Equilibrium strategies in Markovian queues with working vacations and adaptive vacation interruptions

Motivated by resource allocation dynamics in cloud computing environments, this work investigates a strategic queueing system incorporating multiple working vacations and adaptive vacation interruption policies, analyzed through a game-theoretic lens to model customers’ joining decisions. When the system becomes idle, the server transitions to an energy-saving vacation mode, delivering reduced-speed service while remaining operational – a mechanism inspired by cloud platforms’ scalability to balance efficiency and responsiveness during low-demand periods. Upon completion of a vacation, if there are customers in the system, the server resumes normal busy service with full-capacity speed; otherwise, it enters the next vacation period during which the vacation is interrupted with probability p whenever a new customer arrives. Based on a linear reward-cost structure, we study the strategic behavior of customers under three different information cases. Our numerical examples demonstrate the impact of system parameters and information levels on customers’ strategic behavior and the service provider’s profit. It is shown that the adaptive vacation interruption mechanism can significantly inspire customers to join the queue when both the queue length and server state information are disclosed. In addition, the service provider can achieve optimal profit by adjusting the service rates. The optimal strategy involves that a higher (lower) normal service rate should be paired with a lower (higher) working vacation service rate. Furthermore, concealing server state and queue length information is optimal under low demand, whereas disclosing this information is optimal under heavy demand.