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We consider a single-server queueing system with strategic users. The customers (players) log into the service system with certain rules during a fixed time interval [0, T]. There are many such service systems in reality, it can be a bank, a ticket office, lunch in a cafe, etc. Queueing theory provides the methods for the evaluation of the waiting times, delays and other costs. At the same time, the flow of service requests is initially set in the form of some random process with some initially set intensity. We are considering a model where the queue itself is formed as a result of the actions of the visitors themselves. The customers choose the time of entry into the service system themselves. Thus, a game is formed between the visitors of the service system. We demonstrate how game theory can be applied to optimally select the instant of entry into the service system using the examples of a service with preemptive access and a queueing system with retrials