Pay to activate service in vacation queues

We study a vacation queueing model where an arriving customer, upon finding the server to be on vacation, is offered an opportunity to pay a fee to instantaneously end the server's vacation, which is referred to as pay‐to‐activate‐service (PTAS). If no one utilizes PTAS, the service will automatically resume when the system's workload reaches a critical level. We investigate customers' equilibrium strategies: (i) joining or balking and (ii) if joining, accepting PTAS or rejecting PTAS, in response to such a mechanism; we show that customers' equilibrium strategies exhibit both avoid‐the‐crowd (ATC) and follow‐the‐crowd (FTC) types of behavior. Our results indicate that the adoption of PTAS is efficient in improving the system performance (e.g., revenue and throughput) when the demand volume is intermediate. We also discover that, upon selecting the appropriate queue‐length information disclosure policy, the service provider has to trade off between collecting a higher revenue through PTAS and improving the system throughput, because revealing the queue‐length information will impact the aforementioned two performance metrics in opposing directions. Finally, we compare our new setting to other common mechanisms including regular vacation queues and pay‐for‐priority queues.