It is propossed to use foggy calculations to reduce the load on data transmission devices and computing systems in GIS. To improve the accuracy of estimating the efficiency of foggy calculations a non-Markov model of a multichannel system with queues, "warming up" and "cooling" is used. A method for calculating the probalistic-temporal characteristics of a non-Markov system with queues and with Cox distributions of the duration of "warming up" and "cooling" is prorosed. A program has been created to calculate the characteristics of the efficiency of fog calculations. The silution can be used as a software tool for predictive evaluation of the efficiency of access to geographic information systems, taking into account the features of fog computing technology and the costs of ensuring information security.

Keywords: fog computing, model of a multi-channel service system with queues, “warming up”, “cooling down”, geographic information systems, Cox distribution