MATHEMATICAL MODELING OF THE OPERATION OF RAILWAY ACCESS TRACK LOADING/UNLOADING FRONTS USING THE RAMS APPROACH

Source abstract

The article is devoted to the development of a multi-criteria mathematical model for optimizing the parameters of the operation of freight fronts of railway access tracks with the integration of RAMS analysis (Reliability, Availability, Maintainability, Safety) in accordance with the EN 50126 (IEC 62278) standard. The station-access track system is formalized as a multi-channel M/M/Z mass transit system using the Erlang-C formula, which allows taking into account the stochastic nature of the train flow. The objective function is constructed taking into account 14 cost components and two competing stakeholders – the railway (minimization of operating costs, downtime and queues) and the cargo owner (minimization of capital freezing and own operating costs), which determines the multi-criteria nature of the problem.The key scientific novelty is the introduction of a deterministic equivalent of the chance-constrained problem Z_min(RAMS), which takes into account the coefficient of variation of the incoming car flow (CV_N) and the readiness of the storage and distribution machines (A_HRM) through the effective system parameters μ_eff and T_sys_eff. It is shown that traditional deterministic optimization systematically underestimates the required number of HRM: for a typical scenario (CV_N = 0.30, A_HRM = 0.95, reliability level α = 0.95) the deterministic calculation gives Z_min = 5, while the RAMS constraints require Z_min = 7, which is 40 % more. The proposed stochastic risk premium C₁₁(RAMS) with the multiplier (1+z_α·CV_N) allows us to quantitatively assess the economic consequences of neglecting the variability of the flow.Based on a numerical example (grain approach track, N_row = 34 weights/day), a comparative analysis of optimization options for both stakeholders was performed, sensitivity tables were constructed (Z_min(RAMS) from CV_N and A_HRM, TCO components depending on Z, parameter dynamics during the year) and a RAMS objective tree was formed. Verification of the model on actual data showed a deviation of model values from the accounting values of no more than 6 % (according to the Fisher criterion). The results can be used for technological standardization of wagon processing time, justification of investment decisions regarding the number of HRM and formation of contractual terms between the railway and cargo owners taking into account stochastic risks.