MARTA Survey: Transit Systems & Cosmic-Ray Detectors

• MARTA Survey is a comprehensive investigation into two domains: transit system optimization using detailed AFC data and precise muon detection in cosmic-ray physics.
• In transit analysis, advanced clustering and hybrid LR+RF models effectively predict event-driven ridership surges and enhance dynamic train scheduling.
• In the cosmic-ray context, the MARTA concept integrates water-Cherenkov detectors with RPCs to achieve high-efficiency muon measurement for improved air shower reconstruction.

The MARTA Survey encompasses two distinct research contexts: (1) the analysis and optimization of the Metropolitan Atlanta Rapid Transit Authority (MARTA) rail system in handling special event–driven passenger demand surges using advanced data-driven methods (Santanam et al., 2021), and (2) the MARTA concept in astroparticle physics (Muon Array with RPCs for TAGging Air showers) for precise muon measurements in extensive air shower detection (Abreu et al., 2017). Both applications combine systematic data acquisition, statistical modeling, and simulation, yet operate in fundamentally different scientific domains. The following entry surveys both domains under the unifying label of "MARTA Survey."

1. MARTA Rail System: Large-Scale Special Event Demand Analysis

The MARTA rail system in Atlanta is both a case study and a testbed for developing methodologies to predict, quantify, and operationally manage highly peaked passenger demand during major special events such as sporting games and concerts. Automated Fare Collection (AFC) data provide high-resolution observations of ridership spanning January 2016 through mid-2020, facilitating analyses at the granularity of individual station tap events. Data fields include anonymized UserID, timestamped entries and exits, and station identifiers; after trip-chaining, these generate structured Origin–Destination (O–D) records. Genuine O–D pairs, aligned to a 3 AM–3 AM operational day, form the basis of finely binned demand signatures.

Event-specific extraction uses the baseline median and 90th percentile signatures, producing for each station binary time series and thresholded event ridership estimates:

$$r_{a,s}(t) = [r_{e,s}(t) - r^{b}_s(t)] \cdot \mathbb{1}_{r_{e,s}(t) > r^{b^+}_s(t)}, \qquad T_{a,s} = \sum_{t=t^s}^{t^e} r_{a,s}(t)$$

where $r_{e,s}(t)$ is observed ridership, $r^{b}_s(t)$ is baseline, and $(t^s,t^e)$ define event-excess window boundaries.

2. Passenger Clustering and Train-Assignment Inference

Reconstructing train-by-train passenger loads and rider wait-times for post-event surges requires probabilistically inferring which train each rider boarded. For event stations $e$ and each O–D trip:

• Infer DepartureTime$_e =$ ExitDT$_d -$ TravelTime$_{e,d}$
• Infer ArrivalTime$_e =$ EntryDT$_o +$ TravelTime$_{o,e}$

An unsupervised clustering approach based on HDBSCAN identifies clusters in $(\text{ArrivalTime}_e, \text{DepartureTime}_e)$ space, each corresponding to a physical train. The minimum cluster size (MinPts) is set to 50. For the Atlanta United game, 13 clusters matched 13 observed departures (Santanam et al., 2021). Assignment of riders left behind per train is deduced by identifying arrivals between consecutive departure times not associated with any cluster. The validity of this mapping is confirmed via the expected “horizontal stripes” structure in the time–time scatter and concordance with schedule anomalies.

3. Data-Driven Ridership Prediction Models

Special event ridership prediction leverages multivariate event-features, comprising attendance, event category (soccer, football, basketball), location, team performance differentials, and temporal flags (weekend indicator, month, two-event day status). Predictive models include:

• Linear Regression (LR): $ŷ = -1,201 + 0.1739 \times \text{Attendance}$
• Random Forest (RF): Tree ensemble (up to $B=1,500$), one-hot encoding of categorical variables
• Hybrid LR+RF: RF trained on LR residuals, final prediction as $ŷ_{LR} + ŷ_{RF}$

Performance was measured under leave-one-out cross-validation (LOOCV) over 134 event days. The LR+RF hybrid achieved a Mean Absolute Error (MAE) of 506 riders, Mean Absolute Percentage Error (MAPE) of 11.6%, and RMSE of 743.4, slightly outperforming standalone models. The linear relationship between attendance and ridership—across sports categories—is pronounced, while model residuals incorporate additional event covariates.

Model	MAE	MAPE	RMSE
LR	509	11.7%	761.6
RF	582	14.1%	844.9
LR+RF	506	11.6%	743.4

4. Throughput Analysis and Frequency Optimization

The two-stage simulation framework first computes realized train loads, left-behind counts, and wait-times from the HDBSCAN clusters and inferred departure/arrival times. At each departure, per train $i$ and station $s$:

• $r_i^s$ (queued riders), $l_i^s$ (left behind), $C_i^s$ (remaining capacity), processed with

$$r_i^s = l_{i-1}^s + d_i^s, \quad l_i^s = \max(r_i^s - C_i^s, 0), \quad C_i^{s+1} = \max(0, C_i^s - r_i^s)$$

Here $d_i^s$ is downstream demand between successive departures. Empirically, station capacity calibration used a best-fit of $C = 707$ (vs. nominal 576), with observed overcrowding rates of 23%.

Dynamic frequency optimization reallocates train dispatches to match peak post-event demand using normalized average throughput curves $\mu(t)$. Trains are simulated as departing once capacity is filled, resulting in substantial improvements:

• Average wait time: reduced from 5–7 min to 3–4 min
• Left-behind rate: reduced from 20–40% to 1–13%
• Additional trains required: ∼1 per event, with peak load more closely tracking demand surges (Santanam et al., 2021).

5. Operationalization and Extensions for Public Transit Management

Deployment scenarios for MARTA operations include real-time forecasting and reactive scheduling pipelines:

• Ticket sale feeds drive near-instantaneous event attendance predictions
• Ridership estimates from LR+RF models inform projected $\mu(t)$
• Dynamic short-turns on selected MARTA lines effectuate load-matching

Constraints include a limited special-event sample size (2018–2019), potential inaccuracies for diffuse or non-sport events, and idealizations such as FCFS boarding and perfect capacity adherence. Anticipated extensions are: live AFC stream integration, real-time demand curve recalibration (e.g., via Bayesian updating), network-wide demand-based dispatch and sharing, hybridization with on-demand microtransit, and transferability analyses to other metropolitan transit systems.

6. MARTA Concept in Cosmic-Ray Physics: Muon Array with RPCs

The MARTA (Muon Array with RPCs for TAGging Air showers) detector is proposed as a high-accuracy instrument for the muonic component $N_{\mu}$ in extensive air showers (EAS) at ultra-high energies ($E > 10^{18}$ eV). Each MARTA hybrid station couples a surface water-Cherenkov detector (WCD) with a shielded array of Resistive Plate Chambers (RPCs). The WCD provides an active shield and an electromagnetic (EM) calorimeter; the RPCs, placed under $\sim$170 g/cm² (water + concrete), offer near-pure ($\gtrsim 80\%$) high-efficiency ($\epsilon_\mu \sim 90\%$) muon detection with 5 ns time and $\sim4$ cm spatial resolutions. Deployment on the Pierre Auger Observatory surface stations—4 RPC modules per WCD—is under way (Abreu et al., 2017).

7. Detector Performance, Physics Applications, and Future Prospects

Quantitatively, RPC modules achieve long-term stable muon efficiency (85–90%), low background ($5$–$7$ Hz/pad), and reliable environmental compensation. Compared to alternatives (buried detectors, standalone RPC/WCD), MARTA uniquely offers surface-level, cross-calibrated, high-purity muon measurements without extensive civil works. Key analytic observables include the muon lateral distribution function (LDF), muon production depth (MPD), and variables for photon/hadron shower discrimination. Time and spatial resolutions enable shower core and angle reconstruction improving arrival direction fits to $\sigma_\theta \sim 0.1^\circ$–0.3$^\circ$. A mini-array (8 stations) is under construction at Auger for shower-by-shower validation.

The design is conducive to adaptation for high-altitude gamma-ray arrays, potentially lowering muonic thresholds to the tens of TeV range.

• "Public Transit for Special Events: Ridership Prediction and Train Optimization" (Santanam et al., 2021)
• "MARTA: A high-energy cosmic-ray detector concept with high-accuracy muon measurement" (Abreu et al., 2017)