arXiv subjects

Karim Ismail

Publications and source records attributed to Karim Ismail.

3 recordsLinked to original sources

arXiv2026

Q-SCM: A Quantum-Sequential Choice Model for Driver Mental State Evolution

We propose a Quantum-Sequential Choice Model (Q-SCM) for modelling driver mental state evolution in interactive traffic environments. The proposed framework retains the classical latent class choice structure, but replaces the conventional class membership formulation with a quantum cognitive state model. A unique feature of this model is that the quantum component is confined to the class membership layer, while the action choice layer remains a classical RUM. The driver's latent state is represented as a two-state quantum system on the Bloch sphere including neutral and defensive states. Perceptual cues, including separation distance, closing time-to-collision (CTTC), and lane deviation induce sequential unitary rotations governed by Pauli matrices. This formulation allows the model to capture memory, phase effects, cue order dependence, and transitions between behavioural regimes that depend on prior cue history. To ensure well-behaved state evolution, we introduce three control mechanisms: a monotonicity constraint that prevents pendulum-like overshoot, a geodesic safeguard mechanism that ensures convergence toward the defensive state under sustained threat exposure, and a relaxation step that allows recovery toward the neutral baseline when the threat weakens. The model is estimated using 85,754 observations from 9,610 drivers extracted from naturalistic trajectories. The empirical results show that defensive state formation is not governed only by the instantaneous values of traffic cues, but also by the accumulated cue history and the order in which cues are processed.

econ.EM↗

arXiv2025

Latent Class Logit Kernel Framework for Surrogate Safety: Identifying Behavioural Thresholds through Conflict Indicator Profiles

Crash data objectively characterize road safety but are rare and often unsuitable for proactive safety management. Traffic conflict indicators such as time-to-collision (TTC) provide continuous measures of collision proximity but require thresholds to distinguish routine from safety-critical interactions. Extreme Value Theory (EVT) offers statistically defined thresholds, yet these do not necessarily represent how drivers perceive and respond to conflict. This study introduces a behavioural modelling framework that identifies candidate behavioural thresholds (CBTs) by explicitly modelling how drivers adjust their movements under conflict conditions. The framework is based on a Latent Class Logit Kernel (LC-LK) model that captures inter-class heterogeneity (routine vs. defensive driving) and intra-class correlation between overlapping spatial alternatives. This yields probability curves showing how the likelihood of defensive manoeuvres varies with conflict indicators, from which CBTs such as inflection points and crossovers can be extracted. The framework tests four hypotheses: (1) drivers exhibit varying degrees of membership in both low- and high-risk classes; (2) membership shifts systematically with conflict values, revealing behavioural thresholds; (3) this relationship follows a logistic shape, with stable behaviour at safe levels and rapid transitions near critical points; and (4) even in free flow, drivers maintain a baseline caution level. Application to naturalistic roundabout trajectories revealed stable TTC thresholds (0.8-1.1 s) but unstable MTTC2 estimates (e.g., 34 s), suggesting cognitive limits in processing complex indicators. Overall, the framework complements EVT by offering a structured, behaviourally grounded method for identifying and validating thresholds in surrogate safety analysis.

physics.soc-ph↗

arXiv2025

Towards the Safety-Relevant Dimension of Driver Behaviour: A Dual-State Model

We make a methodological contribution by introducing a new dimension of traffic conflict severity: the probability that a driver is in a defensive state. This behavioural probability reflects an internal response to perceived risk and is estimated using a latent class Discrete Choice Model (DCM) that captures driver behaviour as a probabilistic mixture of two latent driving states: a defensive state, representing heightened caution and collision-avoidance intentions under perceived risk, and a neutral state, reflecting routine driving behaviour under low-threat conditions. The framework is grounded in psychological theory, particularly the triad of affect, behaviour, and cognition. It is also informed by two key concepts. First, that event severity exists on a continuum, rather than being confined to binary categories of safe or unsafe. Second, that drivers perceive risk through a dynamic spatial safety field, one that varies with direction, proximity, and the motion of surrounding road users. Applied to the publicly available rounD dataset, the framework yields interpretable estimates of state membership probabilities. The defensive state consistently reflects stronger sensitivity to spatial and temporal risk, while the neutral state captures context-appropriate yet less reactive driving patterns. Importantly, the paper also proposes a method to assess the quality of the estimated probability of being in a defensive state. Because of the duality between the defensive and neutral states, evaluating the consistency of one offers insights into the reliability of the other. To explore this, a multi-step validation procedure is applied across five data subsets representing different driving contexts, including free-flow and diverging scenarios, to examine how well the neutral state generalises beyond the estimation sample.

physics.soc-ph↗