A Model For Detecting Change Of Usage Of A System

There are many applications where it is necessary to identify the pattern of usage of a system or facility by independent users. The only information available is the number of times a user may have accessed the system in a certain time interval. If the identified pattern varies significantly from the normal pattern of the user, then some special action may be required. Threshold levels are used to demarcate different types of usages and the detection problem becomes one of choosing appropriate threshold levels. A simplest approach is to use constant threshold levels. This talk describes a mathematical model used to determine optimal threshold levels. In this model, the assumption is made that calls are generated either by a source 0, or by a source 1 according to a Poisson process with rate lambda sub o or lambda sub 1, respectively. At each call arrival point, a decision about which process generated call is made. A monitoring time interval of a given length is considered. The optimal decision is chosen according to a Bayes risk performance measure. It is shown that the optimal strategy is not given by a constant threshold but by a time variant threshold. The best constant threshold is also obtained.