Abstract

A multi-server queueing system with an infinite buffer operating in the Markovian random environment is analyzed. Under the fixed state of the random environment, the arrival flow is described by the Markovian arrival process. Customers in the buffer may be impatient and leave the system. The number of available servers, the arrival process, the rate of customers’ service, and the impatience intensity depend on the state of the random environment. Behavior of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. Algorithm for computation of the stationary distribution is provided. The main performance measures of the system are calculated.

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 call

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.