Method of potentials for a closed system with queue length dependent service times

A method to determine characteristics of a single-channel closed queueing system with exponential distribution of the customer generation time and arbitrary distribution of service time is proposed. An increase in the capacity of the system is reached using the distribution law of service times that depends on the number of customers in the system at the starting moment of servicing. The Laplace transforms for the distribution of the number of customers in the system during the busy period and the distribution function of the busy period are derived. An algorithm for calculation of the stationary characteristics is tested using a simulation model that is developed with the assistance the GPSS World tools.