Analysis of a priority queueing system with the enhanced fairness of servers scheduling

A multi-server queueing system with two types of customers is analyzed. Both types of customers have own reserved servers and also there is a pool of servers that can be used by both types of customers. Type 1 customers have almost preemptive priority with flexible use of a priority depending on the current number of customers of this type in an infinite buffer. Type 2 customers do not have an input buffer and are lost in cases of absence of available servers upon arrival or expelling (forced termination) from service by Type 1 customers. A multi-dimensional Markov chain, which defines the dynamics of the considered system under the fixed total number of servers, numbers of reserved servers, a pattern of the correlated arriving processes, service rates, and the thresholds defining the mechanism of expelling Type 2 customers from service, is analyzed. A numerical example of solving an optimization problem based on the obtained results is considered. Results can be used for the elaboration of enhanced protocols of servers scheduling in many real-world systems including cognitive radio networks with channels leasing. © The Author(s) 2022.