On the Arrival Curves Calculation for Facilities of Increased Danger

For present-day facilities of increased danger, such time-related performance measures as delays in control actions transmission and emergency signals presentation are critical. Taking into consideration the appropriate control systems, one can note that the knowledge of arrival processes is necessary for the assessment of such delays. A couple of significant branches of applied mathematics: queueing theory and a theory of deterministic queuing systems network calculus operate with arrival processes and can help with delay evaluation. Arrival curves, a representation of arrival processes in network calculus, seem to be much easier to handle and obtain than probability distributions used in queueing theory. Nevertheless, many different arrival curves can be distinguished, each of them having its pros and cons. The article considers the problem of arrival curve representation and calculation for facilities of increased danger. It discloses the duality of the concept of arrival curve and investigates different types of them: the classical minimal arrival curve, the empirical one, linear arrival curves based on the empirical ones, and arrival curves on finite intervals. For the empirical arrival curve, the algorithm is presented, and the drawbacks are revealed. The advantages and disadvantages of empirical-based linear arrival curves are pointed out. The concept of arrival curves on finite intervals is considered, and the linear representation of them is highlighted. The algorithm for the calculation of linear arrival curves on finite intervals is presented, and their advantages are discussed.