A reproducible Monte Carlo simulation of an inland railway container terminal under stochastic arrival and finite yard capacity constraints

Global containerization has become the backbone of international supply chains, and container terminals continue to face difficulties caused by random and irregular cargo flows. These challenges are even more evident in landlocked countries such as Uzbekistan, where terminals must handle rising trade volumes with limited infrastructure. We developed a discrete time Monte Carlo simulation framework to quantify how arrival variability, service uncertainty, and batch dispatch rules jointly determine inventory dynamics and congestion risk. Each scenario is evaluated using 3000 independent replications over 365 days horizon with a 60-day warm-up and 305 steady state observation days. The terminal is modeled with fixed operational constraints; yard C = 60 containers, batch size Q = 40 containers per train, and a maximum of one train departure per day. Six demand service configurations vary the arrival intensity λ and a non-train service capacity µ. Results reveal a pronounced threshold driven behavior. The annual train formations increase from 0.01 under low demand (mean yard occupancy 0.109) to 31.99 under peak and disruption conditions (occupancy 0.405). In the base case (λ = .52, µ = 4.8), mean steady state inventory is 18.73 containers (31.2% occupancy), which is producing an average 4.65 trains per year with no observed overflow across approximately 915,000 simulated terminal days. Congestion, defined as P(It ≥ 0.9C), is zero in four scenarios and remains rare under the most stressed conditions with pooled probabilities of 2.73 × 10–5 and 5.25 × 10–5. Importantly, mean inventory increases from 6.54 to 24.30 containers as occupancy rises from 0.109 to 0.405 even when binary congestion and overflow indicators remain near zero. This demonstrates that inventory accumulation provides an earlier and more sensitive signal of operational stress than both dispatch rules induce nonlinear operating regimes that are not captured by mean value analysis, with direct implications for capacity planning and batch sizing decisions in inland railway terminals.