## 1 Introduction
### Literature Review  
#### 1.2.1 Definitions of Circuity  
In previous research, quantitative studies on transportation efficiency have concentrated on the following three approaches: (1) analyzing the topology of the transportation network [22; 23; 24], which examines the overall network efficiency of information and transportation; (2) comparing the actual time spent with the theoretical minimum commuting time [25; 26], which focuses on the balance between job and housing locations or excessive commuting; and (3) investigating the geometric characteristics of the spatial network [27; 28], with circuity being a prominent area of study. The initial two studies focus on evaluating the effectiveness of transportation operations within urban areas and may not be entirely relevant when considering efficiency metrics on broader regional levels. In contrast, the latter approach is suitable for conducting studies on a larger scale.  
For a road or transit network, circuity is commonly described as the ratio between the network distance and Euclidean distance [18]. Network distance, whether representing the movement trajectories of people or goods, denotes the overall length of the physical route or the shortest path from the point of origin to the destination, within a specific transportation network. Euclidean distance refers to the direct distance between two points in the XY coordinate plane. Due to the extensive scope of the study, the great circle distance, upon which the network was constructed--an approximately spherical surface--proves to be more accurate than Euclidean distance [29]. Therefore, certain studies employ the great circle distance to quantify the level of indirectness in the transportation network.  
Circuity, as defined originally, pertains to the comprehension of networks based on spatial distance. As research progresses and the road network expands, the number of available travel routes between nodes increases. This leads to real-time updates of optimal routes, posing challenges in accurately determining the actual route length. However, this calculation method is not suitable for scenarios involving various modes of transportation in real traffic conditions. The phenomenon of equating the same value of circuitry to different traveling times, due to the utilization of various modes of transport, can lead to an erroneous assumption of uniform efficiency across networks with equivalent actual distances. The central concept underlying all traffic analyses is the aspiration to minimize travel time. The evaluation of a transportation system's worth is predominantly contingent on the benefits accrued by users through time saved during travel. This underscores the ongoing efforts to enhance technology for achieving higher traffic velocities and reduced travel distances [30]. Travel time is widely recognized as an intuitive indicator of a passenger's perception of distance impedance [31], with individuals showing a greater focus on travel time over distance [20]. [PERSON] [14] initiated experimentation regarding the ratio of the actual travel time to the theoretical minimum time, as a metric for circuity. However, the concept of theoretical minimum time has not been firmly established as a calculation method. However, it offers an efficient method to utilize travel time for studying the effectiveness of transportation networks.