Efrosinin, D.; Stepanova, N.; Sztrik, J. Robustness of the cμ-Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates. Mathematics2023, 11, 4002.
Efrosinin, D.; Stepanova, N.; Sztrik, J. Robustness of the cμ-Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates. Mathematics 2023, 11, 4002.
Efrosinin, D.; Stepanova, N.; Sztrik, J. Robustness of the cμ-Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates. Mathematics2023, 11, 4002.
Efrosinin, D.; Stepanova, N.; Sztrik, J. Robustness of the cμ-Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates. Mathematics 2023, 11, 4002.
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.
Keywords
Queueing system; cm-rule; scheduling problem; static policy; average cost
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
