Modeling Marshaling Yard Processes with M/HypoK/1/m Queuing Model Under Failure Conditions

This study presents a comprehensive analysis of the M/HypoK/1/m queuing model to evaluate the performance of marshaling yards in freight rail classification systems. The model effectively captures the complex, multi-phase nature of service and repair processes by incorporating hypo-exponential probability distributions. The marshaling yard is modeled as a finite-capacity, single-server queue subject to potential server failures, reflecting real-world disruptions. Two complementary methodological frameworks are employed: a mathematical model based on continuous-time Markov chains (CTMCs) and a simulation model constructed using Colored Petri Nets (CPNs). In the analytical approach, both service time and repair time follow hypo-exponential distributions, which are used to approximate the gamma distribution. The simulation model built in CPN Tools allows for dynamic visualization and performance evaluation. In the CPN model, we applied a gamma distribution, which allowed us to evaluate the accuracy of the approximation implemented in the analytical model. The result indicated that utilization of the marshaling yard in primary shunting was approximately 23.81%, and with secondary shunting, 22.53%. The study output proves that the hypo-exponential distribution is able to approximate the gamma distribution. This dual-framework approach, combining analytics with simulation, provides a deeper understanding of system behavior, supporting data-driven decisions for capacity planning, failure mitigation, and operational optimization in freight rail networks.