Congestion-Based Repair Policy for a Failure-Prone Service System With Strategic Customers
研究了服务提供商采用基于拥堵的修复策略（根据等待人数调整修复速度）与策略性顾客的决策互动，发现该策略能在吞吐量和成本间取得平衡，相比经典修复策略利润最高可提升34.4%。
This study examines the decision-making interaction between a service provider adopting a congestion-based repair policy and strategic customers in a failure-prone M/M/1 queueing system. The server’s lifetime is exponentially distributed, and a repair starts immediately upon the server’s breakdown. The repair rate is adjustable: the service provider employs a high repair rate (with a high cost) if the number of waiting customers reaches a threshold; otherwise, a low repair rate (with a low cost) is adopted. We model the interaction as a two-stage Stackelberg game: the provider (leader) sets the price, repair threshold, and information policy before customers (followers) decide whether to join. Using backward induction, we characterize the resulting Stackelberg equilibrium. Under fully unobservable and almost unobservable cases, both follow-the-crowd (FTC) and avoid-the-crowd (ATC) behaviors are found to coexist in the customer’s equilibrium joining strategy. Two special models, the classic repair model (when the threshold approaches 0) and the delayed repair model (when the low repair rate approaches 0), are discussed extensively. The classic repair policy maximizes throughput but incurs the highest costs, while delayed repair minimizes costs at the expense of throughput. The proposed congestion-based repair strategy balances these tradeoffs, achieving intermediate throughput and cost levels. Notably, it can increase profits by up to 34.4% compared with classic repair, with its effectiveness amplified under high-cost scenarios. By comparing the unobservable case with the almost unobservable counterpart, we demonstrate that hiding server state information when prices are low and disclosing server information when prices are high can increase profit for the service provider, but at the expense of reducing social welfare.