The study proposes a mathematical framework to explain the stochastic behavioural patterns of personal mobility (PM) devices under low-carbon heterogeneous traffic conditions in shared lanes. We create a set of anticipation factors in a stochastic PM behaviour model to tackle sensitivities to both space headway and relative speed against intra- and inter-modes. The proposed behaviour model involves a deterministic and a stochastic force. In the deterministic force, the anticipation factors are used in an optimal velocity model and a full velocity difference model. In the stochastic force, the Langevin equation is used to capture PMs’ stochastic characteristics against movements of other PMs, pedestrians, and bicycles, and the effect of lateral interactions. We carried out real-world circular experiments of mixed sustainable modes to verify the performance of the proposed models. Five models’ performances are compared under four different traffic conditions, including bike-mixed, pedestrian-mixed, low-speed, and high-speed conditions. We confirmed that newly created anticipation factors play a significant role in all models under all conditions to partially influence the following PM devices’ behaviour from the leading two different sustainable modes. The validation results illustrate the excellence of the proposed method. Consequently, behavioural uncertainty is well captured by the stochastic PM devices following models under all traffic conditions, although it requires more parameters than the deterministic PM behavioural models. The proposed method paves the way for the stochastic CF model’s applicability to describe PM devices’ behavioural dynamics under mixed traffic conditions using anticipation factors. Besides, it lays the foundation stone of PM devices’ dynamics in a shared lane to construct effective regulations and safety standards.

该研究提出了一个数学框架来解释在共享车道的低碳异构交通条件下个人移动性（PM）设备的随机行为模式。我们在随机的PM行为模型中创建了一组预期因素，以解决对空间前进和相对速度的敏感度，以反对内部和内部模式。所提出的行为模型涉及确定性和随机作用力。在确定力中，将预期因子用于最佳速度模型和全速度差模型。在随机力中，Langevin方程用于捕获PM相对于其他PM，行人和自行车的运动以及横向相互作用的影响的随机特性。我们进行了混合可持续模式的真实世界循环实验，以验证所提出模型的性能。比较了五种车型在四种不同交通状况下的性能，包括自行车混合，行人混合，低速和高速情况。我们确认，新创建的预期因素在所有条件下的所有模型中均起着重要作用，从而部分地从领先的两种不同的可持续模式中影响了以下PM设备的行为。验证结果说明了所提出方法的优越性。因此，在所有交通情况下，随机PM设备遵循模型都可以很好地捕获行为不确定性，尽管与确定性PM行为模型相比，它需要更多的参数。所提出的方法为随机CF模型的应用铺平了道路，该模型可以使用预期因子来描述混合交通条件下PM设备的行为动态。此外，它为构建有效的法规和安全标准奠定了永磁设备动力学的基石。