Optimal maintenance and pricing strategy for online service providers: A Stackelberg queueing game approach

With the intensification of cybersecurity threats, there is an increasing urgency for the online service providers (OSPs) to adopt robust maintenance strategies to protect its services. This paper explores OSPs’ optimal pricing and maintenance planning when implementing enhanced Preventive Maintenance (EPM): purchasing Security-as-a-Service (SECaaS), or establishing a Cybersecurity Department (CSD). A Stackelberg queueing game model is employed to characterize the dynamic decision-making process between the OSP and customers, followed by the derivation of customers’ equilibrium purchasing strategies. Then, a two-phase decision-making framework is constructed to determine OSPs’ jointly optimal maintenance-pricing strategies. Finally, the benchmark is extended to scenarios with budget constraints on technical investments. This paper draws the following core findings: (1) Online service providers capable of offering higher rewards to customers possess greater profit potential, enabling them to set higher prices and benefit accordingly; (2) once OSPs reach a certain scale (characterized by high failure costs and high potential demand), establishing a CSD becomes an inevitable trend to ensure their profitability; (3) when customers gain high rewards from reliable services, establishing a CSD is more likely to become a win-win strategy for both OSPs and customers; (4) when the technical budget is sufficient and OSPs possess development capabilities, they must convert technological progress into price competitiveness and utilize price reduction strategies to maximize profitability.