Mathematical model of detecting disorders in service systems

This paper concerns identification of switching times of parameters characterizing several service systems. Each system is described by a marked point process - or compound Poisson process. Intensity of the Poisson process representing arrival demands´ times and probability distributions of service costs change at a random unobserved time interpreted as time of unexpected disorders - disturbances. Service systems are independent, hence disorder times are independent random variables. The aim of a decision maker is to detect the first time of a change in parameter distributions as soon as possible. We construct an optimal detection time which is a stopping time minimizing appropriate mean cost function reflecting penalty for stopping too early or too late. The proposed model is motivated by disorder problems for a compound Poisson process.