Modelling of the process of payments in an insurance company at exponential distribution of the size of payments

Nowadays insurance business is covering more and more different spheres of human’s life and activity. Methods of queuing theory are offered to use for the description of the process of payments in an insurance company. One channel model of queuing theory, where incoming flow is a claim flow on a special type of insurance, and the process of service is the size of payments on claims, is considered. The distribution function of one payment value has exponential distribution. The model has two modes of the operation: with attraction of the reserve fund and without it. Analytical expressions to share the total claim size at each moment of time are received. The offered results can be used for the analysis and the forecast of the activity of an insurance company.