Horizon-Aware Forecasting of Passenger Assistance Demand for Rail Station Workforce Planning

Michael Sheehan; Irina Timoshenko

stat.APApr 8, 2026

Horizon-Aware Forecasting of Passenger Assistance Demand for Rail Station Workforce Planning

Authors: Michael Sheehan, Irina Timoshenko

Organizations: London North Eastern Railway, Digital and Innovation Department, York, UK

Abstract

Passenger assistance services are essential for accessible rail travel, yet demand varies substantially across stations and over time, creating challenges for workforce planning and staff rostering. This paper presents a data-driven decision support framework for forecasting station-level passenger assistance demand and translating forecasts into workforce plans. The forecasting component applies a horizon-aware Prophet modelling approach using multi-source operational data, while the planning component maps demand forecasts to staffing requirements under service and operational constraints through an interpretable red-amber-green risk framework. The approach has been implemented within a production-grade system to support routine planning and staffing decisions across LNER-managed stations. Results demonstrate improved forecast accuracy relative to year-on-year baseline methods, with absolute error reduced by up to 76.9%, and show that forecast-informed staffing is associated with an approximate 50% reduction in failed passenger assistance deliveries attributable to staff availability. These findings highlight the value of integrating interpretable forecasting with operational work.

Figures & tables

Figure 1: Station-level passenger assistance requests over the last four years, illustrating strong seasonality and peak demand periods.

Figure 2: Cumulative distribution of passenger assistance booking lead times.

Planning horizon	Responsible role/team	Typical duties
8–12 weeks ahead	Strategic / resource planning	Coordinate timetable and works impacts; set high-level station allocations; plan recruitment to close gaps.
2–4 weeks ahead	Roster clerks / accessibility planning teams	Build rosters aligned to expected demand; manage leave, training, and planned overtime.
Less than 1 week ahead	Service delivery & Station managers	Deploy staff day to day; approve short-notice overtime or rest day working

Table 1: Passenger assistance workforce planning horizons, responsibilities, and typical duties.

Horizon bucket	Days	Primary operational use	Additional regressors
Very Short-term	1–2	Station Managers & Deputy Team Leaders	• Cumulative as-of booking counts at fine lead-time thresholds ( $\tau\leq 2$ days) • Adjacent-threshold differences capturing late-booking accumulation • Short-horizon meteorological covariates (forecast precipitation, temperature, humidity)
Short-term	3–7	Near-term service delivery management	• Cumulative as-of booking counts at fine lead-time thresholds ( $\tau\leq 1$ week) • Adjacent-threshold differences capturing late-booking accumulation • Short-horizon meteorological covariates (forecast precipitation, temperature, humidity)
Medium-term I	8–14	Tactical workforce adjustments	• As-of booking counts at intermediate thresholds ( $\tau\approx 2$ –4 weeks) • Adjacent-threshold differences
Medium-term II	15–28	Short-range roster planning	• As-of booking counts at longer thresholds ( $\tau\approx 4$ –8 weeks) • Adjacent-threshold differences
Long-term	$>28$	Strategic resource and roster planning	• As-of booking counts at coarse thresholds ( $\tau\geq 8$ weeks)

Table 2: Horizon-bucket routing and horizon-specific regressor availability.

Figure 3: Forecast error across horizon buckets for representative stations at hourly (left) and daily (right) resolutions. Solid lines denote asymmetric RMSE and dashed lines denote MAE.

Berwick-upon-Tweed
Station	Horizon (days)	MAE	aRMSE	Coverage (%)
Baseline (YoY)	Baseline	4.8	7.7	100.0
Long Term	$>28$	3.8	6.1	100.0
Medium II Term	15–28	2.8	4.8	100.0
Medium I Term	8–14	2.4	4.1	100.0
Short Term	3–7	2.2	3.6	100.0

Table 3: Daily forecast performance by station and horizon (in days).

Berwick-upon-Tweed
Station	Horizon (days)	MAE	aRMSE	Coverage (%)
Baseline (YoY)	Baseline	1.1	2.1	98.1
Long Term	$>28$	0.9	1.9	99.2
Medium II Term	15–28	0.9	1.6	99.9
Medium I Term	8–14	0.8	1.4	100.0
Short Term	3–7	0.7	1.2	100.0

Table 4: Hourly forecast performance by station and horizon (in days).

Figure 4: Workforce planning RAG heatmap for York (06:00–21:00, 50 days). Green indicates forecast demand is within primary capacity; Amber indicates secondary capacity is required; Red indicates forecast demand exceeds total capacity.

Figure 5: Prophet component decomposition for York (Medium II horizon), illustrating the contribution of trend, multiple seasonalities, holiday effects, and external regressors to the final forecast.

Figure 6: Residual diagnostics for York (Medium II horizon), including the residual distribution, Q–Q plot, and residuals over time. Circled observations correspond to periods of engineering works not explicitly captured in the model.

Time Series Forecasting

Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.

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Accurate and coherent passenger demand forecasting is essential for Urban Rail Transit (URT) operations. Passenger demand has a hierarchical structure in which origin-destination (OD) flows aggregate to station-level inflows and outflows through conservation constraints. In practice, station-level and OD-level forecasts are often generated independently, producing incoherent predictions that violate these constraints and introduce inconsistencies into operational decision-making. Such issues become more severe during disruptions, when forecasting reliability is most critical. This paper presents the first hierarchical forecast reconciliation framework for joint station-level and OD-level URT demand prediction. A neural Fully Connected Reconciler (FCR) learns a non-linear mapping from incoherent base forecasts to coherent hierarchical predictions while guaranteeing exact structural consistency by construction. The method is benchmarked against OLS, WLS, and Minimum Trace (MinT) variants using Rejsekort smart-card data from the Copenhagen S-train network under one-step, multi-step, and disruption forecasting scenarios. Results show that reconciliation consistently improves OD forecasting accuracy while ensuring hierarchical coherence. Under normal conditions, FCR performs competitively with MinT-based methods. An oracle analysis indicates that perfect station-level forecasts could reduce OD prediction error by up to 34 percent, highlighting the value of improved base forecasts. Under severe disruptions, FCR outperforms classical methods, reducing OD forecasting error by up to 17.45 percent in multi-step destination-side delay scenarios. These findings establish hierarchical reconciliation as an effective mechanism for improving forecast robustness, with the largest benefits occurring under the most challenging operating conditions.

Abstract

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