A Note on the Distribution of Times Reported by a Low Resolution Interval Timer

Abstract

A number of recent papers (for example Mitrani [3]) have discussed the application of queueing theory models to the operation of a computer. These papers make assumptions about the form of service time distributions (for example that they are exponential) but do not assign explicit values to the parameters of these distributions. Before the results of such a queueing theory analysis can be applied to a particular environment, these unknown parameters must be assigned values by some means. One method is the estimation of the parameters from data obtained by experimentation on the actual environment-for example if the service time of a request for a disk record is believed to be exponential with unknown parameter, then we may estimate this parameter by making requests in the actual environment modelled and studying the resultant service times. Such a procedure provides parameter estimates and a check on the goodness of fit of the postulated distribution. One difficulty which arises in this experiment is that the service times will usually be measured by the computer's interval timer, and so will be some multiple of the timer's increment, which means that the reported service time may differ from the actual service time by as much as one increment in either direction. One popular range of computers has a standard timer increment of 23 msec, which is of the same order as service time for disk requests, and it is clear that this reporting error may be quite serious. The object of this note is to derive expressions connecting reported and actual service times, and to indicate how reported times might be used for inference.