The Robustness of the cμ-Rule for a Unreliable Single-Server Two-Class System with Constant Retrial Rates

Description

Abstract—We study the robustness of the cμ-rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FCFS retrial discipline, when the customers at the head of queues repeatedly tries to occupy the server in a random time. It is proved that for the scheduling problem in the system without arrivals the cμ-rule minimizes the total average cost. For the system with arrivals it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes for the certain values of system parameters the service exclusively for the class- i customers if both of queues are not empty with the aim to minimize the average cost per unit of time. It is also shown that in a finite-buffer case the cμ-rule fails.

Period	17 May 2022
Event title	The 2022 IEEE 2nd Conference on Information Technology and Data Science
Event type	Conference
Location	HungaryShow on map