limited capacity

This paper considers the problem of optimal pricing in a system serving two classes of customers differentiated by their delay sensitivities. We derive the revenue maximising pricing policies whether or not price discrimination is an option. We find that in both cases the optimal policy causes the less delaysensitive class to enter first, and the optimal prices are increasing in capacity under price discrimination, which is not generally true when price discrimination is not allowed. Furthermore, under price discrimination, less capacity is needed to capture a customer class or the entire market, while, more customers are served and higher revenue is generated. Finally, we use an M/M/1 system to provide further insights and numerical analysis. © 2011 Inderscience Enterprises Ltd

Priority option pricing in an M/M/m queue

We study a system where the service provider offers priority options. We identify the optimal option pricing policy, by deriving the optimal number a customer would buy and the customer's exercise policy as a function of system congestion, options remaining, time to expiration and possibility of balking

Admission control policies in a finite capacity Geo/Geo/1 queue under partial state observations

We consider the problem of admission control in a discrete time Markovian queue with a finite capacity, a single server, and a geometric arrival and departure processes. We prove the threshold structure of the optimal admission policy under full information on the number of customers in the system. We also consider the admission control problem under partial state information, where the decision maker is only informed whether the system is empty, full, or in some intermediate state. We formulate this problem as a Markov Decision Process with the state representing the posterior distribution of the number of customers and apply a heuristic algorithm from the literature to approximate the optimal policy. In numerical experiments we demonstrate that the pair of the mean and variance of the posterior distribution may be effectively used instead of the full distribution, to implement the optimal policy. We also explore the behavior of the profit function and the value of information with respect to several system parameters. © 2014, Springer International Publishing Switzerland

Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construct a class of consistent adaptive policies, under which the average outcome converges with probability 1 to the true value under complete information for all distributions with finite means. We also compare the rate of convergence for various policies in this class using simulation. © 2012, Springer Science+Business Media New York