Boundary values evaluation for average response time to an information system user request

The paper proposes methods for estimating the upper and lower bounds of the average response time of large information systems to a user request. A user request is a transaction consisting of a sequence of commands for which computing resources are reserved. The transaction is formalized as a route, which is a chain of “server-buffer” pairs, their number is equal to the number of transaction commands. At the same time, the service device is a mean of executing transaction commands; the buffer is a memory for fixing the results of executing transaction commands and waiting for the time to arrive for service. Allocation of loosely coupled route groups allows parallel processing of transactions. The authors propose a mathematical scheme of a large information system that organizes transaction routes in the form of a queuing network, so that each user request passes a certain route from the service devices. The method for estimating the upper bound on the average response time of the system to a user request is based on adding redundant dependencies and duplicating some service nodes. The method for estimating the lower bound of the average response time of the system to a user request is based on the removal of serving nodes that play the role of a weak connection between neighboring routes of the queuing network. The proposed methods allow selecting such parameters that meet the requirements for the information system being developed and, accordingly, meet the indicators of the quality of service for users of information systems.