Detecting the Maintenance Disruption in Competitive Queue

The aim of the paper is to adopt the game theory models to determine the appropriate moment to stop the stochastic (queue) system in order to correct its parameter (to do service of the system). There are M point processes which form the M-variate counting process. Each of them has a random moment of changing the parameters. The resultant marked point process can change its characteristics in many moments. If there are observers of each coordinating process to detect the change point and their discoveries are collected in the maintenance center then the set of critical security events could be defined. On this basis, action is being taken on maintaining the system in standby mode. In the presented research the definition of the maintenance time is proposed based on observers' discoveries with the game theory model. The observers' action is administered to collect information or make decisions based on conditions of rivalry and cooperation following the rules of the management system. The former research on such problem has been devoted to the discrete time systems (cf. [27], [41]). The results insignificantly extend the range of application, explain the structure of the optimal detector in various circumstances and shows new details of the solution construction. The problem is reformulated to optimal stopping of the observed sequences by the players. The detailed analysis of the problem is presented to show the form of optimal decision function.