Mathematical Models of Cloud Computing with Absolute-relative Priorities of Providing of Computer Resources to Users in Conditions of Functioning Features and Failures

Source abstract

Analytical models of cloud systems (СS) are developed as queueing systems with a mixed discipline of resource allocation. The models take into account failures and various functioning features and have arbitrary distribution laws for many stochastic processes. Such models for the СS are used for the first time. One of the main indicators of the effectiveness of the СS are indica- tors based on the evaluation of the time characteristics of these systems. Viola- tion of the permissible time constraints, for example, the response time of the cloud system, adversely affects the efficiency of solving the target tasks of the user. This is particularly important for real-time systems and, first of all, for specific information systems built using private cloud systems. General description of the models is as follows. The input of the cloud sys- tem, which implements a mixed queuing discipline (with relative and absolute priorities), receives N Poisson flows of requests for resources with correspond- ing N priorities. The duration of requests queuing of various flows has their own arbitrary distribution laws. Are quest with relative priority interrupted by requests with absolute priority, returns to the queue. Two disciplines of the re- sumption of A and Bqueuing are considered. Within the same priority, requests are processed on a first-come, first-served basis. The СS fails according to the Poisson law, and is restored under an arbitrary law. During the recovery period, elements of adaptation to failures are used: re- quests of some flows to the queue are accepted and accumulated, while others are not accepted (the discipline of the queue replenishment, I and II, respective- ly,). The failure of service device can occur both during of its free state and dur- ing of the requests queuing. Two disciplines of queuing resumption after resto- ration C and D are considered. An interrupted request is processed from the point of its interruption. The combination of queuing resumption and reple- nishment of queue disciplines allows us to consider independent models of var- ious types of systems that have the respective designation. Different functioning features consist of various combinations of disciplines A, B, C, D, I and II. 151