Optimal joining strategy and pricing analysis in unreliable retrial queues with predictive maintenance

¹ School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100081, P.R. China
² School of Science, Yanshan University, Qinhuangdao, Hebei 066004, P.R. China
³ College of Humanities and Information, Changchun University of Technology, Changchun, Jilin 130117, P.R. China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 13 November 2024
Accepted: 8 November 2025

Abstract

The timely improvement of systems, based on the feedback from the service data, is becoming an increasingly common practice to enhance system reliability. This generates a novel predictive maintenance policy: after each service is completed, the server performs predictive maintenance to reduce the server’s failure rate at the next service. We study an unreliable M/G/1 retrial queue with predictive maintenance. First, the stationary distribution and performance measures are analyzed using the supplementary variable method. Then, the threshold strategy of the predictive maintenance is proposed from the perspective of customers’ waiting time. Based on the linear reward-cost structure, the customer’s equilibrium strategy and socially optimal strategy are derived. Next, the optimal pricing strategy is obtained, in order to eliminate the difference between equilibrium and socially optimal strategies. Finally, numerical examples are provided to illustrate how system parameters affect customers’ strategic behavior. These examples also demonstrate the accuracy of the closed-form solution for the socially optimal joining probability using a Particle Swarm Optimization (PSO) algorithm and a Genetic Algorithm (GA).