Optimization-based method for effective organization of local wagon-flows

2.1. Data collection and preprocessing

The initial data set includes the following operational parameters:

1) Average wagon turnover rate per section ($\lambda$).

2) Pickup-train circulation time (${\tau }_p$).

3) Station processing time ($t_s$).

4) Section capacity ($C_s$).

5) Number of idle wagons at each node ($N_I$).

The dataset was compiled from the 2024-2025 operational reports of UTY JSC and field observations on Fergana and Andijan lines.

Similar methodologies for traffic capacity estimation were previously applied in [10-13], [19].

2.2. Optimization model formulation

The objective function minimizes the total downtime of wagons within the studied region:

where $Z$ – total cumulative downtime of wagons in the network, $t_{si}$ – service time of wagons at station $i$, $t_{\omega i}$ – waiting time before pickup train formation at the same station, and $n$ – number of operational stations within the analyzed section.

The optimization is subject to the following constraints:

where $N_i$ – number of idle wagons at station $i$, $C_s$ – track or section capacity (maximum number of wagons handled simultaneously), ${\tau }_p$ – pickup-train circulation time, $N_{total}$ – total number of wagons in the considered network, $T_{op}$ – total operational time of wagon movement, $t_s$ – average station processing time, $t_{\omega }$ – average waiting time, and $t_t$ – average travel time of wagons between adjacent stations.

To ensure realistic modeling, stochastic variations of wagon arrivals are represented by a Poisson distribution:

where $P\left(k;\lambda \right)$ – probability of k wagons arriving in a given time interval, and $\lambda$ – mean wagon arrival rate per hour, determined from operational statistics.

The optimization process is implemented iteratively by adjusting train departure schedules and redistributing wagon flows among intermediate stations.

At each iteration, the algorithm minimizes Z using a Simplex-based linear programming solver and updates pickup-train dispatch times accordingly [4], [5], [7].

2.3. Validation procedure

The developed optimization model was validated through field data and simulation experiments for the Fergana-Andijan section of the Uzbek railway network.

Operational data from three consecutive months were analyzed to compare baseline and optimized scenarios.

Validation included the following criteria:

1) Reduction in wagon idle time (%).

2) Increase in section throughput (%).

3) Utilization coefficient of pickup locomotives.

4) Total travel time of local wagon-flows ($T_{op}$).

The comparison showed that optimized scheduling reduced average wagon downtime by 18-22 % and increased throughput by 10-12 %, with model deviations under ±5 %.

These results confirm the model’s adequacy and compliance with railway operation standards [10], [11], [18].

3.1. Model application and baseline conditions

The developed optimization model was applied to analyze the local wagon-flow organization on the Andijan–Fergana section of the Uzbek railway network.

The initial (baseline) scenario was based on operational data from UTY JSC, reflecting typical pickup-train schedules and wagon turnover rates during a standard working week in 2024.

The baseline parameters were as follows:

1) Average number of pickup routes per day: 18.

2) Average number of wagons handled per route: 52.

3) Mean waiting time of wagons before train formation: 4.6 h.

4) Average section capacity utilization: 73 %.

4) Locomotive idle coefficient: 0.28.

These values served as reference for assessing the effect of optimization.

3.2. Results after optimization

After implementing the proposed optimization algorithm, updated pickup-train schedules and station workload redistribution were generated.

The optimized results demonstrated significant improvement in operational efficiency.

The results indicate that the optimized scheduling reduced wagon downtime by nearly 24 %, improved throughput by 15 %, and increased locomotive efficiency by over 20 %.

These quantitative improvements confirm that the proposed model ensures more uniform distribution of workload across stations and minimizes idle capacity.

As shown in Fig. 1 and Fig. 2, the introduction of the ShSPL algorithm eliminated overlapping train paths and reduced wagon idle time ($T_2<T_1$).

Fig. 1Fragment of train-traffic schedule (TTG) before optimization showing conflicts between passenger and pick-up trains (idle time T1)

Fig. 2Train-traffic schedule after introduction of the ShSPL optimization scheme showing reduced idle time T2 and improved throughput

3.3. Model validation and discussion

Field verification and simulation testing demonstrated high correlation between the predicted and observed operational indicators, with average deviation below ±5 %.

This confirms the reliability of the model for practical use in real-time dispatch systems.

The results are consistent with previous studies on transport system optimization and local wagon management [4-9], [12], [15], [20].

Similar improvements in scheduling efficiency and capacity utilization were reported in [2], [5], [7], validating the applicability of deterministic-stochastic optimization for railway logistics.

The main factors contributing to the improved performance include:

1) Reduced overlapping of pickup routes due to balanced scheduling,

2) Better synchronization between wagon readiness and locomotive availability,

3) Elimination of redundant waiting periods at low-traffic stations,

4) Automated redistribution of wagon flows between nearby terminals.

These outcomes align with the methodological principles defined in operational standards [10], [11] and national programs for transport efficiency improvement [18], [20].

3.4. Comparative evaluation with existing methods

Compared with conventional manual planning systems, the developed algorithm offers several advantages:

1) Flexibility – dynamic adjustment to stochastic wagon arrivals ($\lambda$-based control).

2) Reliability – deterministic constraint satisfaction ensures schedule feasibility.

3) Scalability – applicable to multiple adjacent stations and regional networks.

4) Integration readiness – compatible with UTY JSC’s digital logistics platform.

Overall, the integrated optimization technique demonstrated significant operational and economic benefits for local wagon-flow management, paving the way for intelligent decision-support systems in the railway sector of Uzbekistan.