The potentials method for a closed queueing system with hysteretic strategy of the service time change

We propose a method for determining the characteristics of a single-channel closed queueing system with an exponential distribution of the time generation of service requests and arbitrary distributions of the service times. In order to increase the system capacity, two service modes (the main mode and overload mode), with the service time distribution functions F ( x ) and F ( x ) respectively, are used. The overload mode starts functioning if at the beginning of service of the next customer the number of customers in the system ξ(t ) satisfies the condition ξ (t ) > h2. The return to the main mode carried out at the beginning of service of the customer, for which ξ (t ) = h1, where 1 ≤ h1 < h2. The Laplace transforms for the distribution of the number of customers in the system during the busy period and for the distribution function of the length of the busy period are found. The developed algorithm for calculating the stationary characteristics of the system is tested with the help of a simulation model constructed with the assistance of GPSS World tools.