On the Features of Service Rate Control in Fork-Join Queueing System

A classical fork-join queueing system is considered. The model is proposed for determining the optimal cost of such a system, taking into account the need to minimize the average response time simultaneously with reasonable costs for the resources required for this. The term “resources” within the framework of the mathematical model under study means the intensities of service on servers, the cost of which is directly proportional to the system performance, i.e., the rate of service requests. For the special case when the number of subsystems is equal to two, an exact analytical expression for determining the optimal cost is presented, for a more general case when the number of subsystems of a fork-join queueing system is greater than two, equation is obtained, the numerical solution of which allows calculating the desired value. In addition, the asymptotic analysis of the obtained solutions behavior is carried out.