Transient Analysis of M/M/1 Queue with Server Vacation Customers Impatient and a Waiting Server Timer

The customers’ impatience and its effect plays a major role in the economy of a country. It directly affects the sales of products and profit of a trading company. So, it is very important to study various impatient behaviors of customers and to analyze different strategies to hold such impatient customers. This situation is modeled mathematically in this research work along with working vacation and reserved idle time of server, balking and re-service of customers. This paper studies the transient analysis of an M/M/1 queueing model with variant impatient behavior, balking, re-service, reserved idle time and working vacation. Whenever the system becomes empty, the server resumes working vacation. When he is coming back from the working vacation and finding the empty system, he stays idle for a fixed time period known as reserved idle time and waits for an arrival. If an arrival occurs before the completion of reserved idle time, the server starts a busy period. Otherwise, he resumes another working vacation after the completion of reserved idle time. During working vacation, the arriving customers may either join or balk the queue. The customers waiting in the queue for service, during working vacation period, become impatient. But, the customer who is receiving the service in the slow service rate, does not become impatient. After each service, the customer may demand for immediate re-service. The transient system size probabilities for the proposed model are derived using generating function and continued fraction. The time-dependent mean and variance of system size are also obtained. Finally, numerical illustrations are provided to visualize the impact of various system parameters.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Transient Analysis of M/M/1 Queue with Server Vacation Customers Impatient and a Waiting Server Timer

Cited by 2 publications

References 0 publications

Retraction Note to: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations

Retraction Note to: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations

Variant impatient behavior of a Markovian queue with balking reserved idle time and working vacation

Contact Info

Product

Resources

About