Dynamic Matching Strategies for Mobility Services

Updated 4 October 2025

Dynamic matching strategies are algorithmic and control-theoretic approaches for pairing vehicles with trip requests under uncertain, heterogeneous conditions.
These methods integrate traffic flow theory, online optimization, behavioral economics, and stochastic modeling to address real-time supply–demand imbalances.
Key algorithmic paradigms such as hierarchical greedy, graph-based methods, and adaptive pooling enable efficient, scalable, and responsive mobility service systems.

Dynamic matching strategies for mobility services encompass a spectrum of algorithmic, control-theoretic, and behavioral approaches for optimally pairing vehicles with trip requests under real-time, uncertain, and often highly heterogeneous spatiotemporal conditions. This domain integrates insights from traffic flow theory, online optimization, behavioral economics, and stochastic modeling, serving both traditional ride-hailing and emerging autonomous, pooled, and multi-modal mobility platforms.

1. Foundational Concepts and Theoretical Models

Dynamic matching in mobility systems is fundamentally rooted in the bipartite matching problem—matching two sets (supply and demand) distributed in spatial and temporal domains, commonly under constraints of proximity, waiting time, and service quality. Classical random bipartite matching problem (RBMP) studies assume m (demand) and n (supply) vertices independently sampled in a D-dimensional L^p space, with the matching cost dictated by the metric distance (Shen et al., 18 Jun 2024, Shen et al., 2 Oct 2025). Analytical expressions, such as

$E[X] = \sum_{k=1}^m P(k) \, E[Y_k],$

where $P(k)$ is the probability a customer is matched to their k^th neighbor and $E[Y_k]$ is the expected k^th-nearest neighbor distance, provide closed-form tools for quantifying expected system performance. These models can be further constrained by a maximum matching radius, introducing additional feasibility criteria and performance trade-offs (Shen et al., 2 Oct 2025).

Spatial heterogeneity and temporal arrival dynamics introduce further complexity. The Spatiotemporal Random Bipartite Matching Problem (ST-RBMP) generalizes static RBMP to allow for zones with arbitrary densities, non-stationary Poisson arrivals, and dynamically adjustable pooling intervals and search radii, often optimized via continuum approximation methods and optimal control frameworks (Shen et al., 2 Oct 2025).

2. Hierarchical and Multi-layered Frameworks

Modern research frequently employs hierarchical modeling frameworks that decompose the mobility matching problem across multiple layers of abstraction:

Physical layer (traffic flow dynamics): Vehicle densities and motions are modeled by nonlocal conservation laws or PDEs, e.g.,

$\frac{\partial \rho(t,x)}{\partial t} + \frac{\partial}{\partial x}\left( \lambda\left(t,\int_{b(x)}^{d(x)} \rho(t,y)\,dy\right)\rho(t,x) \right) = 0,$

accommodating for dynamic speed-density relationships, stochastic weather, and road capacity changes (Keimer et al., 2017).

Routing and decision-making layer: Distinction is made between “routed” versus “non-routed” users, with split functions $\theta_a^v(t)$ guiding flow at network nodes (Keimer et al., 2017).
Cooperative control (dynamic matching) layer: Optimal control formulations—both continuous (e.g., coordinated truck platooning with objectives such as minimizing spatial variance) and discrete (e.g., integer programs over departure times and routes)—are leveraged to maximize matching opportunities. Distributed learning rules facilitate real-time, privacy-preserving decentralized control (Keimer et al., 2017).
Social planning/incentive design layer: System-wide behavior is influenced through economic incentives (e.g., congestion charges or dynamic tolls) and mechanisms that can be included in both the routing and dynamic matching cost functions.

This multi-layer approach underscores the interplay between physical constraints, informational structure, local coordination, and high-level societal objectives (Keimer et al., 2017).

3. Algorithmic Strategies for Dynamic Matching

Several algorithmic paradigms have been identified as effective for dynamic matching:

Partitioned/Hierarchical Greedy Algorithms: Algorithms such as "Hierarchical Greedy" partition the service area into multi-scale hypercubes, dynamically tracking supply at different scales. At each arrival, assignments are made to balance local and global supply, reducing long-term matching cost nearly to the information-theoretic minimum, particularly in higher dimensions (d ≥ 2) (Kanoria, 2021).
Tree-based and Graph-based Methods: Dynamic tree algorithms maintain a library of feasible service sequences, allowing fast insertions for new requests and aggressive pruning of infeasible branches in the presence of time and capacity constraints. Graph-based many-to-one and maximum weight matching approaches (e.g., GMOMatch) iteratively combine requests and vehicles to optimize assignment, reducing vehicle kilometers traveled and improving service rate (Meshkani et al., 2021, Yao et al., 2020, Yao et al., 2021).
Meta-heuristics and Optimizers: Genetic algorithms, alternating minimization (e.g., AltMin), bipartite and maximum-weight matching (e.g., in robust roundtrip hub-based transit design), and robust optimization/column-and-constraint generation (CCG) methods address the combinatorial nature and demand uncertainty in large-scale dynamic pooling and transit assignment (Guan et al., 2019, Woo, 2021, Qian et al., 2020).
Analytical and Control-theoretic Approaches: Closed-form matching distance formulas directly inform the selection of matching intervals (batching/pooling) and matching radii, facilitating real-time optimal control that balances waiting times against unproductive vehicle movement (Shen et al., 18 Jun 2024, Shen et al., 2 Oct 2025).

4. Adaptive Pooling, Batching, and Radius Control

A key dimension in dynamic matching is the choice of:

Pooling interval $\tau(t)$ : Determines the batch size of accumulated requests before matching. Models show that when idle supply is much larger than demand, instant matching (small $\tau$ ) minimizes cost, but in supply-constrained regimes, larger pooling intervals reduce deadhead distance at the cost of increased wait times (Shen et al., 18 Jun 2024, Shen et al., 2 Oct 2025).
Matching radius $r_z(t)$ : The spatial search boundary for candidate assignments. Dynamic tuning (tightening when supply exceeds demand, enlarging under scarcity) enables robust response to temporal and spatial heterogeneity (Shen et al., 2 Oct 2025).
Zone-wise parameter adaptation: In spatially heterogeneous regions, controls may be set locally per zone, with analytical formulas estimating matching probability and cost as a function of local densities (Shen et al., 2 Oct 2025).

The dynamic control of these parameters is formalized as an optimal control problem, minimizing cumulative system cost: $\min_{\mathbf{u}(t)} \;\; \phi[\mathbf{x}(T)] + \int_0^T \mathcal{L}[\mathbf{x}(t), \mathbf{u}(t)]\, dt,$ where $\mathbf{u}(t)$ collects intervals and radii, and system evolution is governed by demand/supply arrival rates and local matching probabilities.

5. Integration with Routing, Incentives, and Behavioral Models

Dynamic matching does not occur in isolation, but interacts with:

Routing applications: Real-time and forecast-informed split functions $\theta_a^v(t)$ are adjusted not solely for selfish shortest-path objectives, but to globally coordinate and maximize matching opportunities (e.g., for ride-pooling or freight platooning) (Keimer et al., 2017).
Incentive and tariff mechanisms: Dynamic pricing strategies, leveraging behavioral models such as Cumulative Prospect Theory (CPT), modulate the acceptance rate, align risk preferences, and influence dynamic matching efficiency. Monotonic behavioral response functions (e.g., acceptance probability $p^s_R = f(\gamma)$ ) permit inversion to achieve system targets (Guan et al., 2019).
Hybrid predictive analytics: Systems combining individual behavioral regularity and aggregated conformity, as in BuScope, enable proactive vehicle repositioning for last-mile services and dynamic matching based on real-time multi-scale demand forecasting (Meegahapola et al., 2019).
Multi-modal integration: Flexible frameworks allow private ridesharing and public transit to be dynamically matched and scheduled, assigning detour burdens and optimizing multi-hop journeys via meta-heuristics (Woo, 2021).

6. Performance Evaluation and Scaling Laws

Analytical scaling laws provide concise, robust predictors of matching system performance given critical dimensionless system parameters. For high-capacity pooling, vehicle occupancy and service rate scale as follows with system load $u = \lambda t̄/N$ (arrival rate × average trip duration / fleet size):

$\begin{align*} \bar{C} &= \begin{cases} u, & \text{if } u \leq 1\ \dfrac{u}{C-1+u} \cdot C, & u > 1 \end{cases} \ \bar{R} &= \begin{cases} 1, & u \leq 1\ \dfrac{C}{C-1+u}, & u > 1 \end{cases} \end{align*}$

These laws, observed to be universal across network topologies and city contexts, characterise the trade-offs between utilization and service level. Understanding these scaling regimes allows platforms and regulators to tune matching policies, pooling behavior, and fleet size to optimize for congestion, occupancy, and user satisfaction (Chen et al., 2023).

7. Practical Implications and Managerial Insights

Dynamic matching strategies, underpinned by the models and algorithms above, equip mobility operators and urban planners with actionable levers:

Real-time adaptation: Operators can monitor supply–demand balance, dynamically select pooling intervals and matching radii, and control matching batch sizes in response to localized spatiotemporal heterogeneity (Shen et al., 2 Oct 2025).
Balancing quality of service and efficiency: Instant matching is generally optimal in surplus supply regimes; batching and spatial selectivity become crucial when demand stretches available vehicles. Analytical expressions (closed-form E[X]) permit direct calculation of expected pickup times under varying policies (Shen et al., 18 Jun 2024).
Integration with incentive design: The ability to embed behavioral models in tariffs and to adjust pricing in line with CPT responses (risk aversion, reference dependence) further harmonizes market efficiency and user experience (Guan et al., 2019).
Performance prediction and resource planning: Scaling laws and closed-form performance models enable rapid resource planning and robust policy testing, reducing reliance on repeated costly simulation (Chen et al., 2023, Shen et al., 18 Jun 2024).
Resilience to uncertainty: By explicitly modeling and optimizing against spatiotemporal randomness and heterogeneity, these dynamic matching frameworks provide robustness in uncertain, real-world urban environments, outperforming purely static or sequential approaches (Shen et al., 2 Oct 2025, Tuncel et al., 2022).

In sum, dynamic matching strategies for mobility services comprise a multifaceted field that combines canonical matching theory, flow and control models, behavioral economics, and algorithmic optimization. The state of the art supports the design of responsive, efficient, and equitable mobility systems that robustly adapt to the stochastic, heterogeneous character of real-world transport demand and supply.