AN UNRELIABLE SERVER CHARACTERIZATION OF THE EXPONENTIAL-DISTRIBUTION

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is ins tantaneously repaired, and the server restarts the uncompleted job fro m the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter lambda, then because of the lack -of-memory property of the exponential, P(T > t) = G(t)BAR = exp( - la mbdat), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.