Abstract
In this article, we deal with Markov models of multi-channel [M|M|m|m+n](∞)–systems with repeated calls and queues with a variable rate of input flow controlled by threshold strategies without restrictions on the capacity of the orbit. An effective calculating algorithm for the characteristics of such systems in stationary regimes is proposed. First, stationary probabilities for a truncated model are investigated. Second, the obtained result is extended to a general model with an infinite number of servers. For threshold control strategies the optimization problem of the total income of the system is formulated and solved. In a particular case with one server and one place in the queue, the direct formulas for stationary probabilities are obtained, and the rate of convergence of the stationary distribution of a finite system to that of an infinite system under threshold strategies are estimated.
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.
