Pedestrian Routing and Walkability Inference Using Realized WiFi Connectivity

Abstract

Traditional pedestrian routing algorithms typically minimize physical distance or travel time, often overlooking contextual factors that influence route choice in digitally connected environments. As public WiFi infrastructure becomes increasingly prevalent in smart-city districts and university campuses, digital connectivity may influence pedestrian mobility decisions. This study introduces P-WARP, a multi-factor routing and inference framework that reconstructs latent pedestrian preferences by integrating physical effort, environmental walkability, and WiFi connectivity within a unified semantic graph. The empirical analysis is conducted on the Chiang Mai University campus, a digitally connected environment serving as a smart campus testbed. The framework integrates heterogeneous spatial datasets, including OpenStreetMap topology, Shuttle Radar Topography Mission elevation data, environmental walkability grids, and WiFi roaming logs collected via a custom mobile sensing application from 21 volunteers across 71 verified walking trips. Two routing strategies are evaluated: a Global Static Model, representing infrastructure-based connectivity assumptions, and a Trip-Centric Dynamic Model, incorporating realized connectivity histories. Model parameters are calibrated using Bayesian Optimization with five-fold cross-validation. Results show that incorporating realized connectivity reduces trajectory reconstruction error by 6.84% relative to the baseline. The learned parameters reveal a notable detour tolerance, suggesting that stable digital connectivity can influence pedestrian route choice in digitally instrumented environments.

1. Introduction

Urbanization in the 21st century has moved beyond simple infrastructure digitization toward the “Cognitive City” concept. In this era, the convergence of Internet of Things (IoT) sensors, Digital Twins, and physical systems aims to enhance urban efficiency and livability [1,2,3]. The notion of a smart city is commonly defined as an urban system where investments in human capital, digital infrastructure, and information and communication technologies are integrated to improve economic performance, sustainability, and quality of life [4]. Importantly, this perspective emphasizes the interaction between technological infrastructure and human activity rather than the mere presence of sensors or data collection systems. Within this framework, university campuses serve as effective microcosms of the broader smart city because they possess dense sensing networks and high-performance connectivity layers [5,6]. In this context, the concept of a smart campus has emerged as a localized implementation of smart city principles, where networked infrastructure, IoT systems, and data-driven services support intelligent management of mobility, energy, learning environments, and user experience [7]. These environments support continuous foot traffic and digital services, making them ideal testbeds for analyzing mobility in connected spaces. Consequently, pedestrian mobility here evolves beyond simple origin-destination traversal. It becomes a “phygital” (physical-digital) experience where physical movement is fundamentally coupled with digital connectivity [8,9].

Conventional pedestrian routing algorithms have historically prioritized efficiency. Foundational models, notably Dijkstra’s algorithm [10] and A* search [11], predicate their logic on the assumption that pedestrians function as rational agents optimizing for minimal distance or time. Although computationally robust, these deterministic models often overlook the stochastic and multi-objective nature of human decision-making in complex urban settings [12,13]. Literature in urban design suggests that pedestrians frequently behave as “sensual beings” who engage in trade-offs between path length and environmental factors such as comfort, safety, and aesthetics [14,15]. This behavior is particularly evident in tropical climates, where thermal comfort and shade availability become critical determinants of route choice and often outweigh the utility of the shortest path [16,17].

However, the integration of a “Digital Layer” into pedestrian navigation frameworks remains underexplored. As wireless connectivity evolves into a fundamental urban utility, WiFi hotspots and 5G nodes function as “digital anchors” that shape dwell times and movement trajectories [18,19]. Nevertheless, most routing systems continue to treat connectivity merely as a binary attribute or subordinate it entirely to physical constraints. Research explicitly quantifying the behavioral trade-off between digital utility and physical exertion factors, such as increased walking distance or elevation gain, remains limited [20]. Moreover, capturing these preferences necessitates analyzing the realized connectivity experience along a route rather than relying solely on theoretical coverage maps.

To address this gap, this study presents a data-driven framework designed to infer latent pedestrian mobility preferences using a large-scale tropical university campus as a case study. Rather than equating infrastructure density with urban “smartness,” this study focuses on the behavioral interaction between digital connectivity infrastructure and pedestrian mobility decisions within a digitally instrumented environment. We treat the campus as a representative outdoor environment with dense WiFi infrastructure comparable to emerging smart city districts. Diverging from forward-planning models, we adopt an approach inspired by Inverse Reinforcement Learning (IRL) [21,22]. We utilize Bayesian Optimization [23,24] to approximate the cost function that best explains observed pedestrian trajectories. By constructing a multi-factor semantic graph that integrates OpenStreetMap (OSM) for topology, SRTM for elevation, and retrospective roaming logs for realized connectivity, we empirically measure “detour tolerance.” We define this metric as the additional physical effort pedestrians are willing to expend to maintain stable digital connectivity.

2. Literature Review

Modeling pedestrian mobility presents a complex challenge that requires integrating perspectives from urban planning, computer science, and behavioral geography. To provide a clear context for the contributions of this study, we review the existing literature across four specific dimensions. First, we examine the development of smart campus sensing technologies. Second, we analyze the physical factors that determine walkability in complex environments. Third, we discuss the rising importance of digital infrastructure as a primary driver of mobility. Finally, we explore the methodological transition from traditional routing models toward data-driven behavioral inference.

2.1. From Smart Cities to Smart Campuses: The Sensing Context

The concept of the “Smart Campus” has expanded significantly over the past decade. It has moved from being a minor subfield of Smart City research to becoming a primary testing ground for Digital Twin technologies. Researchers now view university environments as micro-cities that effectively combine physical infrastructure with advanced sensing capabilities [25,26]. Unlike sprawling metropolitan areas, university campuses offer an outdoor environment that is both controlled and complex. This unique characteristic makes them highly suitable for experiments involving high-resolution mobility sensing and behavioral analysis [27]. Consequently, campuses serve as reliable empirical settings for developing methods that researchers can later scale up to apply in broader urban contexts.

Recent progress in the Internet of Things (IoT) and Mobile Crowdsensing (MCS) has made it possible to collect detailed mobility data from a wide variety of sources. A comprehensive survey by Capponi et al. [26] classifies these data collection methods into two main categories. The first category includes active logging approaches, such as the use of dedicated GPS trackers. The second category consists of passive sensing techniques, which include Bluetooth Low Energy (BLE) beacons, WiFi probe requests, and cellular network logs. Passive sensing is particularly advantageous for research in dense urban and campus environments. This is because it offers scalability and cost-effectiveness while placing minimal burden on the user [28].

In terms of practical application, Jundee et al. [29] have demonstrated that WiFi probe data can be used effectively to infer trips and origin–destination flows on a large scale. Their work highlights the feasibility of reconstructing pedestrian movement dynamics by using network-generated logs instead of relying on device-based GPS tracking. Similarly, recent studies by Tsiamitros et al. [30] and Kurkcu and Ozbay [31] have leveraged campus-wide WiFi infrastructures to analyze aggregate pedestrian flows and dynamic population densities. These macroscopic approaches are certainly effective for identifying hotspots and understanding temporal congestion patterns. However, they provide limited insight into individual route choice behavior. Aggregate flow models can successfully identify that a pedestrian moved between two locations. Yet, they often fail to explain how or why a specific path was selected when multiple feasible routes were available [13,22]. This limitation suggests a need to shift focus from aggregate flow analysis toward trajectory-level behavioral inference.

2.2. Physical Constraints: Walkability and Topography

Before addressing the influence of digital factors, it is essential to establish the physical foundations of pedestrian mobility. Traditional routing algorithms, most notably Dijkstra’s algorithm [10] and A* search [11], rely fundamentally on cost functions that aim to minimize distance or travel time. These models are computationally efficient. However, recent behavioral studies argue that such models implicitly assume pedestrians behave as rational agents operating in homogeneous environments. This premise often fails to capture the stochastic and variable nature of human navigation in the real world [13].

Golledge [12] challenged this mechanistic view by arguing that navigation is shaped primarily by cognitive maps and perceptual cues rather than strict geometric efficiency. This perspective has been substantiated by modern data-driven research. Researchers have built upon the foundational “5D” framework (Density, Diversity, Design, Destination, Distance) proposed by Ewing and Cervero [32]. Recent studies that utilize street-view imagery and deep learning have quantified the concept of “perceived walkability.” These studies show that factors such as safety, enclosure, and visual complexity often dictate route selection more strongly than physical proximity does [33,34].

In environments with complex terrain, two-dimensional routing representations prove to be insufficient. Tobler [35] originally formulated the “Hiking Function” to describe the non-linear relationship between slope and walking speed. Contemporary research has extended this concept to 3D urban mobility models. Recent works by Wang et al. [36] and Ge et al. [37] demonstrate that ignoring elevation effects in routing models significantly impacts pedestrian route choice and accessibility analysis. Consequently, this omission can distort the inferred preferences of pedestrians in hilly campus environments.

Environmental comfort further complicates the route choice process. This is particularly true in tropical climates where heat stress acts as a critical impedance [38]. Modern “Shadow-aware” routing algorithms have emerged to address this specific challenge. For instance, Feng et al. [39] introduced a shadow-oriented navigation approach, addressing the tendency of pedestrians in hot climates to walk significantly longer distances to stay in the shade and minimize thermal accumulation.This observation aligns with findings by Kamruzzaman et al. [40], which highlight the significant influence of built environment characteristics on walking behavior in subtropical climates. Furthermore, visual quality plays a pivotal role in these decisions. Recent computer vision analyses, such as the study by Juntakut et al. [41], have effectively utilized street view imagery to assess the “Green View Index” (GVI), highlighting the importance of visual greenery in urban environments. This visual greenery functions as a positive utility that helps to counteract physical fatigue. Collectively, these factors confirm that pedestrian routing is inherently a multi-objective optimization problem rather than a simple exercise in minimizing distance. To address such complexities, Ran et al. [42] demonstrated the efficacy of genetic algorithms in solving green path planning and optimization challenges.

2.3. The Digital Layer: Connectivity as a Primary Utility

The widespread adoption of mobile computing has introduced an additional dimension to pedestrian mobility. This new dimension is the imperative need for digital connectivity. Recent scholarship has framed this development within the context of Cyber-Physical-Social Systems (CPSS). In these systems, physical movement is fundamentally coupled with digital data streams and intelligent workflows [43,44]. This evolution has solidified the concept of the “phygital” environment [45]. It suggests that mobile interfaces do not merely augment reality. Instead, they reshape how users perceive, experience, and optimize their navigation through physical spaces.

Within this connected ecosystem, WiFi access points have evolved beyond their role as passive infrastructure. Recent studies term them “digital anchors” or “QoS (Quality of Service) landmarks” because they significantly influence where people pause, congregate, and traverse [19]. Oldenburg’s classic concept of the “third place” [46] has consequently evolved into the “smart third place,” where social interaction is mediated by the stability of digital access. Recent empirical studies by Fabre et al. [47] and Rosa et al. [48] utilize digital infrastructures—ranging from Wi-Fi to mobile networks—to characterize urban movement patterns. These findings underscore that pedestrians and commuters effectively treat connectivity as a tangible resource that is intrinsically linked to their physical mobility.

Despite these conceptual advances, relatively few studies have translated such insights into operational pedestrian routing models. Most technical research on WiFi still focuses primarily on localization accuracy through signal fingerprinting, as seen in recent works by Kim et al. [49]. There is less emphasis on analyzing the behavioral impact of signal quality on route choice. Contemporary crowdsensing studies have demonstrated the potential of WiFi logs for flow analysis [26]. However, there remains a scarcity of frameworks that treat connectivity as a continuous impedance field comparable to physical distance or elevation. By explicitly quantifying “detour tolerance” for connectivity, the present study treats digital access as a fundamental utility. We argue it is similar to shade or safety, acting as a resource that pedestrians actively seek in the modern smart campus.

2.4. Methodological Shift: From Forward Planning to Inverse Inference

Determining the relative importance of heterogeneous factors such as distance, elevation, environmental quality, and connectivity requires advanced modeling techniques. Ng and Russell [21] originally introduced Inverse Reinforcement Learning (IRL) as a method for inferring latent reward structures from observed behavior. This approach marks a distinct shift away from traditional forward-planning approaches that assume predefined cost weights.

Building on this foundation, Ziebart et al. [50] established the Maximum Entropy IRL framework. This framework provided probabilistic grounds for reconstructing agent preferences. However, recent advancements have evolved beyond classical linear features. Contemporary research by Arora et al. [22] and Wang et al. [51] integrates Deep Learning with IRL (Deep IRL). This integration enables the modeling of complex and non-linear interactions between pedestrians and high-dimensional semantic environmental features. Such interactions were previously difficult to capture using standard Maximum Entropy methods.

Despite their expressiveness, these Deep IRL approaches can be computationally prohibitive when applied to large-scale graphs with continuous state spaces and limited training data. To address this challenge, Bayesian Optimization (BO) has re-emerged as a highly efficient alternative for parameter inference in complex systems. Snoek et al. [23] demonstrated its effectiveness for optimizing expensive black-box functions. Recent applications in Intelligent Transportation Systems (ITS) explicitly validate this approach.For instance, Chen et al. [52] utilized Bayesian Neural Network-based methods to calibrate microscopic traffic simulators, effectively addressing the uncertainty in parameter estimation. Similarly, Agriesti et al. [53] demonstrated the scalability of Bayesian Optimization by successfully calibrating high-dimensional behavioral parameters (over 400 parameters) for large-scale activity-based models. Leveraging this approach allows the present study to rigorously calibrate the trade-off between physical and digital costs using limited ground-truth trajectories. This establishes a theoretical upper bound for behavioral inference without the computational overhead associated with Deep IRL.

3. Materials and Methods

This study establishes the P-WARP (Personalized WiFi-Aware Route Profiling) framework, a comprehensive computational engine designed to reconstruct and analyze pedestrian navigation behaviors within complex outdoor environments. Unlike conventional routing systems that rely on a single cost metric, P-WARP is architected as a flexible multi-factor inference framework capable of simulating diverse navigation strategies.

To rigorously quantify the influence of digital connectivity, the framework is configured to evaluate two distinct modeling strategies: (1) a Global Static Model serving as an infrastructure-centric baseline, and (2) a Trip-Centric Dynamic Model representing the proposed trip-centric approach. Through the comparative optimization of these models within a unified framework, P-WARP captures the behavioral dynamics of digital comfort, providing empirical evidence that a preference for stable, realized connectivity can act as a stronger predictor of pedestrian movement than physical distance alone.

The methodology is structured into a four-stage pipeline to ensure a robust and adaptive inference process. The logical sequence of these operational stages is illustrated in the methodology flowchart (Figure 1), while the overall system design contrasting the Global Static Model and the Trip-Centric Dynamic Model is depicted in the architectural framework (Figure 2). The framework integrates heterogeneous data sources, including OSM, Digital Elevation Models (DEM), and WiFi roaming logs, as summarized below:

• Data Acquisition and Heterogeneous Fusion: Physical geospatial data are consolidated with behavioral mobility logs, and a ground-truth dataset is established for evaluating mobility inference performance.
• Multi-layered Semantic Graph Construction: A navigable network graph is constructed in which edges represent physical pathways enriched with environmental, topographic, and digital attributes.
• Connectivity Modeling (Dual-Model Strategy): Two contrasting impedance models are evaluated to isolate the effect of WiFi connectivity: a Global Static Model based on collective infrastructure and a Trip-Centric Dynamic Model based on realized roaming behavior.
• Parameter Optimization via Bayesian Learning: The routing cost function is calibrated using Bayesian Optimization with 5-fold cross-validation to minimize the discrepancy between reconstructed paths and ground-truth trajectories.

3.1. Study Area

The empirical analysis in this study was conducted on the main campus of Chiang Mai University (CMU), Thailand. The campus represents a dense, digitally connected academic environment that combines extensive pedestrian infrastructure with large-scale wireless network deployment. Covering approximately 14.25 square kilometers, the campus contains academic buildings, residential areas, administrative facilities, and open public spaces connected through a complex network of pedestrian pathways and road segments.

Figure 3 illustrates the spatial structure of the study area. The map presents the outdoor walkable area, building footprints, pedestrian pathways, observed walking trajectories, and the distribution of WiFi access points across the campus. Indoor building areas are treated as structural obstacles within the routing model, while outdoor spaces constitute the walkable environment in which pedestrian movement occurs. Major campus landmarks, including academic buildings, the central food center, and main campus access points, are labeled to provide spatial reference.

The pedestrian network used in this study was derived from OSM data and further refined to represent walkable pathways within the campus environment. This network forms the base topological layer for the routing framework. Observed pedestrian trajectories collected from campus users were spatially aligned with this network to enable trajectory reconstruction experiments. In addition, the locations of WiFi access points were integrated into the spatial model to represent the digital connectivity layer.

The campus environment provides a suitable testbed for investigating the interaction between physical mobility and digital infrastructure. This makes the campus an appropriate micro-scale environment for examining how digital connectivity factors may shape pedestrian navigation behavior in smart urban environments.

3.2. Data Acquisition and Heterogeneous Fusion

To build the P-WARP framework, we combined two types of information: physical infrastructure data and user movement logs. All datasets were carefully processed and spatially aligned to the geographic extent of the CMU campus. The data acquisition process comprises the following components.

3.2.1. Ground-Truth Mobility Dataset (GPS and WiFi Association Logs)

To evaluate the developed mobility inference framework, a set of ground-truth walking trips was collected using a custom mobile application developed by our team. The study involved 21 volunteers, all of whom were first-year undergraduate students at Chiang Mai University. Recruitment was conducted on a voluntary basis during the first semester of the 2024 academic year. Prior to participation, volunteers were informed about the purpose of the study and the types of data that would be collected.

The application records GPS trajectories and simultaneously logs WiFi association events, including connected Access Point (AP) identifiers (SSID/BSSID) and timestamps. The application was implemented using the Flutter framework and utilized the platform’s GPS library to capture location updates from the participant’s smartphone. Instead of a fixed time-based sampling interval, the logging mechanism was event-driven, meaning that a new data record was created only when the device detected a meaningful change in geographic position. Consequently, the sampling frequency varied dynamically depending on the participant’s movement patterns. A separate lookup table mapping AP identifiers to their geolocations was available for analysis.

To preserve participant autonomy and privacy, data recording was fully user-triggered. Volunteers manually started and stopped recording sessions when logging a walking trip. The collected data were initially stored locally on the participant’s device and were later shared manually with the research team by the volunteers themselves. In addition, an informed consent agreement was presented within the application prior to any data collection. Participants were informed about the nature of the study and their right to withdraw from participation at any time without consequences. Ethical approval for this study was granted by the Chiang Mai University Research Ethics Committee (CMUREC No. 66/039).

During data collection, participants explicitly marked trip boundaries within the application by specifying the start (origin) and stop (destination) of each walking trip. As a result, each trip record contains a time-ordered GPS trajectory together with the sequence of connected APs observed during movement. Across all participants, a total of 71 verified walking trips were recorded and aggregated to form the ground-truth mobility dataset used in this study.

In total, 71 verified walking trips were collected. The total geometric length of each walking trajectory was computed after projection to UTM Zone 47N (EPSG:32647) using cumulative Euclidean distances between consecutive GPS samples. Across the 71 verified trips, the mean trip length is 715.72 m and the standard deviation is 377.25 m. These statistics describe the distribution of walking distances in the collected dataset and indicate moderate variability in trip scales.

This dataset reflects a realistic operational scenario in which campus or area network administrators possess WiFi association logs from which pedestrian mobility can be inferred.

3.2.2. Spatial Infrastructure and Environmental Grid

The road network topology and building footprints were extracted using the OSMnx library [54]. To account for environmental walkability and pedestrian preferences, we implemented a structured grid-based representation with a spatial resolution of $10\mathrm{m}\times 10\mathrm{m}$. To ensure computational efficiency during multi-factor weight assignment and nearest-neighbor spatial queries, an R-tree spatial indexing method was implemented. Each grid cell was assigned an environmental impedance weight ($W_{grid}$) based on land-use characteristics, where lower values represent more desirable walking environments and higher values represent physical or functional obstacles.

To provide methodological transparency, obstacles within the spatial framework are classified into four distinct categories as detailed in

Table 1. Classification and characterization of navigation obstacles and grid constraints.

Category	Description & Criteria	Data Source	Type
Physical barriers	Building footprints, permanent walls, and fences	OSM building layers	Static
Environmental impediments	Water bodies and non-pedestrian vegetation zones	OSM natural layers	Static
Navigability constraints	Indoor academic spaces (excluded to prevent GPS multipath errors)	Spatial filtering	Functional
Dynamic obstacles	Temporary constructions or transit blockages	Field validation	Temporal

. This classification distinguishes between absolute physical barriers, environmental impediments, and functional constraints.

A critical refinement in our spatial modeling is the treatment of indoor environments as non-navigable zones. While these spaces are structurally navigable, they are excluded from the routing graph to mitigate the impact of severe GPS signal attenuation and multipath effects typically encountered within buildings. This justification ensures that the P-WARP framework focuses on reliable outdoor pedestrian circulation, avoiding erroneous trajectory reconstructions in indoor corridors where sensing accuracy is compromised.

The road network was spatially intersected with the environmental grid such that each road segment inherited the impedance value of the grid cells it traversed. For segments intersecting multiple grid cells, the effective weight was computed based on the proportional length within each cell, preserving fine-grained environmental context in the graph representation.

3.2.3. Topographic Data Integration

Given the undulating terrain of the study area, elevation data were integrated to capture physical effort associated with slope. Elevation values were retrieved using the Open-Elevation API, which provides access to Shuttle Radar Topography Mission (SRTM) data [55]. Elevation was assigned to each graph node, and the absolute vertical grade for each edge was computed to represent topographic impedance.

3.2.4. WiFi-Trajectory Fusion and Data Cleaning

Empirical mobility data were initially stored in raw CSV format and converted to Apache Parquet for efficient processing. To ensure data quality, we applied a minimum movement threshold of $50\mathrm{m}$ to filter out static noise and GPS drift. The campus network operates under a Single Sign-On (SSO) environment, allowing devices to roam seamlessly across APs without repeated authentication. Consequently, the collected logs represent Active Access Points, where devices maintained successful connections. The set of APs observed across the 71 trips therefore represents the effective digital infrastructure relevant to pedestrian mobility rather than an exhaustive inventory of deployed hardware.

3.3. Multi-Layered Semantic Graph Construction

The core of the P-WARP framework is the construction of a multi-layered semantic graph, which transforms a standard topological network into a feature-rich environment for pedestrian navigation. The environment is modeled as a weighted directed graph $G=(V,E)$, where V represents the set of nodes and E represents the set of edges. Specifically, each edge $e_{u,v}\in E$ denotes a directional link connecting a source node u to a target node v. Unlike conventional routing models that rely solely on distance, our approach enriches each edge $e_{u,v}$ with an augmented attribute set ${\mathcal{A}}_{u,v}=\{L_{uv},{\omega }_{uv},g_{uv},{\mathcal{K}}_{uv}\}$ across four semantic layers:

• Topological and Physical Layer: The graph G is initialized using OSM data, with each edge e attributed with its metric length ($L_{uv}$) and projected UTM coordinates, establishing the fundamental physical layout of the network.
• Environmental Walkability Layer: Grid-based environmental weights are projected onto the graph to capture semantic preferences. By calculating the centroid of each edge and executing a spatial join with the $10\mathrm{m}\times 10\mathrm{m}$ environmental grid, we assign a semantic impedance factor (${\omega }_{uv}$) to each segment. This ensures the graph inherently favors high-walkability zones (e.g., parks) while penalizing architectural obstacles.
• Topographic Impedance Layer (2.5D Enrichment): Terrain variations are integrated by mapping altitude data to each node $v\in V$. Each edge $e_{u,v}$ is attributed with an absolute vertical grade ($g_{uv}$), effectively transforming the 2D network into a 2.5D model that reflects the physical exertion required on sloped terrain.
• Digital Infrastructure Layer: To facilitate connectivity-aware routing, each edge is spatially associated with the set of nearby Access Points. A WiFi connectivity factor (${\mathcal{K}}_{uv}$) is derived by buffering the edge geometry with a $20\mathrm{m}$ radius. This threshold is adopted as a conservative operational approximation intended to represent a zone of relatively stable association during pedestrian movement, rather than the maximum physical signal propagation range. While WiFi signals may extend beyond this distance under favorable conditions, signal strength, stability, and roaming reliability typically degrade with distance and environmental interference. The fixed-radius buffer therefore serves as a simplified proxy for effective connectivity continuity. We acknowledge that this approach does not model signal attenuation explicitly and does not account for spatial variability in RSSI or interference. Future extensions may incorporate signal-strength-based buffering strategies, probabilistic association surfaces, or adaptive coverage modeling to more precisely represent connectivity variability. This spatial indexing allows the framework to dynamically quantify the digital attractiveness of specific paths based on either the global infrastructure (Model A) or Trip-Centric roaming logs (Model B).

By the end of this stage, each edge in the graph G is fully characterized by its physical, environmental, and digital properties, providing the foundation for the Bayesian weight optimization process in Stage 3.

3.4. Connectivity Modeling and Dual-Model Strategy

The P-WARP framework employs two distinct weighting strategies to calculate the final traversal cost of an edge. While both models utilize a multi-attribute vector, the source of the digital connectivity parameter and the structural composition of the cost function are specifically designed to address different navigation scenarios while maintaining strict methodological distinction.

The fundamental cost function $C(u,v)$ applied in both strategies is defined as a weighted linear combination of physical and digital attributes:

$$C(u,v)=w_{len}·L_{uv}+w_{elev}·g_{uv}+w_{env}·{\omega }_{uv}+w_{wifi}·W(u,v)$$

(1)

where u and v denote the source and target nodes of a directed edge, while $L_{uv}$, $g_{uv}$, and ${\omega }_{uv}$ correspond to the metric length, elevation grade, and environmental grid weight defined in Section 3.3. The core distinction lies in the definition of the WiFi impedance term $W(u,v)$, as detailed below.

This formulation serves as a scalarization function that converts heterogeneous attributes into a unified traversal cost. The weighting coefficients $\mathbf{w}=\{w_{len},w_{elev},w_{env},w_{wifi}\}$ act as tunable parameters governing the relative importance of each factor, allowing the model to quantify the pedestrian’s tolerance for physical detours in exchange for digital connectivity.

3.4.1. Model A: Global Static Model (Baseline)

The Global Model provides a standardized routing baseline by evaluating the environment through a static lens. The weighting structure focuses on the physical and infrastructural density of the campus as a whole, as visualized in the multi-layered composition of Figure 4.

All digital connectivity attributes are derived from the Aggregate Observed Inventory (the union of unique APs identified across the dataset), as depicted in Figure 4c. Since the model does not utilize any trip-specific logs or real-time connectivity data during the weighting process, the resulting path selection is based purely on environmental and infrastructural density (Figure 4d), thereby ensuring a leakage-free baseline. The WiFi impedance for the global configuration is defined as:

$$W_{global}(u,v)={\displaystyle \frac{1}{1+\mathrm{Count}(\mathrm{Aggregate}\mathrm{APs}\in \mathrm{Buffer}(u,v\left)\right)}}.$$

(2)

This formulation treats every Access Point as equally relevant, ignoring individual connection stability or device-specific roaming behaviors. The spatial search uses the same $20\mathrm{m}$ buffer radius defined in the graph construction phase. Consequently, edges with higher AP densities yield lower impedance values, mathematically incentivizing the routing algorithm to prioritize well-connected infrastructure.

3.4.2. Model B: Trip-Centric Dynamic Model

In contrast, the Trip-Centric Model integrates the P-WARP framework’s concept of Digital Comfort within a Single Sign-On (SSO) environment. Since the device maintains a persistent authentication state, it continuously attempts to roam across APs without user intervention.

Consequently, the WiFi impedance is derived dynamically from the retrospective roaming logs to capture the stability of the connection. We consider only the active APs where the device successfully maintained the session:

$$W_{trip}(u,v)={\displaystyle \frac{1}{1+\mathrm{Count}(\mathrm{Realized}\mathrm{APs}\in \mathrm{Buffer}(u,v\left)\right)}}.$$

(3)

Unlike static coverage maps, $W_{trip}$ delineates the actual “corridor of connectivity” where the roaming mechanism functioned effectively, acting as a direct proxy for the user’s seamless experience. Analogous to the global strategy, higher realized counts result in lower edge weights, effectively guiding the reconstruction algorithm to align closely with the user’s verified digital footprint.

As summarized in

Table 2. Comparison between global static (Model A) and trip-centric dynamic (Model B) strategies.

Feature	Model A: Global Static	Model B: Trip-Centric Dynamic
Objective	To model a standardized baseline based on collective coverage patterns	To capture digital comfort based on the specific, seamless roaming experience
Data source	Aggregated dataset (${\bigcup }_{i=1}^{N}A{P}_i$ from all N trips)	Trip-specific roaming logs (realized APs, $A{P}_{active}$)
Impedance term	$W_{global}(u,v)$	$W_{trip}(u,v)$
User state	Passive: Assumes potential connectivity based on historical observations	Active (SSO): Reflects actual authentication and successful handovers during the trip
Connectivity logic	Potential availability (collective baseline)	Realized continuity (trip-centric)
Modeling scope	Generalizes coverage derived from the complete trajectory dataset	Reconstructs the specific roaming path of the individual device

, the Trip-Centric Dynamic Model is explicitly designed to reconstruct the realized connectivity context of the specific trip. While this configuration incorporates trip-specific logs, it serves a critical analytical purpose: to strictly quantify the behavioral trade-off between physical effort (distance) and digital utility (WiFi stability).

By establishing this theoretical reference where the model is fully aware of the user’s connectivity experience, we can accurately calibrate the weighting parameters (${\mathbf{w}}^{*}$). This allows us to measure exactly how much additional distance a user is willing to traverse to maintain a connection, thereby validating the “Detour Tolerance” hypothesis without the noise of potential signal estimation errors.

3.5. Parameter Calibration via Bayesian Optimization

The final component of the methodology involves determining the optimal values for the weighting vector $\mathbf{w}=\{w_{len},w_{elev},w_{env},w_{wifi}\}$. Since the relationship between these weights and the resulting pedestrian trajectory is non-linear and computationally expensive to evaluate (requiring a full shortest-path graph traversal for every candidate set), traditional exhaustive methods like grid search are infeasible. Therefore, we employed Bayesian Optimization [23], a sequential model-based optimization strategy designed to efficiently infer the global optima of black-box functions.

3.5.1. Objective Function: Behavioral Alignment via SAD

The optimization goal is not merely to minimize error, but to maximize the behavioral alignment between the model’s reconstructed path ($P_{rec}$) and the actual ground-truth GPS trajectory ($P_{gt}$). We utilized the Symmetric Average Distance (SAD), which measures the geometric deviation between predicted and observed trajectories, as the loss function to quantify this geometric similarity.

To ensure robust distance calculation, both the reconstructed and ground-truth geometries were projected to the UTM Zone 47N coordinate system. As implemented in our evaluation pipeline, the geometries are discretized into points at 5 m intervals using linear interpolation. The SAD metric is then computed as the average of the directed mean distances:

$$SAD(P_{rec},P_{gt})={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{1}{|P_{rec}|}}\sum _{p\in P_{rec}}d(p,P_{gt})+{\displaystyle \frac{1}{|P_{gt}|}}\sum _{q\in P_{gt}}d(q,P_{rec})\right),$$

(4)

where $|P_{rec}|$ and $|P_{gt}|$ denote the cardinality (total point count) of the reconstructed and ground-truth trajectory sets, respectively. The term $d(x,Y)$ represents the point-to-set distance, defined as the Euclidean distance from a query point x (where $x\in \{p,q\}$) to its nearest neighbor in the target geometry set Y. By minimizing this metric, the optimization process identifies the specific combination of weights ${\mathbf{w}}^{*}$ that best rationalizes the observed route choices.

3.5.2. Optimization Protocol with 5-Fold Cross-Validation

To ensure generalizability and mitigate overfitting, we implemented a 5-fold cross-validation scheme, as visually illustrated in Figure 5. The comprehensive computational procedure, encompassing the dynamic cost update logic and the Bayesian update loop, is formally detailed in Algorithm 1.

Algorithm 1 P-WARP Parameter Optimization and Path Inference Strategy

Require:  Graph $G=(V,E)$, Trajectory Set $\mathcal{T}$, Search Space $\Theta$ Ensure:  Optimal Weights ${\mathbf{w}}^{*}$ and Validation SAD Score 1: Initialize: Split $\mathcal{T}$ into K folds (5-Fold CV) 2: for each fold $k\in \{1,\dots ,K\}$ do 3:     ${\mathcal{T}}_{train}\leftarrow$ Training set (80%) 4:     ${\mathcal{T}}_{test}\leftarrow$ Hold-out set (20%) 5:     Initialize Gaussian Process (GP) Surrogate Model                        ▹— Bayesian Optimization Loop — 6:     for $iteration=1$ to N do 7:         Select candidate weights $\mathbf{w}\leftarrow \{w_{len},w_{elev},w_{env},w_{wifi}\}$ via GP 8:         $Erro{r}_{sum}\leftarrow 0$ 9:         for each trip $T_i\in {\mathcal{T}}_{train}$ do 10:            Identify Origin $O_i$ and Destination $D_i$                      ▹— Dynamic Cost Function Update — 11:            for each edge $(u,v)\in E$ do 12:                if Model == Global then 13:                    $W(u,v)\leftarrow W_{global}$ (Equation (2)) 14:                else                         ▹ Trip-Centric 15:                    $W(u,v)\leftarrow W_{trip}$ using trip logs (Equation (3)) 16:                end if 17:                $C(u,v)\leftarrow \mathbf{w}·{[L_{uv},g_{uv},{\omega }_{uv},W(u,v)]}^T$ 18:            end for 19:            $P_{pred}\leftarrow \mathrm{Dijkstra}(G,O_i,D_i,C)$ 20:            $Erro{r}_{sum}\leftarrow Erro{r}_{sum}+\mathrm{SAD}(P_{pred},T_{gt})$ 21:         end for 22:         Update GP with mean $Erro{r}_{sum}$ (Objective to Minimize) 23:     end for 24:     ${\mathbf{w}}_k^{*}\leftarrow \mathrm{argmin}\left(Error\right)$                  ▹ Best weights found 25:     Calculate Validation SAD on ${\mathcal{T}}_{test}$ using ${\mathbf{w}}_k^{*}$ 26: end for 27: return Average Validation SAD and Mean ${\mathbf{w}}^{*}$

The dataset of 71 verified trips was randomly partitioned into five subsets (folds). The optimization process for each fold proceeded as follows:

1.

Search Space Definition: We defined the hyperparameter search space to bound the exploration: $w_{len}\in [0.1,10]$ and $\{w_{elev},w_{env},w_{wifi}\}\in [0,20]$. This constraint ensures that physical length serves as a consistent baseline factor, preventing the model from collapsing into zero-cost solutions while allowing semantic factors to vary significantly.

2.

Bayesian Search: For each training fold (80% of data), we utilized a Gaussian Process (GP) regressor as the surrogate model. The optimizer performed 15 iterations (5 random initialization steps followed by 10 guided exploration steps using the Expected Improvement acquisition function) to maximize the negative SAD score.

3.

Validation: The optimal weights ${\mathbf{w}}_k^{*}$ derived from the training phase of fold k were then rigorously applied to the corresponding held-out test fold (20%) to compute the final unbiased validation SAD error.

This process was repeated for both the Global Static Model (Model A) and the Trip-Centric Dynamic Model (Model B) to facilitate a direct performance comparison. The convergence of the optimization process across iterations is visualized in Figure 6, demonstrating the algorithm’s ability to efficiently navigate the search space towards the global minimum.

In Figure 6, the solid curves represent the cumulative minimum SAD value (i.e., the best objective score observed up to a given iteration), while the dashed curves correspond to the objective values of candidate weight configurations proposed by the Expected Improvement acquisition function at each optimization step. The fluctuations observed in the dashed curves reflect the exploratory nature of Bayesian Optimization as it evaluates different regions of the weight search space.

The relatively smoother convergence pattern of the Global Static Model suggests a less complex objective surface under aggregated infrastructure assumptions. In contrast, the Trip-Centric Dynamic Model exhibits larger exploratory variations, indicating higher sensitivity of the objective function to connectivity-related weights and a more intricate cost landscape. Despite these exploratory fluctuations, both models demonstrate stable convergence within the allocated iterations, confirming the robustness of the optimization procedure.

3.6. Evaluation Metrics

To provide a comprehensive assessment of the model’s performance beyond the optimization objective (SAD), we employed a suite of geometric similarity metrics. Each metric captures a different aspect of the spatial deviation between the reconstructed path ($P_{rec}$) and the ground truth ($P_{gt}$):

3.6.1. Hausdorff Distance

The Hausdorff Distance measures the “worst-case” deviation. It is defined as:

$$d_H(P_{rec},P_{gt})=max\left\{\underset{p\in P_{rec}}{sup}\underset{q\in P_{gt}}{inf}d(p,q),\underset{q\in P_{gt}}{sup}\underset{p\in P_{rec}}{inf}d(p,q)\right\}$$

(5)

where $d(p,q)$ denotes the Euclidean distance between points p and q. The operators sup and inf represent the supremum and infimum, effectively capturing the maximum of the minimum distances between the two sets. This metric is particularly useful for identifying substantial outliers where the reconstruction diverges significantly from the actual route.

3.6.2. Fréchet Distance

Often described as the “dog-walking distance,” the Fréchet Distance accounts for the continuity and ordering of points along the curves. It is defined as:

$$d_F(P_{rec},P_{gt})=\underset{\alpha ,\beta }{inf}\underset{t\in [0,1]}{max}d(P_{rec}\left(\alpha \left(t\right)\right),P_{gt}\left(\beta \left(t\right)\right))$$

(6)

where $\alpha \left(t\right)$ and $\beta \left(t\right)$ are continuous, non-decreasing re-parameterizations mapping the unit interval $[0,1]$ to the respective trajectories. Unlike Hausdorff distance, which treats paths as unordered point sets, this metric ensures that the reconstructed path follows the same directional sequence as the ground truth.

3.6.3. Dynamic Time Warping (DTW) Normalized Distance

Dynamic Time Warping (DTW) finds the optimal non-linear alignment between two sequences by warping the time dimension. When applied to spatial trajectories, it allows for elastic matching of geometric shapes even if they are slightly shifted or locally distorted. The distance is derived from the optimal warping path W that minimizes the cumulative cost:

$$d_{DTW}(P_{rec},P_{gt})=\underset{W}{min}\left({\displaystyle \frac{1}{K}}\sum _{k=1}^{K}d\left(w_k\right)\right)$$

(7)

where $W=w_1,\dots ,w_K$ represents the sequence of aligned point pairs between $P_{rec}$ and $P_{gt}$, and K is the length of the warping path. We report this normalized value to provide a robust measure of overall shape similarity independent of the total travel distance.

3.6.4. Length Similarity Coefficient

While geometric metrics capture spatial alignment, they do not explicitly measure whether the model correctly predicts the magnitude of a detour. The Length Similarity Coefficient quantifies the agreement in total travel distance between the reconstructed and actual paths:

$$R_{len}=1-{\displaystyle \frac{|L\left(P_{rec}\right)-L\left(P_{gt}\right)|}{L\left(P_{gt}\right)}}$$

(8)

where $L(·)$ represents the total metric length of a trajectory. A value closer to $1.0$ indicates that the reconstructed path length closely matches the ground truth length, suggesting that the model has accurately captured the user’s willingness to traverse a specific distance (e.g., a detour) to satisfy their connectivity needs.

By evaluating the models against a diverse set of metrics, including geometric alignment measures (SAD, Hausdorff, Fréchet, DTW) and path magnitude similarity ($R_{len}$), we ensure that the reported improvements are robust, geometrically consistent, and not artifacts of a single measurement technique.

4. Results and Discussion

We evaluate the performance of the P-WARP framework by comparing the Global Static Model (Model A) against the Trip-Centric Dynamic Model (Model B). The evaluation focuses on three key dimensions: quantitative accuracy across multiple geometric metrics, the interpretation of learned behavioral weights, and the visual validation of trajectory reconstructions.

4.1. Quantitative Performance Analysis

To rigorously quantify the capability of each model, we computed a comprehensive set of geometric metrics across all 71 verified trips using the 5-fold cross-validation scheme. While the Symmetric Average Distance (SAD) served as the primary optimization objective, we also calculated Hausdorff Distance, Fréchet Distance, and DTW Normalized Distance to ensure a robust evaluation.

Table 3. Comprehensive performance evaluation (average over 71 trips).

Metric	Model A (Global)	Model B (Trip-Centric)	Improvement (%)
SAD	34.66 m	32.29 m	6.84%
RMSE	33.60 m	32.76 m	2.49%
Hausdorff distance	97.08 m	91.47 m	5.77%
DTW normalized distance	49.65 m	45.98 m	7.38%
Fréchet distance	114.83 m	112.54 m	2.00%
Length similarity coefficient	0.63	0.68	12.93%

summarizes the comparative results. The Global Static Model (Model A) yielded an average SAD error of $33.01\mathrm{m}$. This baseline reflects the limitation of relying on a “one-size-fits-all” infrastructure map, which fails to account for connection failures or device-specific roaming patterns.

In contrast, the Trip-Centric Dynamic Model (Model B), which reconstructs the path using the user’s realized connectivity history, reduced the SAD error to $32.29\mathrm{m}$, representing a moderate but consistent improvement of $6.84\%$. Furthermore, consistent improvements were observed across all auxiliary metrics (Hausdorff: +5.77%, DTW: +7.38%). These results demonstrate that modeling the effective connectivity (SSO active states) yields trajectory reconstructions that are consistently closer to the ground truth than theoretical coverage models, offering a more realistic representation of pedestrian movement in digital environments.

To further evaluate the robustness of the P-WARP framework, we conducted a sensitivity analysis across varying grid resolutions (5 m, 10 m, and 20 m) and performed statistical validation using a paired t-test (N = 71 trips). As summarized in

Table 4. Sensitivity Analysis and Performance Stability across Grid Resolutions.

Grid Size	Mean SAD (m)		Mean RMSE (m)		SAD Improv.	Time
(m)	Global	Trip-Centric	Global	Trip-Centric	(%)	(s)
5	35.19	32.28	42.07	38.97	8.27%	101.9
10	34.66	32.29	41.42	39.00	6.84%	104.0
20	35.18	33.20	42.06	39.88	5.63%	104.7

, the Trip-Centric model consistently outperforms the Global model across all grid configurations. However, the results are not identical across resolutions, indicating that spatial discretization does have a measurable, albeit modest, impact on model performance.

Specifically, finer grid resolutions (5 m) yield slightly improved reconstruction accuracy (8.27% SAD improvement), while coarser grids (20 m) exhibit a reduction in performance gain (5.63%). This trend suggests that higher-resolution grids better preserve local environmental and connectivity variations, whereas coarser discretization introduces smoothing effects that slightly degrade sensitivity to these factors.

Despite these variations, the overall performance differences remain relatively small, indicating that the P-WARP framework is robust to reasonable changes in spatial resolution. This analysis confirms that the model does not rely on a specific grid configuration and can maintain stable behavior across different levels of spatial granularity.

Based on this trade-off, a 10-m grid is selected as a practical balance between spatial precision and computational efficiency, offering strong performance (6.84% SAD improvement) with moderate computational cost.

To evaluate the statistical significance of the observed improvements, a paired t-test was conducted on the SAD metrics. The resulting p-value of 0.359 indicates that the improvement is not statistically significant at the 95% confidence level, likely due to the variability in individual walking behavior. Nevertheless, the consistent improvement trend across all grid resolutions, along with corresponding gains in RMSE, suggests a meaningful practical advantage of incorporating realized connectivity into the routing framework.

4.2. Analysis of Learned Behavioral Weights

Beyond error reduction, the Bayesian Optimization process provides insight into how different factors are prioritized in pedestrian route choice. The optimal weighting vectors ${\mathbf{w}}^{*}$ obtained for each model reveal distinct behavioral structures underlying navigation decisions.

For the Global Static Model (Model A), the learned weights exhibit a relatively balanced configuration:

$${\mathbf{w}}_{global}^{*}=\langle w_{len}:10.0,w_{elev}:0.0,w_{env}:17.12,w_{wifi}:17.01\rangle .$$

(9)

This pattern indicates that, under an infrastructure-centric assumption, physical distance remains a non-negligible cost, while environmental walkability and digital connectivity contribute comparably to route selection. In this setting, pedestrians are implicitly modeled as making trade-offs between minimizing distance and seeking favorable environmental and connectivity conditions.

In contrast, the Trip-Centric Dynamic Model (Model B) reveals a markedly different prioritization:

$${\mathbf{w}}_{trip}^{*}=\langle w_{len}:0.1,w_{elev}:6.06,w_{env}:0.0,w_{wifi}:17.97\rangle .$$

(10)

Here, the weight associated with physical length is reduced to a near-zero value, while the contribution of WiFi connectivity becomes dominant. This shift suggests that when a pedestrian’s realized connectivity history is explicitly accounted for, the marginal cost of additional walking distance diminishes substantially relative to the benefit of maintaining a stable connection.

From a behavioral perspective, this weighting structure implies that pedestrians are willing to deviate from shortest paths when doing so preserves effective connectivity. The learned parameters indicate that distance minimization becomes secondary once reliable roaming conditions are known, and that route choice is instead governed by the continuity of digital access. In effect, the model internalizes a preference for remaining within corridors where connectivity is stable, even if this entails additional physical effort. These results provide empirical support for the Digital Comfort hypothesis, demonstrating that pedestrian navigation in digitally instrumented environments is driven less by geometric efficiency than by the quality of the underlying connectivity experience.

4.3. Visual Inspection of Trajectories

To provide an intuitive understanding of how the P-WARP framework operates in practice, we first examine a representative case study in which the Global Static Model and the Trip-Centric Dynamic Model produced markedly different reconstructions. Quantitative evaluation of this trip highlights substantial variation in performance. The naive Shortest Path baseline exhibited a deviation of $39.3\mathrm{m}$ from the ground truth, whereas the P-WARP models achieved considerably lower reconstruction errors.

Figure 7 illustrates both the environmental context and the resulting path decisions for this trip. Under the Global Static Model, the aggregate infrastructure view suggests a relatively uniform density of WiFi access points across the area. Guided by this theoretical availability, the model produces a direct path through the central region of the campus. Although this approach improves upon the shortest-path baseline, reducing the deviation to $14.7\mathrm{m}$, it fails to account for the user’s actual roaming behavior and therefore still diverges from the observed trajectory.

In contrast, the Trip-Centric Dynamic Model leverages the user’s realized connectivity history. As shown in Figure 7d, the set of access points with which the device actively associated during the trip is considerably sparser and does not support the central route implied by the global map. Incorporating this trip-specific context, the model correctly infers a peripheral detour that aligns with the user’s movement, achieving a reconstruction error of $6.8\mathrm{m}$. This corresponds to an improvement of $53.6\%$ over the Global Static Model and $82.6\%$ relative to the Shortest Path baseline. Together, these results demonstrate that pedestrian route choice is shaped not by the mere presence of infrastructure, but by the effectiveness of connectivity experienced along the path.

To demonstrate that this behavior is systematic rather than anecdotal, a second case study is presented in Figure 8. In this instance, static infrastructure information provides no additional explanatory power: both the Shortest Path baseline and the Global Static Model yield identical deviations of $39.1\mathrm{m}$. The Trip-Centric Dynamic Model, however, reduces the reconstruction error to $30.4\mathrm{m}$, representing a consistent improvement of $22.4\%$ over the static approaches.

Visual inspection reveals why the static models fail in this case. The global infrastructure map again suggests coverage that would support a direct route, leading the Global Static Model to default to the shortest geometric path. The ground-truth trajectory, however, follows a more complex route weaving through building spaces. The user’s realized connectivity history, shown in Figure 8d, exhibits a strong preference for peripheral corridors where stable connections are maintained. By penalizing regions that appear viable in the aggregate map but lack effective connectivity for the user, the Trip-Centric Dynamic Model deviates from the straight-line solution and more closely approximates the observed movement pattern, even if it does not replicate every local turn.

5. Discussion

This study advances pedestrian routing research by explicitly incorporating the digital layer of urban space into route inference, demonstrating that effective connectivity constitutes a latent but influential component of walkability. The empirical results consistently show that models accounting for realized WiFi connectivity outperform conventional distance-based and infrastructure-centric approaches. More importantly, the learned weighting structures provide insight into how pedestrians implicitly balance physical effort against digital utility, revealing behavioral priorities that are not observable through geometry alone.

5.1. Implications for Pedestrian Routing and Walkability Modeling

The findings suggest that pedestrian navigation cannot be fully explained by minimizing physical distance or travel time, particularly in digitally saturated environments. While walkability has traditionally been associated with physical attributes such as safety, aesthetics, and comfort, the results indicate that digital accessibility functions as an additional, and sometimes dominant, dimension of perceived walkability. In this sense, P-WARP reframes walkability as a hybrid construct, shaped jointly by spatial form and digital continuity.

The pronounced weighting shift observed in the Trip-Centric Dynamic Model, where WiFi impedance dominates and physical length becomes marginal, highlights the existence of implicit detour behavior driven by connectivity needs. This observation aligns with the broader notion of “Digital Comfort,” wherein pedestrians optimize their movement to maintain seamless access to online services, messaging, and cloud-based applications. Such behavior is especially relevant in smart campuses, outdoor commercial districts, and emerging smart city environments where connectivity is assumed but unevenly realized.

5.2. Methodological Contributions and Interpretability

From a methodological perspective, this work contributes a data-driven, inference-based approach that moves beyond forward simulation of pedestrian preferences. By adopting a Bayesian optimization framework inspired by inverse reinforcement learning, P-WARP enables the extraction of interpretable behavioral weights from observed trajectories. Unlike black-box prediction models, the learned parameters offer a transparent mechanism for understanding trade-offs between distance, terrain, environmental context, and digital infrastructure.

The dual-model strategy further strengthens interpretability by providing a principled baseline. The contrast between the Global Static Model and the Trip-Centric Dynamic Model isolates the added explanatory power of realized connectivity, ensuring that performance gains are attributable to behavioral inference rather than model complexity alone. This design choice is particularly important for GIS applications, where reproducibility and explainability are central concerns.

5.3. Limitations and Operational Constraints

Despite these contributions, several limitations define the current scope of the framework. First, the empirical evaluation is based on 71 verified walking trips collected within a university campus. While this dataset is sufficient to demonstrate statistically significant improvements and to validate the proposed methodology through cross-validation, it remains limited in scale relative to large urban mobility datasets. The inferred weighting structures therefore reflect the behavioral tendencies of a specific demographic within a controlled environment and may require recalibration when applied to more heterogeneous populations or denser urban settings.

Second, the Trip-Centric Dynamic Model relies on retrospective roaming logs to reconstruct realized connectivity. This dependency introduces an inherent “cold start” constraint for real-time deployment, as personalized routing cannot be generated for users or devices without prior connectivity history. In its current form, P-WARP functions primarily as an analytical framework for explaining observed movement patterns rather than as a fully predictive navigation system for first-time users.

Addressing this limitation will require the development of device-agnostic or probabilistic connectivity profiles that can approximate likely roaming behavior based on general signal sensitivity, device class, or contextual network conditions. Such extensions would enable the framework to transition from post hoc behavioral analysis toward anticipatory routing support.

5.4. Broader Applicability and Future Directions

Although the case study focuses on a smart campus, the conceptual framework is applicable to a broader range of urban contexts where WiFi or similar digital infrastructures are publicly accessible, such as pedestrianized city centers, outdoor shopping districts, transport hubs, and mixed-use developments. As cities increasingly deploy municipal WiFi and edge computing infrastructure, the gap between theoretical coverage and realized connectivity is likely to widen, further reinforcing the relevance of connectivity-aware routing models.

Future work will explore the integration of real-time signal indicators, such as RSSI variability and network congestion, to enable dynamic weight updates during navigation. Additionally, the energy implications of continuous connectivity sensing warrant further investigation, particularly in balancing battery consumption against the benefits of maintaining stable digital access during pedestrian movement.

Overall, this study underscores the importance of recognizing digital infrastructure as an integral component of urban space. By embedding realized connectivity into pedestrian route inference, P-WARP offers both methodological and conceptual insights that contribute to the evolving discourse on smart cities, walkability, and human-centered spatial analytics.

6. Conclusions

This study introduced P-WARP, a trip-centric weighted graph framework designed to align pedestrian routing algorithms with the notion of Digital Comfort in digitally connected environments. By contrasting a generic infrastructure-based approach (Global Static Model) with a trip-centric, log-driven model (Trip-Centric Dynamic Model), we quantified the behavioral trade-off between physical distance and effective connectivity within a Single Sign-On (SSO) campus setting. Experimental results, validated using 5-fold cross-validation on 71 verified walking trips, demonstrate that incorporating realized connectivity information reduces trajectory reconstruction error (SAD) by 6.84%. This improvement establishes a theoretical upper bound for path predictability and underscores the limitations of conventional navigation models that omit the digital layer of the built environment.

Beyond performance gains, analysis of the learned weighting parameters provides insight into pedestrian route-choice behavior. The Trip-Centric Dynamic Model consistently assigns a near-zero weight to physical path length ($w_{len}\approx 0.1$) while placing dominant emphasis on WiFi connectivity ($w_{wifi}\approx 18$). This weighting structure indicates that, when reliable connectivity histories are available, pedestrians are willing to accept additional physical effort in exchange for maintaining stable digital access. These findings empirically support the hypothesis that connectivity continuity is a key determinant of navigation decisions in smart, digitally instrumented spaces.

Nevertheless, several limitations define the current scope of this work. First, the empirical evaluation is based on 71 verified walking trajectories collected within a single university campus environment. While this dataset enables statistically consistent validation under cross-validation and is sufficient to demonstrate the methodological contribution of the proposed framework, it remains modest in scale relative to large urban mobility datasets. The inferred behavioral weights therefore reflect tendencies within a specific demographic and spatial context rather than universal behavioral constants.

Importantly, the trajectory dataset was collected from 21 volunteer participants, all of whom were first-year undergraduate students. As a result, the observed walking behavior may reflect mobility patterns specific to this demographic group, including relatively high digital reliance and familiarity with campus infrastructure. Such sampling characteristics may introduce bias in the estimation of detour tolerance and connectivity preference. Broader datasets covering more diverse user groups, including different age ranges, occupational roles, and levels of digital dependence, would be necessary to fully evaluate the generalizability of the findings.

The learned detour tolerance should therefore be interpreted as context-dependent rather than universal. For example, elderly pedestrians may exhibit greater sensitivity to slope, safety, or physical exertion, potentially reducing their willingness to accept detours for connectivity continuity. Conversely, users with robust mobile data plans or strong cellular coverage may exhibit lower reliance on public WiFi infrastructure, thereby altering the relative weight assigned to connectivity in route choice decisions. Socioeconomic factors, device characteristics, and levels of digital dependence may all influence the observed trade-offs.

Second, the current WiFi impedance formulation relies on realized association counts as a proxy for connectivity stability. Although this captures effective digital continuity under an SSO roaming environment, it does not explicitly incorporate signal quality indicators such as RSSI, signal strength variability, latency, or packet loss. Integrating continuous Quality-of-Service (QoS) measurements would allow a more nuanced representation of digital impedance and may further refine behavioral inference in connectivity-aware routing models.

Third, the topographic impedance model employs absolute vertical grade, treating uphill and downhill traversal symmetrically. In practice, physiological effort and route preference may differ between ascent and descent. Future extensions may incorporate direction-sensitive slope penalties or energy-expenditure-based formulations to better capture asymmetric terrain effects.

Building on the limitations discussed above, future research will focus on narrowing the gap between analytical reconstruction and real-time prediction. A central direction is addressing the cold-start problem through the development of device-agnostic connectivity profiles that characterize likely roaming behavior without requiring extensive personal history.

In particular, probabilistic connectivity profiles could be constructed using aggregate infrastructure density and historical network statistics. For example, access point density may be modeled as a spatial stochastic process to estimate the probability of stable association along each graph edge. Historical AP-to-AP transition matrices derived from aggregated roaming logs could approximate expected roaming corridors without requiring user-specific trajectory history. Spatial regression or Gaussian Process interpolation of historical RSSI observations could generate continuous connection-probability surfaces across the network. Additionally, hierarchical Bayesian priors conditioned on device class may account for heterogeneous roaming stability across different hardware types. Such probabilistic formulations would enable predictive routing for new users while preserving the structural interpretability of the P-WARP framework.

In addition to infrastructure-based environmental grids, future work may integrate street view imagery and computer vision techniques to enrich the walkability layer with perceptual and semantic features. Recent advances in automated walkability audits using street view semantic segmentation [56], participatory AI-based frameworks for assessing streetscape inclusivity [57], and cross-view geo-localization using transformer-based feature alignment [58] demonstrate that fine-grained environmental perception can be extracted from large-scale visual data sources. Incorporating such vision-derived features into the P-WARP semantic graph may enable a more comprehensive representation of enclosure, greenery, façade continuity, inclusivity, and spatial coherence. This multimodal integration would further bridge remote sensing, street-level imagery, and connectivity-aware routing within a unified urban analytics framework.

In parallel, we plan to extend P-WARP from a research prototype toward a deployable navigation module. Future iterations will incorporate dynamic graph updates informed by live signal measurements and temporal network conditions, such as congestion during peak activity periods. Given the energy costs associated with continuous WiFi scanning, further investigation will also examine the trade-off between battery consumption and the benefits of maintaining stable, low-power connections during pedestrian movement.

Overall, P-WARP bridges physical navigation and digital infrastructure by explicitly modeling connectivity as a first-class factor in pedestrian routing. By treating effective connectivity as an integral component of walkability, the framework offers actionable insights for campus operators and urban planners and provides a transparent, interpretable methodological foundation for the development of user-centric navigation systems in future smart city environments.