A periodically sampled queuing system with load regulation

Abstract

AbstractIn connection with the periodical registration processing systems, which is uniquely applied to real‐time processing systems, analysis and evaluation are conducted for a system that has load regulation by restricting registration to finite central processor buffers and CP systems. Under the conditions of a single processor, a constant period T, Poisson arrival calls and holding times (average value h) with negative exponential distribution, the author formulates the population function representation of calls in systems immediately after a certain period, and, based on this, calculates the overflow rate and the maximum traffic to be carried per period. Next, using the above distribution, the average number of waiting calls in the CP buffers and outside the CP system at any time are formulated and the average waiting time is calculated by using Little's formula. The continuity of various characteristics in the above nonsaturated state are then examined based on analysis of the saturation states where there always exist waiting calls in the queue outside the CP system. Finally, numerical computations show that as certain evaluation measures such as the number of CP buffers n vary and saturate at about n = 30 if T/h < 30, then at n greater than T/h, T/h < 30. From the above it can be concluded that load regulation has some effect without decreasing the maximum traffic a0 on the conditions that as many CP buffers as economically possible are installed and the period T (T/h) is kept large enough within the allowable range of the average waiting time.