This paper considers a single-server queueing system in which players send requests into the system with preemptive access and fixed reward for completing request. When a request enters the system, the server immediately starts its service. The current request leaves the system when its service is completed or when the next request comes into the system. We study the non-cooperative game, where each player decides when to arrive at the queueing system within a certain period of time. The objective of the player is to serve his request completely or to maximize the time of receiving service. We investigate Nash equilibrium properties in this game. Finally, we present results of numerical experiments demonstrating the equilibria with different values of the model parameters.