Monitoring remote server accessibility: the optimal filtering approach

The online monitoring problem of a remote server, accessible via the http protocol, is formulated in the terms of optimal filtering. The unobservable server state is treated as a finite-dimensional Markov jump process, meanwhile the observation is supposed to be a multivariate point process with a finite set of possible values. The key point of the investigated observation system is that the random intensity of observations is a linear function of the unobservable Markov state. It is proved that the optimal filtering estimate is a solution to some closed finite system of recursive formulae and ordinary linear differential equations with a random right-hand side. The applicability of the obtained theoretical results is illustrated by an example of monitoring accessibility of the queueing system “communication channel–database server”. The unobservable state of this system consists of three possible values (no connection, low workload, high workload), meanwhile the possible observations belong to the set of two possible values (answer to the query, error message). The conclusion of the paper contains possible prospectives for the further research.