Queue size detection based on covariance function of demand number

This work is focused on analysis of queuing systems for stationary ordinary recurrent demand flows. It was detected that correlation between incoming demands flows influence on queue size. In the present paper it is shown that queue formation process in train flow systems is cycle, and it is divided on active and passive sub-cycles. By using cycle analysis, we derived generalization of known Pollaczek-Khintchine formula that was initially applicable only for analysis of Poisson flows. Correlation influence on queue size is demonstrated. It is proved that maximal value of integral of covariance function for demand number over demand service interval under given duty ratio completely determines mean size of queue in single-device queuing system.