About one task of overload control

The article considers the relatively simple task of congestion control. On the server with a finite number of places of service and potentially infinite queue, jobs are running, coming from the random flow. Control means the adoption of the decision on admission or rejection of each newly incoming job. Accumulation of the queue may result in loss of quality of service, because the period of execution of jobs is limited. At the same time, the rejection of application causes the loss of income. It is proved that in the case of exponentially distributed service time and for input flows, described as the renewal process with an arbitrary interarrival time distribution, optimum is a simple threshold strategy. The dependence of the limiting average income on the threshold value is unimodal. This circumstance greatly facilitates the search for the optimal integer value of the threshold. Experimental analysis shows that this dependence has a place for arbitrary distribution of service time and for general type of Markov modulated input flows.