Estimating the Reliability of Hosts Using the Internet

17 The pattern of failures of many classes of hosts were clearly not exponential. This is not surprising when the data contains points that are obviously invalid, but many classes still failed the test for exponentiality even when such noise is factored out. It is generally true that larger sample sizes provide more evidence against the exponential hypothesis. Massive amounts of data can more easily highlight minute deviations from exponential behavior. The sample comprised of all Internet responses conclusively failed the exponentiality test, pointedly emphasizing this tendency. For moderately-sized samples, it was often not possible to exhibit the deviation from exponentiality, lending credence to the common practice of assuming that MTTF is exponentially distributed. Availability was diicult to estimate accurately using the Internet. This was due to the many possible reasons for a host not responding to a request, most of which are indistinguishable to the polling process. Among these are the host being down, the host not implementing the polling protocol, and both hard and soft network failures. This was addressed by using a two-phase approach that limited the domain to only those hosts that were known to be able to respond to Sun Rpc requests. Unfortunately this method is slightly biased against hosts with poor availabilities, as such hosts may go be unnoticed during the initial samplings. This bias can be minimized by extensive polling at various intervals during the rst phase, to ensure that most existing hosts are marked for participation in the second phase. The rst phase was limited to two weeks due to time constraints and the considerable network traac it generated. The two month interval between the rst and second phases was chosen to ensure that there is negligible correlation between a host being up in the rst phase and being up in the second phase. Although it is unlikely that the sample was drawn from an exponential distribution, the averages obtained are a reasonable approximation of the actual MTTF and closely match those seen in practice by system administrators. If the distributions of up-times is not exponential, but instead governed by a hyperexponential distribution, then the eeect will be to overestimate the MTTF. Acknowledgments The authors are especially grateful to Jim Gray and Robert Hagmann for their many excellent suggestions. Jehan-Frann cois P^ aris, Richard Golding, and Mary Long also contributed through their thoughtful comments. Several of the closed-form solutions were found with …