The study of nocturnal bird migration by cone methods of observation has a century-long history but has continued to be used up to the present. To describe the flux and estimate the number of passing birds a probabilistic model is proposed. This model is based on the concept of dynamic Poisson ensemble of points in appropriate phase space and has two parameters. One is scalar and the other one is functional. We constructed consistent estimations of these parameters and discuss their use for the numerical estimation of the flux of birds observed in a narrow light cone generated by the bright lunar disk and formed by an open angle of telescope. Selection on the same type of birds was suggested as the necessary condition for the model application. Ground speed of each bird was introduced into the model as a new but obligatory value determining the quantification of the flux of bird.