Abstract
This work investigates the optimal pricing strategies of a server and the equilibrium behavior of customers in an unobservable M/M/1 queueing system with negative customers and repair. In this work, we consider two pricing schemes. The first is termed the ex-post payment scheme, where the server charges a price that is proportional to the time spent by a customer in the system. The second scheme is the ex-ante payment scheme, where the server charges a flat rate for all services. Based on the reward-cost structure, the server (or system manager) should make optimal pricing decisions in order to maximize its expected profit per time unit in each payment scheme. This study also investigates equilibrium joining/balking behavior under the server’s optimal pricing strategies in the two pricing schemes. We show, given a customer’s equilibrium, that the two pricing schemes are perfectly identical from an economic point of view. Finally, we illustrate the effect of several system parameters on the optimal joining probabilities, the optimal price, and the equilibrium behavior via numerical examples.
Highlights
Over the past several decades, queueing systems considering customers’ equilibrium behavior have received much attention owing to their applications to the management of various systems
Under the ex-post payment (EPP) and ex-ante payment (EAP) schemes, we show that the two pricing schemes do not affect customers’ joining behavior and the server’s maximum profits, which has not been reported in the literature on an M/M/1 queueing system with negative customers and repair
We deal with numerical experiments in which we investigate trends in the optimal prices and joining probabilities of EPP and EAP schemes according to various input values
Summary
Over the past several decades, queueing systems considering customers’ equilibrium behavior have received much attention owing to their applications to the management of various systems. Wang et al [22] studied the equilibrium behavior of customers in a retrial queue with negative customers and derived corresponding Nash equilibrium joining strategies and a social net benefit maximization problem with respect to the levels of information available to customers upon arrival. In terms of maximizing the operation profits of the cloud data center, analyzing optimal and equilibrium pricing strategies is important. Motivated by the aforementioned studies and the possible application to pricing in a cloud data center, we analyze optimal pricing strategies and the equilibrium joining/balking behavior of customers in an unobservable M/M/1 queueing system with negative customers and repair under the two pricing schemes described above. To the author’s knowledge, this study is the first to consider the pricing strategies together with the customer equilibrium behavior for an M/M/1 queueing system with server failure and repair. We deal with numerical experiments in which we investigate trends in the optimal prices and joining probabilities of EPP and EAP schemes according to various input values
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