An unreliable server characterization of the exponential distribution

Abstract

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 instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.