Abstract
We consider a single-server retrial queue with a Poisson arrival process and exponential service times, where the server is unreliable. Assume there is no waiting space in front of the server and the customer who finds the server unavailable joins an orbit to access the server some time later. We discuss two types of customers’ retrial behavior. One is that each customer in the orbit seeks for services independently and the total retrial rate of the system depends on the number of customers in the orbit. The other type of retrial discipline is called constant retrial policy and it arises from some situations in the computer and communication network where the retrial rate may be controlled by automatic mechanisms. An announced price charged by the server is imposed on customers joining the system and the actual demands for services depend on the price via a decreasing function. We investigate the system characteristics and study how the manager, whose goal is to maximize its own profit, determines the price charging joining customers. Finally, we present an application example to illustrate the obtained results and make comparisons between the two retrial policies from the perspective of customers’ expected waiting time.
Highlights
Over the past decades, advances in computer networking technologies and telecommunications have made it possible for people to communicate with each other and access any content they need everywhere and every time
(ii) By comparing the two retrial policies, we find that the optimal prices and the corresponding probabilities that the server is under different states are the same no matter which retrial policy is adopted
I.e., linear retrial rate and constant retrial rate, are incorporated by assuming service demands decline as the price increases and the customer under service may be interrupted by server’s breakdown
Summary
Advances in computer networking technologies and telecommunications have made it possible for people to communicate with each other and access any content they need everywhere and every time. (i) In the additive demand model and multiplicative demand model, we derive the unique optimal pricing strategy for the service provider It is found the server’s revenue is irrelevant to the breakdown rate of an idle server, but depends on the breakdown rate of the busy server. Failure, numerical examples show that customers’ expected waiting time in the orbit under the optimal price still increases when the server’s breakdown rate at idle state grows, but this monotonicity may change when the breakdown of a busy server occurs more frequently. How customers’ expected waiting time in the orbit under the optimal price changes with respect to the breakdown rate of a busy server may depend on the server’s repair rate.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
