Urban traffic-parking system dynamics model with macroscopic properties: a comparative study between Shanghai and Zurich

The study investigates how urban parking system characteristics and policies influence network traffic dynamics, cruising-for-parking, and environmental outcomes. Motivated by the recognition that searching for parking can constitute up to 30% of road demand in CBDs and exacerbate congestion, delays, and emissions, the research aims to evaluate a macroscopic, dynamic parking-traffic model across distinct urban contexts and quantify policy impacts. The core research questions are: (1) Can a dynamic macroscopic parking-traffic model previously applied in Zurich generalize to different urban settings? (2) How do changes in parking supply, duration, and fees affect cruising time/distance and emissions in different CBDs? The study compares Shanghai’s Xujiahui CBD and Zurich’s Bahnhofstrasse CBD—two areas with contrasting infrastructure, parking regulation, and socio-economic contexts—to assess current performance, elasticity to policy changes, and environmental implications.

Prior work has examined urban parking from socio-economic perspectives (e.g., income, vehicle ownership) and demand relationships, as well as operational aspects using microscopic empirical methods, traffic assignment, and agent-based simulations. Economic analyses addressed parking effectiveness and cost functions but often assume static speed/time and require extensive data. Macroscopic approaches based on the macroscopic fundamental diagram (MFD) have demonstrated effectiveness in representing network dynamics with lower data needs. Cao and Menendez (2015) and Cao et al. (2019) integrated parking equilibrium concepts into a macroscopic model linking parking and traffic, but empirical validation beyond Zurich remained limited. This study addresses that gap by testing the model in two diverse CBDs and extending it to quantify environmental impacts via cruising distance and hot emission factors.

A dynamic parking-traffic system dynamics model with macroscopic properties is applied. The model uses a 1-minute time-sliced framework and represents three parking-related traffic states: non-searching, searching-for-parking, and parked. Five transition events govern flows among these states: entering the area, starting to search, accessing parking, departing parking (to non-searching), and leaving the area. The system comprises two blocks (parking system and traffic system) linked by a transition matrix. Key inputs: (a) Area basics (network radius, total and lane-km lengths, number of parking spaces); (b) Initial conditions and demand (time-varying inflows; fraction of through-traffic β; initial state counts); (c) Traffic properties via the MFD (free-flow speed, critical density/flow, jam density; homogeneous network assumption with searchers and parking evenly distributed); (d) Traveling distances (distance to start searching lns/s, distance to leave from parking lp/, and through-vehicle path length l/; distances approximated from network radius); (e) Parking duration (distribution approximated with a parametric PDF, e.g., Gamma; drivers do not cancel trips while searching); (f) Parking pricing and garage availability. The state update equations deterministically evolve counts per slice: Nns, Ns, Np updated by transitions n/ns, nns/s, ns/p, np/ns, n/ns. Transitions are computed using probabilistic/logical conditions based on distance traveled and availability: - Start searching (nns/s) when vehicles requiring parking (1–β) have traveled at least lns/s since entry and have not started searching earlier. - Access parking (ns/p) as a function of available spaces Ai, number of searchers Ns i, network length L, and average searcher cruising distance di, considering spacing si and different regimes of di relative to si and L. - Depart parking (np/ns) based on the parking duration PDF f(td): departures occur when durations fall into the current time-slice’s interval. - Leave area (n/ns) includes through vehicles and those that have traveled sufficient distance from parking to exit. At each slice, available spaces Ai, density K, and speed v are updated via MFD relationships (free-flow to congested regimes). A cumulative counting (queueing) diagram estimates total travel and cruising times. Model performance/validation uses aggregate daily cruising time and distance: T(a,b)=Σ(Ns·t) and D(a,b)=Σ(v·Ns·t). Policy experiments adjust parking supply (±10% to ±50%) and average parking duration (±10% to ±50%). Elasticity of cruising distance with respect to parking spaces is computed as percentage change per 1% change in supply. Emissions are assessed using the COPERT average-speed approach for hot emissions (CO, VOC, NOx, PM, FC, CH4), focusing on light-duty passenger and light commercial vehicles, with cruising distance as key activity data.

- Baseline differences in parking occupancy and cruising: • Bahnhofstrasse CBD (Zurich) operates near saturation during peaks (≈9–11 a.m. and 7–9 p.m.), with more searchers than available spaces; approximately 16 vehicles enter and leave without finding parking during saturation. • Xujiahui CBD (Shanghai) peaks around 55% occupancy, far from saturation. - Aggregate daily cruising metrics (base case): • Bahnhofstrasse: 213.19 hours of cruising time; 4178.27 km of cruising distance (A=539 spaces; through-traffic ≈23%). • Xujiahui: 60.02 hours; 2090.80 km (A=2768 public spaces; through-traffic ≈70%). - Sensitivity to parking supply changes (±10% to ±50%): • Bahnhofstrasse shows large sensitivity and instability as supply decreases from base: cruising distance rises dramatically from 4178.27 km (base) to 15,403.64 km at −50%; cruising time from 213.19 h to 785.95 h. Even modest increases in supply reduce cruising substantially (e.g., +10%: 833.92 km; 42.55 h). • Xujiahui remains largely stable across −40% to +50% supply changes, with cruising distance/time essentially unchanged at ~2090.8 km and ~60.02 h, only showing notable change by −45% or more (e.g., −45%: 2352.81 km; 67.55 h; −50%: 5392.41 km; 154.81 h). - Elasticity of cruising distance with respect to parking spaces: • Bahnhofstrasse exhibits higher elasticity, up to about 8% per 1% change around the base, indicating pronounced responsiveness to policy shifts. • Xujiahui shows minimal elasticity; significant response begins around −40% supply, reaching ~3% at −50%. - Sensitivity to average parking duration: • In Bahnhofstrasse, increasing mean duration from 227 min raises cruising sharply: 6514.79 km at +10% (249.7 min), 11,081.38 km at +50% (340.5 min); decreasing duration to −50% (113.5 min) reduces cruising to ~674.68 km and time to ~34.42 h. • In Xujiahui, cruising distance/time remain ~2090.8 km/60.02 h across −50% to +50% duration adjustments (63.5–190.5 min), indicating high robustness. - Emissions: Using COPERT hot emission factors, longer average parking durations—and the associated increases in cruising—substantially increase total emissions in Bahnhofstrasse across pollutants (CO, VOC, NOx, PM, FC, CH4). In Xujiahui, emissions remain comparatively flat under the same duration changes due to stable cruising metrics. - Interpretation: Bahnhofstrasse’s higher sensitivity reflects stringent central zone regulations, limited spaces (A=539), and lower through-traffic share, making it more responsive to parking policy changes in terms of cruising and emissions. Xujiahui functions more as a bypass corridor with higher through-traffic (≈70%) and abundant parking, yielding stability against moderate policy adjustments.

The findings confirm that a dynamic macroscopic parking-traffic model can capture key interactions between parking supply/duration and network-wide cruising and emissions in distinct CBD contexts. The model elucidates how near-saturation conditions (Bahnhofstrasse) amplify cruising in response to supply or duration increases, directly linking parking policies to environmental outcomes. Conversely, Xujiahui’s higher through-traffic proportion and larger supply decouple parking policy changes from cruising behavior, maintaining stable performance. These results address the research questions by: (1) demonstrating the model’s applicability and explanatory power beyond its original Zurich application; (2) quantifying policy responsiveness (elasticity) and environmental implications, offering actionable insights. For policy, in constrained CBDs like Bahnhofstrasse, modest increases in supply or reductions in average parking duration can sharply reduce cruising and emissions; conversely, supply reductions or longer stays exacerbate congestion and pollution. In more capacious, through-traffic-dominant CBDs like Xujiahui, policy levers may need to target demand distribution, dynamic pricing, or through-traffic management to influence cruising.

This study extends and validates a dynamic macroscopic parking-traffic model in two contrasting CBDs, integrating feasible inputs and MFD-based dynamics to analyze parking-traffic interactions, policy elasticities, and environmental impacts. It shows Bahnhofstrasse (Zurich) is highly sensitive to parking supply and duration, with large changes in cruising and emissions, whereas Xujiahui (Shanghai) remains stable under comparable adjustments. Contributions include: (a) empirical comparative validation across different urban settings; (b) operationalization of elasticity-based policy evaluation; (c) integration of cruising-based hot emission estimates to connect parking policy with environmental outcomes. Future research should: incorporate spatial heterogeneity in parking distribution; use dynamic demand distributions and account for interactions between local and transit traffic; apply city-specific emission factors; test dynamic pricing and quantify behavioral responses and value-of-time heterogeneity; and evaluate smart parking interventions (e.g., reservations, VMS) within the framework.

- Homogeneous network and uniform parking distribution assumptions may not capture spatial heterogeneity of parking availability and search behavior. - Fixed peak hour and constant demand distributions overlook temporal variability and interactions between local and transit traffic. - Emission estimates use uniform COPERT factors, which may not reflect city-specific vehicle fleets, driving behaviors, or urban forms; the European model may be less accurate in the Chinese context without adaptation. - Case selection (two CBDs) limits generalizability; broader samples are needed. - The model abstracts from detailed driver behavior (e.g., cancellations, individual search paths) and relies on average relationships. - Policy simulations do not include dynamic pricing or detailed behavioral responses (e.g., value-of-time differences), which should be incorporated in future work.