Strategic joining and information disclosing in Markovian queues with an unreliable server and working vacations

We study a queueing system of an unreliable server providing services to customers with two different service rates. When the system is empty of customers, the server takes a vacation and provides a low service rate. Once the vacation is completed, the server is resumed to serve customers, if any, at a higher service rate, or takes another vacation if the server found an empty system. The server is subject to random breakdowns when serving customers and if failed, it enters a repair stage. Under different system information levels, we investigate customers' equilibrium strategies and follow-up system measures. Numerical comparisons among different information levels reveal that when the traffic load is large enough, the service provider (SP) prefers to disclose the server's status and queue length information to customers to maximize the system throughput. While when the traffic load is small enough, there exist two cases with regard to the failure rate: (i) If the failure rate is smaller than a certain threshold, the SP tends to conceal the system information. (ii) If the failure rate is greater than the threshold, revealing the information is helpful to maximize the system throughput.