zbMATH — the first resource for mathematics

The service time properties of an unreliable server characterize the exponential distribution. (English) Zbl 0792.60014
Summary: Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

60E10 Characteristic functions; other transforms
60G50 Sums of independent random variables; random walks
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Full Text: DOI