The approximation of response time of a cloud computing system

Cloud computing is an evolutionary technology that allows a remote user to gain access to resources through Internet services. The article discusses the cloud computing system, which receives complex user queries consisting of several subqueries. The allocation of one unit of the resource is required for processing each subquery. Accurate assessment of effectiveness of cloud computing resources is a prerequisite to ensure the required quality of service. Response time, i. e., the maximum of subqueries service times, is chosen as an indication of effectiveness of a cloud computing system. To analyze the characteristics of response time, a simplified mathematical model of a cloud system was constructed as a queuing system with single Poisson input flow of requests and several subsystems (a buffer and a server). Each request at the instant of arrival is divided into several parts, each of which is served by its queuing subsystem with unlimited storage capacity with exponentially distributed service time. The analytical formulas for approximation of mean response time and its variance are presented. To assess the accuracy of the approximation, a GPSS (General Purpose Simulation System) model was constructed.