Abstract
Suppose a single server has $K$ channels, each of which performs a different task. Customers arrive to the server via a nonhomogenous Poisson process with intensity $\lambda(t)$ and select $0$ to $K$ tasks for the server to perform. Each channel services the tasks in its queue independently, and the customer's job is complete when the last task selected is complete. The stress to the server is a constant multiple $\eta$ of the number of tasks selected by each customer, and thus the stress added to the server by each customer is random. Under this model, we provide the survival function for such a server in both the case of independently selected channels and correlated channels. A numerical comparison of expected lifetimes for various arrival rates is given, and the relationship between the dependency of channel selection and expected server lifetime is presented.
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 callMore From: International Journal of Statistics and Probability
Disclaimer: 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.
