Processing a finite number of entires by unreliable servers

The paper is concerned with two problems of processing a finite number of entries by unreliable servers. In one all entries simultaneously enter a system of one server. The time before the server fails is exponentially distributed and the times of entry processing are arbitrarily distributed. In the other the times of entry arrival and processing are deterministic and the time before the server fails is arbitrarily distributed. In both cases a schedule is sought which would maximize in some way the system income before the servers fail.