Reducing Street Parking Search Time via Smart Assignment Strategies

TL;DR

This paper introduces a practical smart assignment strategy for parking apps that significantly reduces street parking search times in dense urban areas, based on data-driven simulations of Madrid.

Contribution

The study proposes the Cord-Approx strategy, a novel probabilistic approach that improves parking search efficiency without requiring full knowledge of non-user behavior.

Findings

Cord-Approx reduces average search time from 19.98 to 6.69 minutes.

System users experience a 72% reduction in search time in central hubs.

The approach is effective across different urban zones, including residential areas.

Abstract

In dense metropolitan areas, searching for street parking adds to traffic congestion. Like many other problems, real-time assistants based on mobile phones have been proposed, but their effectiveness is understudied. This work quantifies how varying levels of user coordination and information availability through such apps impact search time and the probability of finding street parking. Through a data-driven simulation of Madrid's street parking ecosystem, we analyze four distinct strategies: uncoordinated search (Unc-Agn), coordinated parking without awareness of non-users (Cord-Agn), an idealized oracle system that knows the positions of all non-users (Cord-Oracle), and our novel/practical Cord-Approx strategy that estimates non-users' behavior probabilistically. The Cord-Approx strategy, instead of requiring knowledge of how close non-users are to a certain spot in order to decide whether to navigate toward it, uses past occupancy distributions to elongate physical distances between system users and alternative parking spots, and then solves a Hungarian matching problem to dispatch accordingly. In high-fidelity simulations of Madrid's parking network with real traffic data, users of Cord-Approx averaged 6.69 minutes to find parking, compared to 19.98 minutes for non-users without an app. A zone-level snapshot shows that Cord-Approx reduces search time for system users by 72% (range = 67-76%) in central hubs, and up to 73% in residential areas, relative to non-users.

Figures

Tables

Table 1. Table 1. Table of Notation

Symbol	Description
$n$	grid dimension; city is an $n\times n$ mesh.
$z=(i,j)$	generic grid cell with indices $i,j\in \{0,1,\dots ,n-1\}$.
$T$ ($t\in T$)	discrete simulation horizon; $t$ is a step (one step = one tick).
$𝒟$, $D_t$	all participants (app-enabled drivers); $D_t$ is the subset active at time $t$.
$𝒞$, $C_t$	all competitors (non-users); $C_t$ is the subset active at time $t$.
$t_{max}$	search-time budget; attempts exceeding $t_{max}$ are failures.
$b_{i,j}$	spot (bay) capacity in cell $(i,j)$.
$B$	total spot capacity in the city, i.e., ${\sum }_{i,j}{b}_{i,j}$.
${𝒮}_t$	set of available spots at time $t$.
$R$	competitor observability radius (in grid cells).
$\tau (d,s),\tau (c,s)$	Manhattan distance (travel time) from participant $d$/competitor $c$ to spot $s$.
$x_{d,s,t}\in \{0,1\}$	binary decision variable that equals 1 if participant $d$ is assigned to spot $s$ at time $t$.
${𝒜}_t^{comp}$	all spots captured by competitors at time $t$.
${𝒜}_t^{partc}$	all spots assigned to participants at time $t$.
$t_c$	number of steps available for competitor c before participant $d$ comes within one step of the visibility radius $R$ around spot $s$.
$C_{d,s,t}^{\ast }$	competitors closer than participant $d$ to spot $s$ but still outside radius $R$.
$p(c,s)$	probability competitor $c$ reaches spot $s$ first.
${𝒩}_c^{\le t_c}$	cells competitor $c$ can reach within $\le t_c$ steps.
$s_d^{\ast }$	closest spot chosen by participant $d$.
$\mathscr{H}$	historical corpus of spot parking success ratios.
$g_k$	Geohash label representing the grid cell $z$ at position $(i,j)$; $k$ indexes that cell.
${\rho }_{k,t}$	observed parking success ratio in Geohash $g_k$ at time $t$.
${\hat{p}}_{k\left(s\right),t}$	predicted spot availability probability (Ridge regression).
$\tilde{\tau }(d,s)$	effective distance defined as $\tau (d,s)/{\hat{p}}_{k\left(s\right),t}$, at time $t$.
${𝐌}_t$	cost matrix at time $t$.
${𝐌}_t(d,s)$	entry $(d,s)$ of the cost matrix ${𝐌}_t$.
$k\left(s\right)$	mapping from spot $s$ to its Geohash index $k$.
$𝐗,𝐲$	feature matrix and target vector for Ridge model.
$\beta ,\lambda$	coefficients and L2 regularization weight in Ridge regression.

Table 2. Table 2 . Average success ratio and search time (09:00–17:00).

	Parking Success Ratio (%)		Average Search Time (min)
Strategies	Participants	Competitors	Participants	Competitors
1 Unc-Agn	34.25	38.63	19.24	17.83
2 Cord-Agn	70.04	30.71	9.86	19.79
3 Cord-Approx	77.54	28.71	6.69	19.98
4 Cord-Oracle	85.32	27.76	8.83	19.89

Table 3. Table 3 . Average search times (minutes) for participants and competitors across defined zones in central Madrid during peak hours (09:00–17:00), comparing Working day ( Cord-Approx ) and Weekend ( Cord-Agn ) strategies.

Zone	Working Day		Weekend
	Participants	Competitors	Participants	Competitors
Traditional Residential (avg.)	11.84	27.08	3.81	11.60
Traditional Residential (1)	16.69	28.01	3.85	11.84
Traditional Residential (4)	7.00	26.14	3.77	11.35
Residential & Light Industry (avg.)	4.48	15.91	3.67	5.41
Residential & Light Industry (2)	6.39	19.90	4.17	7.31
Residential & Light Industry (3)	2.58	11.93	3.17	3.52
Culture & Transport Hub (avg.)	4.01	16.83	4.53	6.15
Culture & Transport Hub (5)	4.57	19.70	5.03	7.37
Culture & Transport Hub (9)	3.45	13.97	4.03	4.93
Office & Station District (6)	6.66	13.17	7.43	4.39
Historic Retail & Tourist Core (avg.)	7.38	22.24	6.73	9.64
Historic Retail & Tourist Core (7)	7.69	24.66	6.01	11.69
Historic Retail & Tourist Core (8)	7.07	19.82	7.44	7.59

Equations

$$\begin{split}\mathcal{A}^{comp}_{t}=\bigl{\{}\,s\in\mathcal{S}_{t}\;\big{|}\;&\exists\,c\in C_{t}:\tau(c,s)\leq R\;\land\\ &\quad\tau(c,s)<\min_{d\in D_{t}}\tau(d,s)\,\bigr{\}}\end{split}$$

$$\underset{x}{\min }\sum _{t\in T}\sum _{d\in D_t}\sum _{s\in {\mathcal{S}}_t\setminus {\mathcal{A}}_t^{comp}}\tau (d,s)x_{d,s,t},$$

$$\sum _{s\in {\mathcal{S}}_t}{x}_{d,s,t}\le 1$$

$$\displaystyle\sum_{d\in D_{t}}x_{d,s,t}\;\leq\;\mathbb{I}\!\bigl{[}s\notin\mathcal{A}^{comp}_{t}\bigr{]}$$

$$s_d^{\ast }=\arg \underset{s\in {\mathcal{S}}_t}{\min }\tau (d,s)$$

$${\mathbf{M}}_t(d,s)=$$

$$t_{c}\;=\;\min\bigl{(}\tau(d,s)-R-1,\;R\bigr{)}$$

$$\mathcal{N}_{c}^{\leq t_{c}}\;=\;\bigl{\{}\,z\in\mathbb{Z}^{2}:\tau(c,z)\leq t_{c}\bigr{\}},$$

$$p(c,s)\;=\;\frac{\bigl{|}\{\,z\in\mathcal{N}_{c}^{\leq t_{c}}:\tau(z,s)=R\}\bigr{|}}{\bigl{|}\mathcal{N}_{c}^{\leq t_{c}}\bigr{|}}.$$

$$\tilde{\tau }(d,s)=\frac{\tau (d,s)}{{\hat{p}}_{k(s),t}}$$

$$\hat{\beta }=\arg \underset{\beta }{\min }{\Vert \mathbf{y}-\mathbf{X}\beta \Vert }_2^2+\lambda {\Vert \beta \Vert }_2^2$$

Full text

Intelligent Transportation and Sustainable Mobility, Spatial Geo-social and Trajectory Simulation, Traffic Telematics, Personalized Geospatial Recommendation Systems

1. Introduction

Despite significant advances in vehicular navigation systems, the persistent challenge of locating available street parking spots remains largely unaddressed. In general, drivers spend a substantial amount of time annually, often dozens of hours, looking for parking at their destinations (Shoup, 2007). This exacerbates multiple systemic issues of densely populated areas, such as heightened traffic, increased vehicular emissions, unnecessary time expenditure, elevated driver frustration, stress, and risk of road accidents. Previous research has looked at the street‑parking problem only sporadically. Some experiment with the amount of information available to drivers via an intelligent parking system, showing that real-time availability data can reduce search time (Dalla Chiara et al., 2022; Rodr´ıguez et al., 2024). Other studies examine how drivers compete for parking spots, often relying on game-theoretic or experimental models to simulate strategic decision-making and the effects of pricing or reservations (Tan et al., 2024; Sun et al., 2024). Another line of work focuses on analyzing parking conditions in particular places, using city-specific data to evaluate how demand, land use, and local policies shape curbside occupancy (Millard-Ball et al., 2014; Qin et al., 2022; Wu and Ma, 2022). However, no prior work brings all of the above elements together. Hence, in this study, we split drivers into two groups, one that uses a smart street-parking application providing guidance and routes to available street parking spots (henceforth referred to as participants) and another composed of uninformed non-user drivers who search for street parking without system assistance (henceforth referred to as competitors). With finite parking spots, benefits to Participants necessarily diminish availability for competitors. We vary the levels of coordination and information available to participants and evaluate their impacts on street parking search time and success ratio (Section 4.1) under realistic parking conditions, assuming a fixed adoption rate.

We propose and evaluate four distinct smart parking allocation strategies under varying levels of information and coordination among our participants. 1) Our internal baseline among app users, Uncoordinated Agnostic (Unc-Agn), in which participants obtain system-wide parking availability but navigate independently toward their nearest available spots, while competitors search without system assistance. 2) The Coordinated Agnostic (Cord-Agn) strategy, in which our participants coordinate to avoid contention over parking spots, but are agnostic to competing agents that are outside our system (competitors). 3) The Coordinated Oracle (Cord-Oracle) strategy, in which the system has perfect knowledge of all parking spots and the current positions of participants and competitors. This allows the system to avoid assignments likely to be preempted by closer competitors, minimizing wasted trips. This unrealistic, perfect-awareness setting is included solely as an upper-bound benchmark. 4) The Coordinated Approximate (Cord-Approx) strategy, which is a practical realization of the above oracle strategy leveraging historical data to probabilistically estimate the impact of the presence of competitors without requiring knowledge of their exact locations. For comparability, the numbers of participants and competitors are fixed across all strategies. Our evaluation focuses on search time and success ratio, leaving network-wide congestion to future work. For cross-group comparisons to current practice, competitors serve as the real-world baseline, while Strategy Unc-Agn is the app-user baseline (information only, no coordination).

Our Contributions: This work makes four key contributions to intelligent urban parking systems: First, we quantify the performance benefits of coordinated street parking allocation under varying information conditions. Second, we analyze design trade-offs, including the value of coordination among participants and the impact of awareness of competitors on system efficiency. Third, we develop a comprehensive evaluation framework using realistic parameters: actual traffic-intensity data, a Geohash-aligned grid of Madrid, zone-specific parking capacities, historical occupancy patterns, and empirically calibrated parking duration/turnover. Fourth, we propose a practical forecasting approach that approximates an oracle’s knowledge of competitors current positions. Our methodology combines real-world traffic intensity data with behavioral modeling to bridge the gap between theoretical parking optimization and practical implementation constraints.

Our findings: Using real-world data from over 2 million observations across Madrid, Spain (Madrid City Council, 2024), our experimental evaluation offers key insights into how intelligent parking systems perform and influence driver behavior in realistic urban settings:

$\bullet$ Smart-parking systems provide diminishing benefits at the extremes, when parking spot availability is high (40–45%) or very low (0–5%). In the intermediate range (20–25% availability), however, smart-parking systems have strong potential to improve street parking performance. We show that having hints about free street spots (i.e., Unc-Agn) is insufficient: contention over these spots can erode the advantage of participants over competitors and, in extreme cases, even result in worse performance than competitors.

$\bullet$ Introducing coordination among our participants, through Cord-Agn, Cord-Approx, and Cord-Oracle, leads to substantial improvements in both parking success ratio and reduction in search time.

Parking Success Ratio. Starting with the Unc-Agn strategy, our participants achieve a 34.25% success ratio, trailing the competitors’ 38.63% by about four percentage points. Introducing coordination (Cord-Agn) lifts our participants’ performance sharply to 70.04%, while competitors remain at 30.71%. With the full-information Cord-Oracle, where the positions of all competitors are known, participants attain 85.32%, far above the competitors’ 27.76%. Finally, under the practical oracle approximation (Cord-Approx), participants reach 77.54%, compared with 28.71% for the competitors. Overall, coordination and predictive awareness increase our participants’ parking success ratio by more than double relative to Unc-Agn, an advantage of up to 50 percentage points (pp) over competitors.

Average Search Time. Cord-Approx also excels in time efficiency for successful parking attempts, reducing average search time to 6.69 minutes, compared to 19.98 minutes for competitors. Cord-Oracle averages 8.83 minutes, while Cord-Agn averages 9.86 minutes. Notice that it should not come as a surprise that Cord-Approx has a smaller search time than Cord-Oracle. This is because we compute this metric only for successful parking attempts, and the two strategies have a different success ratio, so the search times are not directly comparable. Overall, looking at both metrics, it is clear that Cord-Approx offers superior performance compared to competitors, while remaining close to the impractical Cord-Oracle upper bound.

$\bullet$ Zooming in on individual neighborhoods in central Madrid reveals that the benefits of our Cord-Approx strategy are even more pronounced than the encouraging reduction in the city-wide mean of 66.5%. Cord-Approx reduces search time for participants by 76% in Culture & Transport Hubs, 72% in the mixed Residential & Light Industry belt, and 73% in the Traditional Residential zone. The strategy not only improves city-wide performance but excels even further at the neighborhood level, turning a global parking challenge into a series of localized advantages that ease the search time across diverse traffic conditions.

2. Related Work

We can break down street‑parking research efforts into three main streams: (i) information‑centric guidance systems, (ii) coordinated allocation strategies, and (iii) empirical field studies. Although each strand is well developed, the literature lacks a metropolitan‑scale, data‑driven comparison across them. Our study addresses this gap.

Information‑centric guidance systems. Sensor‑based systems such as ParkNet (Mathur et al., 2010), recent sensing approaches (University of Pittsburgh, 2023), and comparative evaluations of fixed and mobile sensing (Roman et al., 2018) demonstrate how drive‑by or crowdsourced sensing can publish real‑time occupancy of street maps with high accuracy. More recent work uses parking-meter transaction streams and sparse curbside sensors as a city-wide probe network to forecast block-level vacancy rates without full instrumentation (Kotb et al., 2016). Integrating richer context improves forecasts: Inam et al. (Inam et al., 2022) integrate occupancy, weather, pedestrian count, and traffic data streams to train a Random Forest model that predicts on-street parking vacancy 5–10 minutes in advance with 81% accuracy, achieving a 10 percentage point improvement over models using an occupancy baseline. Hybrid platforms such as D2Park (Zhao et al., 2020) combine real-time sensing with user preferences (e.g., walking distance, cost) to dynamically guide drivers toward likely available spots, reducing average search time by over 20%. Although these methods greatly improve individual awareness, they typically do not resolve contention among multiple informed drivers.

Coordinated allocation strategies. A complementary line of work assigns drivers to spots. A Hungarian‑based optimal matching (Zhao et al., 2014) reduces search time by roughly $50\%$ in simulations. A recent study (Sayarshad et al., 2020) propose a scalable, non-myopic atomic game that jointly optimises assignment and dynamic pricing, raising social welfare by up to 54% on San Francisco data. Tan et al. (Tan et al., 2024) proved, in a congestion‑game model, that advance reservation strictly dominates blind search. However, most coordination studies benchmark against oracle upper bounds in synthetic settings and assume perfect compliance, conditions rarely achievable in practice.

Empirical field studies. Large-scale deployments are rare. The SFpark pilot (Zimmerman et al., 2014), observed a 43% drop in average searching time after introducing demand-based pricing and real-time guidance. Barcelona’s on-street sensor rollout showed how sparse instrumentation plus predictive analytics can reduce cruising under real conditions (Zambanini et al., 2020). A study in a European urban center used a survey-based approach to analyze how pricing reform influenced occupancy and driver behavior (Cats et al., 2016). These studies highlight the complexities of real-world deployments, where sensor coverage, driver compliance, and fluctuating demand collectively influence outcomes.

Positioning of this study. Using street occupancy records for Madrid (Madrid City Council, 2024), we present a unique city‑scale empirical comparison of four strategies: Uncoordinated Agnostic (Unc-Agn), Coordinated Agnostic (Cord-Agn), Coordinated Approximate (Cord-Approx), and Coordinated Oracle (Cord-Oracle). Our experiments (i) quantify the marginal benefits of uncoordinated and coordinated strategies, (ii) show that modest coordination captures most oracle gains, and (iii) introduce a practical approximation (Cord-Approx) that approaches oracle performance without tracking competitors in real time. By empirically bridging the gap between theoretical optima and deployable systems, our findings offer concrete guidance for designing future smart street‑parking deployments.

3. Problem Formulation

This study examines two core questions about smart parking systems: (1) How do key design choices (coordination, information granularity) affect real traffic? (2) How do environmental factors (observability radius, spot availability, traffic intensity) impact performance? Both require analyzing the interaction between information and coordination. To rigorously analyze the impact of smart parking strategies in real deployments, we built a city-scale simulation of Madrid’s curbside ecosystem. We (1) simulate parking supply, demand, and traffic dynamics under controlled conditions, and (2) isolate key factors, information granularity, coordination, and adoption rate, to assess their effects on system performance.

3.1. Definitions

We provide below the formal definitions of the core symbols used in our simulation-based study (summarized in Table 1). Further details on the simulation findings are presented in Section 3.3.

$\bullet$ The city is divided into an $n\times n$ grid, indexed by $(i,j)$ where $i,j\in\{0,1,\ldots,n-1\}$. The simulator evolves over discrete time steps $t\in T$.

$\bullet$ Let $D_{t}\subseteq\mathcal{D}$ be the set of participants (app-enabled drivers) active at time $t$, and $C_{t}\subseteq\mathcal{C}$ the set of competitors (non-users searching without system assistance). Parking infrastructure is defined by a spatial distribution $b_{i,j}\in\mathbb{Z}^{+}$ indicating spots (bays) capacity in grid cell $z=(i,j)$, with total capacity $B=\sum_{i=0}^{n-1}\sum_{j=0}^{n-1}b_{i,j}$. The system maintains perfect knowledge of street parking spot availability through deployed sensors (see Section 3.3).

$\bullet$ The travel time $\tau(d,s)$ is the Manhattan distance between the participant $d$ and spot $s$ (via their Geohash cells); see Section 3.3.

$\bullet$ The observability radius $R$ is maximum distance within which competitors detect spots. Competitor $c\in C_{t}$ observes spot $s\in\mathcal{S}_{t}$ if $\tau(c,s)\leq R$, where $\tau(c,s)$ is Manhattan distance between $c$ and $s$.

$\bullet$ A parking attempt by an agent is successful if the agent reaches the parking spot before anyone else (participants or competitors) and within the per-attempt budget $t_{max}$. Attempts exceeding $t_{max}$ are counted as failures and the agent exits the simulation; real-world recourse (e.g., off-street or farther parking) is out of scope.

$\bullet$ We extend the parking spot allocation problem to a dynamic setting, where agents and spots appear and disappear over a predefined simulation horizon $T$. The binary decision variable $x_{d,s,t}\in\{0,1\}$ equals 1 when participant $d\in D_{t}$ is assigned to spot $s\in\mathcal{S}_{t}$ at time $t$. Let $\mathcal{A}^{comp}_{t}\subseteq\mathcal{S}_{t}$ be the set of spots already secured by competitors at time $t$:

[TABLE]

If multiple agents, participants/competitors are equally close to a spot $s$ or both at the spot $s$, we break ties uniformly at random; This ensures fairness and avoids systematic bias. If the selected agent is competitor c, the spot s is added to the set $\mathcal{A}^{comp}_{t}$, as defined in Equation 1. The dispatcher then minimizes the current assignment cost over eligible pairs while respecting competitor preemption:

[TABLE]

subject to

[TABLE]

where $\mathbb{I}[\cdot]$ is the indicator function. Constraint (3) enforces participant exclusivity, whereas Constraint (4) blocks allocation of spots already captured by competitors. We solve this problem online by recomputing a Hungarian bipartite match at every $t\in T$ with updated participants/competitors current positions and spot availability. Unassigned participants propagate to $t{+}1$ while moving toward their previous targets, yielding a rolling-horizon scheme that captures (1) real-time occupancy changes, (2) continuous agents’ movement, and (3) fluctuating demand.

3.2. Strategies

We evaluate four distinct parking allocation strategies, each representing a different level of situational awareness and coordination among participants. Together, they isolate how information and coordination affect outcomes for app users and non-users. For cross-group comparisons to current practice, competitors (blind search) are the real-world baseline; Strategy 1 is an app-user baseline (information only, no coordination).

3.2.1. Strategy 1: Uncoordinated Agnostic (Unc-Agn)

In this strategy, each participant $d\in D_{t}$ has full visibility of all available spots $\mathcal{S}_{t}$ at time $t$ (information only; no coordination among participants). Each participant $d\in D_{t}$ independently selects their nearest unoccupied spot:

[TABLE]

where $s^{*}$ is participant $d$’s target spot. Due to uncoordinated decision-making, multiple participants may target the same spot, resulting in conflicts. Failed assignments trigger renewed search behavior, introducing inefficiencies from contention and redundant travel (Algorithm 1).

3.2.2. Strategy 2: Coordinated Agnostic (Cord-Agn)

Here, the global orchestrator knows all free spots and receives participants’ current positions, but not competitors’ positions. At each time step $t$, participants report their positions to a global orchestrator. Then, the global orchestrator constructs a cost matrix $\mathbf{M}_{t}\in\mathbb{R}^{|D_{t}|\times|\mathcal{S}_{t}|}$. Each cost entry $\mathbf{M}_{t}(d,s)\in\mathbf{M}_{t}$ represents the travel time $\tau(d,s)$ that a participant $d$ needs to take for reaching the spot $s$. The orchestrator then solves an optimization problem using $\mathbf{M}_{t}$ to assign each spot $s_{d}^{*}$ to a single participant $d$ with minimum cost on $d$.

This optimization problem reduces to an assignment problem that minimizes total travel time. The assignment problem is then solved by deploying the Hungarian algorithm (Kuhn, 1955) whose time complexity is O\bigl{(}|D_{t}|^{3}\bigr{)}. This approach eliminates contention among our own participants but may still fail to secure spots by ignoring the effect of non-participating competitors (See Algorithm 2).

3.2.3. Strategy 3: Coordinated Oracle (Cord-Oracle)

This strategy, denoted by Cord-Oracle, assumes perfect global knowledge: current positions of all participants, all available spots, and all competitors in real time $t$ as shown by Algorithm 3. This infeasible setting is used only as an upper-bound benchmark. To compute $\mathbf{M}_{t}(d,s)$ (the $\mathbf{CalculateCost}$ procedure in Algorithm 3), we must consider three conditions as specified by Equation 6, which are detailed below:

$\bullet$ Condition 1: A participant $d$ takes the spot $s$ if $d$ is closer to $s$ than all the competitors ($\tau(d,s)<\min\limits_{c\in C_{t}}\tau(c,s)$). In this case, $\mathbf{M}_{t}(d,s)$ is $\tau(d,s)$ since it takes $\tau(d,s)$ for $d$ to reach to $s$.

$\bullet$ Condition 2: A competitor $c$ takes $s$ if any competitor is within the visibility radius $R$ and closer to $s$ than any participant is ($\exists\,c\in C_{t}\ |\tau(c,s)<\tau(d,s)\wedge\tau(c,s)\leq R$). Now, the chance of $s$ being assigned to $d$ is effectively zero, which means that $\mathbf{M}_{t}(d,s)$ is too high; thus, we determine $\mathbf{M}_{t}(d,s)$ as infinity.

$\bullet$ Condition 3: In this last condition, if $c$ is closer than $d$ but still outside $R$ ($\tau(c,s)>R$), $\mathbf{M}_{t}(d,s)$ depends on a distance-weighted probability. This probability, denoted by $p(c,s)$, is the probability of competitor $c$ being able to reach a range $R$ of spot $s$ before participant $d$. The cost matrix adapts dynamically using a piecewise distance-based function.

[TABLE]

Here, $C^{*}_{d,s,t}=\{\,c\in C_{t}:\tau(c,s)<\tau(d,s)\ \wedge\ \tau(c,s)>R\}$ denotes the set of competitors who are closer to spot $s$ than participant $d$, yet lie outside the visibility radius $R$. For any such competitor $c$, let

[TABLE]

be the number of steps available before participant $d$ comes to within one step of the visibility radius $R$ around spot $s$. Define the reachable set

[TABLE]

where $z=(i,j)$ denotes a generic grid cell. Each element of $\mathcal{N}_{c}^{\leq t_{c}}$ is a location that $c$ could occupy after at most $t_{c}$ uniform–random moves (one step north, south, east, or west per tick). We define the distance-weighted probability,

[TABLE]

Since Manhattan distance on our grid corresponds directly to travel time, $t_{c}$ denotes the competitor’s total time budget before participant $d$ comes to within one step of the visibility radius $R$ around spot $s$. Assuming each move direction at every tick is chosen uniformly at random, all endpoints in $\mathcal{N}_{c}^{\leq t_{c}}$ are equally likely. A favorable outcome occurs precisely when that endpoint lands on the radius $R$ circle around spot $s$, i.e., $\tau(z,s)=R$ and no closer. Equation (9) is simply the familiar “favorable/total” ratio, which produces the smooth penalty term in Equation (6) and seamlessly bridges the two deterministic Cases 1 and 2. Once $\mathbf{M}_{t}$ has been constructed, we apply the Hungarian algorithm to $\mathbf{M}_{t}$ to obtain $\mathcal{A}^{partc}_{t}$, yielding the optimal participant–spot assignment under this cost structure.

3.2.4. Strategy 4: Coordinated Approximate (Cord-Approx)

Due to the infeasibility of obtaining real-time competitor locations, the Cord-Oracle strategy is impractical in real-world settings. The Cord-Agn strategy, while feasible, suffers from suboptimal allocations as it lacks awareness of competitors. Geographic proximity is a poor proxy for payoff because a “close” space may already be on many participants’ radar and disappear before arrival. To account for this hidden competition, we fold in an empirically learned success ratio. We introduce the Cord-Approx strategy, which uses historical data to probabilistically estimate the behavior of participants and competitors, enhancing decisions without live competitor tracking. This probability modulates travel time, penalizing spots that often snap up quickly and favoring those that are more likely to remain available. The model implicitly captures participant rivalry without simulating each potential competitor explicitly: the lower the historical parking success ratio, the greater the implied crowd pressure. The resulting effective distance steers participants toward spots that are not only near but realistically attainable, reducing wasted searching time and smoothing street parking demand. Let $\mathcal{H}=\{(g_{k},\rho_{k,t},t)\}$ be a historical record of occupancy probabilities, where $\rho_{k,t}$ denotes the observed success ratio of finding a spot in Geohash $g_{k}$ at time $t$. Each cell $z$ in the simulation grid is associated with a Geohash string $g_{k}$, where $k$ is a unique integer index assigned to that cell for ease of lookup. A forecasting model generates $\hat{p}_{k(s),t}$, the estimated probability of availability in $g_{k}$ at time $t$. The cost matrix is weighted inversely by success likelihood

[TABLE]

where $k(s)$ returns the index $k$ of the Geohash $g_{k}$ containing spot $s$. This effective distance inflates travel time by the inverse of the spot-success prediction. The resulting cost matrix is passed to the Hungarian assignment algorithm, which computes a one-to-one participant-spot match that minimizes the total effective distance. By favoring spaces that are both close and likely to remain free, the scheme reduces futile detours and increases overall parking success compared to distance-only matching. This encodes probabilistic competitors awareness and bridges the gap between the Cord-Agn (no awareness) and Cord-Oracle (perfect awareness) extremes, achieving near-optimal efficiency while remaining practical. Empirical results in Section 4.1 show that Cord-Approx achieves, on average, 77.54% of the participants success ratio attained by Cord-Oracle (85.32%). To estimate spot availability probabilities $\hat{p}_{k(s),t}$, we use Ridge Regression (L2-regularized linear regression) (Hoerl and Kennard, 1970), a robust method for high-dimensional spatiotemporal data with multicollinearity. It mitigates overfitting by penalizing large coefficients, optimizing

[TABLE]

where $\mathbf{X}$ contains time-of-day, weekday, Geohash (location), and recent occupancy trend features, $\mathbf{y}$ is the historical availability, and $\lambda$ controls regularization strength via cross-validation. This yields stable predictions under sparsity and noise (Hoerl and Kennard, 1970; Murphy, 2012). Assignments are logged and merged online, so each round trains on up-to-date observations. This online update loop lets the success ratio estimator track non-stationary demand and gradually refine its forecasts, enabling the assignment policy to converge toward optimal performance. For a detailed description of the procedure, see Algorithm 4.

3.3. Data and Simulation Design

To capture Madrid’s traffic dynamics, we developed a custom simulator from scratch, implementing all algorithms and components ourselves. We first retrieved fine‑grained traffic‑intensity measurements released by the Community of Madrid, Spain (Madrid City Council, 2024). These counts, recorded at the street‑segment level, capture the temporal and spatial variability of vehicle flow in the city center. Using this dataset, we overlaid a $22\times 22$ geospatial grid where each cell corresponds to a 7-character Geohash ($\approx 152.8\,\mathrm{m}\times 116.4\,\mathrm{m}$). The grid aligns with the cadastral boundaries of central Madrid, encompassing residential neighborhoods and dense commercial corridors (Figure 1). This granularity allows us to model the heterogeneous distribution of on‑street parking and link each street’s traffic intensity to its enclosing Geohash cell(s). The simulator inherits the “pulse” of the real city: streets that are busy in the empirical record remain busy in the synthetic world, and quiet residential lanes stay quiet. We use a mesoscopic 7-character Geohash grid simulator because the goal is assignment under information limits, not lane dynamics. Coupling to SUMO/MATSim would add overhead without changing the mechanism: the four strategies differ only in how they build the cost matrix passed to the Hungarian algorithm. The grid lets us run 24-h, city-wide, multi-seed sweeps and ablation studies while staying consistent with sensor statistics. We checked correctness on toy cases for Hungarian and by matching simulated diurnal flows to the sensor profile. A microscopic model is only needed for lane-level effects (spillback, signals), which are out of scope. Figures 1,  5, 6, and  7 are produced with kepler.gl. Basemap data © OpenStreetMap contributors; tile layer © CARTO (Voyager).

$\bullet$ Geospatial Data Extraction: We extract the latitude and longitude coordinates corresponding to each Geohash and map them onto our simulation grid. (Geohashes derived from (Geohash.es, nd)).

$\bullet$ Spot Identification: For each 7-character Geohash, we calculated the maximum on-street parking capacity by summing legally parkable street lengths, accounting for zoning, road class, and municipal restrictions (loading zones, no-stopping, etc.). In simulation, agents park and depart based on real-world dwell times, dynamically updating each Geohash cell’s spot availability. We adopt an extreme-case baseline because producing a complete street space inventory city-wide remains elusive. Existing options, sensor-equipped stalls (Zimmerman et al., 2014), overhead vision (Zambanini et al., 2020), mobile crowd-sensing (Nawaz et al., 2013), and crowdsourced maps (Supaplex030 and Riiga, 2022), are partial, costly, or uneven, so no method yet yields a definitive count. Our one-time manual street length audit, meter-accurate for Madrid’s core, thus provides a reproducible supply ceiling that any empirical estimate will lie below.

$\bullet$ Traffic Intensity Data Extraction: We extract traffic intensity records for each Geohash cell over a 24-hour period using publicly available data from traffic sensors distributed across Madrid (Madrid City Council, 2024). These sensors record a count each time a vehicle passes, reporting aggregated totals at 15-minute intervals, each linked to a specific street segment. To align this data with our simulation framework, we first map each street to its corresponding Geohash cell(s) based on geographic overlap. These counts are then proportionally assigned to the overlapping Geohash according to the fraction of each street segment contained within each cell. To achieve minute-level granularity, we disaggregate the 15-minute counts into one-minute bins via uniform split, generating a continuous 24-hour intensity profile for each Geohash. Finally, we estimate the share of counts in each cell and time interval that are actively searching for parking, yielding a fine-grained approximation of parking demand intensity at the minute level. Following FHWA guidance, we assume $\approx$10% of vehicles are searching for parking (Weinberger et al., 2023). Accordingly, we model 1.5% as participants and 8% as competitors; the remaining 90.5% (through-traffic) is outside our simulation scope. We hold adoption shares fixed across strategies to isolate the effect of information and coordination. Across the 24-hour window, the simulator instantiates a total of $\approx$270,000 participants (app users) rides and $\approx$1,600,000 competitors rides (non-users), dispatched hour by hour from the empirical arrival series. The system comprises 12,365 fixed on-street parking spots, distributed across 484 Geohash cells. To reduce stochastic variation, each strategy was run three times.

4. Experimental Results

This study models traffic conditions for the week of 15–21 April 2024. We focus on the five working days (Monday 15 – Friday 19), when intensity is relatively stable. Each street segment in the dataset was assigned to a 7-character Geohash (Geohash.es, nd), yielding a 22 × 22 lattice (484 Geohashes) that preserves spatial adjacency. Observed traffic counts were projected onto this grid. 18 April 2024 was chosen as the main evaluation date because it is mid-week, avoids holidays, and reflects typical demand. Cord-Approx was trained on 15–17 April and tested on 18 April. A parallel weekend experiment was conducted on April 20–21 using the Unc-Agn, Cord-Agn, and Cord-Oracle strategies. Weekend demand is low-pressure; in that regime Cord-Agn closely tracks the oracle bound, so we omit Cord-Approx for brevity. Due to the lower traffic during that period, this experiment is discussed only in Section 4.2.

We present a 24-hour simulation-based analysis of street parking dynamics within Madrid’s central Geohash grid, where competitors operate within a radius $R=1$; larger $R$ values were tested but are excluded: since at $\approx 152.8{\times}116.4$ m per cell, broader visibility is unrealistic for street parking. We evaluate how varying levels of information-sharing and coordination impact participants’ ability to successfully secure street parking. First, we compare overall parking success ratios and average search times for four strategies: Unc-Agn, Cord-Agn, Cord-Approx, and Cord-Oracle. Second, we examine how each strategy widens the gap between participants and competitors as availability and demand shifts during the day. Finally, we present a spatial breakdown of performance across land-use zones: commercial, residential, and mixed, on the working day of 18 April 2024, to highlight where Cord-Approx yields the greatest reductions in search time. We then analyze the same zones under the Cord-Agn strategy during the weekend (21 April 2024) to examine how different urban areas respond under lower traffic conditions typical of non-working days. These analyses reveal where coordination via historical and real-time data matters most.

4.1. City-wide Results

4.1.1. Comparative Analysis of Parking Success Ratios Across Strategies and Time Periods

Figure 2(a) shows full working day parking success ratios for participants and competitors. During peak hours (09:00–17:00), Unc-Agn yields a 34.25% success ratio for participants, slightly below competitors due to uncoordinated participants converging on the same spot. Coordinated strategies, Cord-Agn, Cord-Approx, and Cord-Oracle, raise success ratios to 70.04%, 77.54%, and 85.32%, respectively, achieving gains of 35.79 to 51.07 percentage points (pp) over Unc-Agn strategy. These improvements stem from more efficient participants distribution and reduced contention. Notably, Cord-Approx closely approaches Cord-Oracle, showing that historical data can approximate competitors effects without real-time tracking. The 35.79 pp gap between Cord-Agn and Unc-Agn illustrates that coordination alone offers greater benefits than spot-level information. During off-peak hours, differences are narrow, as low competition allows uninformed competitors to park successfully.

Figure 2(b) illustrates how different parking strategies affect the success gap between participants and competitors. Counter-intuitively, using only information about parking alone can actually harm the participants (-4.38 pp). This occurs because Unc-Agn may direct multiple participants to the same spot, leaving most without parking; when frequent, random searching can outperform informed but uncoordinated choices. Coordinated strategies yield substantial improvements in participants parking success ratios: Cord-Agn achieves 70.04% (+39.33 pp), Cord-Approx reaches 77.54% (+48.83 pp), and Cord-Oracle attains 85.32% (+57.56 pp), all relative to competitors. These results confirm that while information helps, coordination is essential for parking success ratio (see Table 2). However, participants who couldn’t find parking within $t_{max}=30$ minutes were effectively “forced out”, they either had to park farther away and arrange alternate transport back to their destination, or pay for costly private parking.

4.1.2. Comparative Analysis of Average Search Time Across Strategies and Time Periods

Figure 3 presents the average participant search time across the 24-hour duration of the working day. Table 2 complements this view by presenting peak‑hour (09:00–17:00) search time for participants and competitors. We benchmark each strategy against the Unc-Agn strategy and evaluate two objectives: (i) reducing participants search time and (ii) widening the gap over competitors. As expected, Unc-Agn performs worst: participants require on average 19.24 minutes to locate a spot, marginally more than competitors at 17.83 minutes, confirming the poor parking success ratio reported in Figure 2(a). Adding coordination substantially improves performance. Under Cord-Agn, participants search time drops to 9.86 minutes, a 48.7% reduction relative to Unc-Agn, while competitors time increases to 19.79 minutes. Cord-Approx further reduces participant search time to 6.69 minutes (65.2%) and raises competitors time to 19.98 minutes. Finally, Cord-Oracle yields 8.83 minutes for participants (54.1%) and 19.89 minutes for competitors. The fact that Cord-Approx achieves shorter search time than Cord-Oracle is not unexpected. The metric is computed only for successful parking events, and the two strategies differ in success ratio; therefore the values are not directly comparable. Overall, Cord-Approx delivers the best trade‑off, cutting participants search time by 66.5% relative to competitors and by 65.2% with respect to the baseline of the participants, Unc-Agn strategy.

4.1.3. Comparative Analysis of Agents’ Parking Success Ratios Across Strategies Under Varying Parking Spot Availability.

Figure 4 visualizes the average parking success ratio gap in the working day between participants and competitors under different information, coordination strategies, and traffic conditions (i.e., street parking availability). Under high parking availability (40–45%), both agents perform well, with limited contention for spots, resulting in moderate but consistent success gaps ranging from +0.31 to +0.47. These gaps reflect the residual benefit of coordination, even when parking is relatively abundant. However, under low parking availability (0–5%), overall success ratios decline sharply, ranging from +0.38 to +0.5, due to fierce competition and spot scarcity. Interestingly, while the success gaps remain slightly wider, the benefits of coordination are diminished, as structural limitations, namely, the severe shortage of available spots, leave little room for any strategy to improve outcomes, regardless of planning. The most informative regime emerges at intermediate availability (20–25%), where supply and demand are balanced enough to enable effective competition. Here, coordination strategies demonstrate their full potential. All coordinated approaches maintain high parking success ratios (above 70%), and the participants–competitors gap reaches its maximum, peaking at +0.56 under the Cord-Oracle strategy. This regime highlights the ideal operating point where predictive coordination most effectively differentiates participants outcomes, leveraging limited but actionable information to outperform competitors.

4.2. Zooming in on Particular Zones of Madrid

We discretized the central Madrid study area into nine distinct zones, each characterized by one of five predominant land-use archetypes: Historic Retail & Tourist Core, Cultural & Transport Hub, Traditional Residential, Office & Station District, and Residential & Light Industry. As shown in Figure 5, each zone is numbered to facilitate clearer referencing and interpretation throughout our analysis. This spatial categorization allows us to capture the heterogeneity of urban environments and explore how different patterns of land use shape parking behavior and search dynamics. By zooming into this grid-level view, we uncover performance variations that are not evident from city-wide aggregates.

4.2.1. Working Day Peak Hour (18 April 2024, 09:00–17:00)

In Figure 6, during peak working-day hours, participants using the Cord-Approx strategy significantly outperform competitors across all zones, demonstrating the strategic value of coordination and predictive modeling. Table 3 reveals how zone-specific traffic form and usage patterns mediate these gains:

$\bullet$ Traditional Residential. Participants in Cell (4) achieve a substantial 73% improvement (7.00 min vs. 26.14 min for competitors), primarily due to moderate density, regular street layouts, and consistent demand patterns that enhance the reliability of predictive coordination. In contrast, Cell (1), featuring narrower roads and higher congestion, yields a lower but still meaningful 40% improvement (16.69 min vs. 28.01 min), reflecting the limitations of prediction under more constrained spatial conditions.

$\bullet$ Residential & Light Industry. These zones offer predictable demand cycles, such as morning arrivals and afternoon departures tied to shift work and local commerce. Cell (2) shows a 68% decrease (6.39 min vs. 19.90 min), while Cell (3), with its lower baseline congestion, demonstrates an even stronger 78% improvement (2.58 min vs. 11.93 min), underscoring how excess capacity amplifies the benefits of strategic guidance.

$\bullet$ Cultural & Transport Hubs. These zones exhibit high turnover due to continuous taxi, tourist, and passenger activity, making real-time spot prediction highly effective. Cell (5) records a 77% reduction (4.57 min vs. 19.70 min), while Cell (9) achieves a similar 75% improvement (3.45 min vs. 13.97 min). High spot turnover enhances the effectiveness of Cord-Approx, particularly when coordinated with known traffic patterns.

$\bullet$ Office & Station District. This zone features strong temporal rhythms due to synchronized train schedules and commuter flows. Cell (6) shows a 49% improvement (6.66 min vs. 13.17 min), as the predictability of demand surges allows preemptive assignment strategies to operate effectively within structured time windows.

$\bullet$ Historic Retail & Tourist Core. Rapid spot turnover driven by short-term visitors, deliveries, and shopping trips allows predictive strategies to substantially reduce search burden. Cell (7) achieves a 69% improvement (7.69 min vs. 24.66 min), and Cell (8), despite a more complex and irregular street layout, still yields a notable 64% reduction (7.07 min vs. 19.82 min), highlighting that turnover frequency can offset geometric inefficiencies in the road network.

4.2.2. Weekend Peak Hour (21 April 2024, 09:00–17:00)

Weekend conditions, with lower traffic and competition, diminish the benefits of the advanced Cord-Approx strategy (Figure 7). We therefore focus on the Cord-Agn strategy, which closely mirrors Cord-Oracle performance under these simpler dynamics.

$\bullet$ Traditional Residential. Participants in these zones experience a consistent 67% reduction in search time (3.8 min vs. 11.6 min), as weekend travel patterns ease pressure on street parking. With many residents inactive or away, natural availability improves, making even simple coordination highly effective.

$\bullet$ Residential & Light Industry. Weekend dynamics yield mixed results. Cell (2) shows a 43% reduction (4.17 min vs. 7.31 min), likely due to residual working day patterns, even though commercial deliveries are largely inactive. Cell (3), with minimal congestion, sees only marginal gains (3.17 min vs. 3.52 min), showing limited value of coordination in low-pressure settings.

$\bullet$ Culture & Transport Hubs. These zones benefit from ongoing but lower-intensity weekend movement, such as leisure trips, museum visits, or local transit use, yielding modest yet consistent gains. Cell (5) improves by 32% (5.03 min vs. 7.37 min), and Cell (9) by 18% (4.03 min vs. 4.93 min), suggesting that even light but steady turnover sustains coordination value.

$\bullet$ Office & Station District. On the weekend, this area lacks the structured commuter flows seen on the working day. Instead, irregular and unpredictable visitor patterns dominate, leading to weaker participants’ outcomes (7.43 min vs. 4.39 min) as Cord-Agn becomes less effective without consistent demand rhythms.

$\bullet$ Historic Retail & Tourist Core. These zones show contrasting behaviors. Cell (7) benefits from continued visitor activity; shopping, dining, and sightseeing, leading to a 49% improvement (6.01 min vs. 11.69 min). However, Cell (8), where café and restaurant patrons occupy spaces for extended periods, shows almost no gain (7.44 min vs. 7.59 min), highlighting how static parking behavior limits strategy effectiveness.

Comparative analysis of working day and weekend results highlights that Cord-Approx is particularly effective under working day conditions, where higher traffic demand and competitive pressure necessitate more advanced strategies. On weekends, however, the reduced demand and naturally improved street parking spot availability render such complexity unnecessary. In these cases, simpler coordination approaches suffice, maintaining strong performance without the overhead of approximation.

5. Conclusion

We studied how information and coordination shape on-street parking outcomes at city scale, comparing four strategies from information-only (Unc-Agn) to an oracle full knowledge upper bound (Cord-Oracle). Information alone is not enough: when many participants chase the same spots, Unc-Agn can harm them, whereas coordination (Cord-Agn) yields large gains but still trails the oracle. To bridge this gap, we introduced Cord-Approx, which weights distance by learned success probabilities from historical occupancy and then solves a Hungarian assignment, capturing much of the oracle’s benefit without live tracking of competitors or new sensing. Under weekday operating conditions (with competitors observability fixed at $R{=}1$), Cord-Approx reduces participants’ average search time to 6.69 minutes vs. 19.98 for competitors, with gains peaking at intermediate availability ($\approx$20–25%) and tapering at extremes. On low-pressure weekends, Cord-Agn nearly matches the oracle, so approximation adds little. We report both users (participants) and non-users (competitors) outcomes and flag equity/access considerations. Limitations include fixed adoption, $R{=}1$, and search-time computed for successful attempts only. Future work will study adoption (scaling) sensitivity, congestion/VKT and emissions, robustness to imperfect sensing/partial observability (incl. $R$ sensitivity), and privacy-preserving or decentralized variants. Overall, Cord-Approx offers a practical balance: near-oracle benefits with deployable data and no live competitors tracking.

Acknowledgements.

This work was supported by the MLEDGE project (TSI-063100-2022-0004), funded by the Ministry of Economic Affairs and Digital Transformation and the European Union NextGenerationEU/PRTR.