# Notes on Bus User Assignment Problem Using Section Network Representation Method
## 2 Background
It may also manifest itself in lengthier wait times due to the bunching phenomena or the likelihood of full vehicles (i.e., being unable to board the first vehicle). The decrease in the nominal line headway is called the effective line headway and is used to account for the rise in wait times [1]. In [23], a novel model for crowded transit assignment is introduced, and it is founded on the hyper-path graph depiction that contains queuing models [24]. The stringent capacity of lines has also been addressed in transit assignment schemes. In [25], the same algorithm provided in [23] is modified to include stringent capabilities, while the main objective is to demonstrate the algorithm requirements for solution uniqueness and existence. The model minimized a newly designed gap function by using the method of successive averages (MSA). In [26], an alternative method for analyzing congestion is devised. The presented formulation included consumers' aversion to the possibility of missing the next ride. Failure to board links and nodes is added to each station's graph representation. The chance of failure to board is assigned based on the remaining capacity of the vehicle, and the line flows using Markov chains. In [27], the research of [26] is expanded by taking into account the availability of seats. In lieu of \"failure to board\", the phrase \"fail to sit\" was used to describe the route selection based on the pain of standing. All of the aforementioned models ignored the phenomenon of First-In-First-Out (FIFO) queuing, assuming that passengers mix at the stations. In [28], an FB-capacitated method is developed by taking the FIFO paradigm into consideration. The hyper-path graph is expanded to the dynamic situation, and the CLP is directly included in the path selection modeling. A bottleneck queue model with varying exit capacity over time is often used to represent congestion [29]. The concept allows users with various appealing sets to pass one another while waiting at a single stop. Due to the proliferation of internet travel information, non-equilibrium assignment models have recently been a popular area of study. This makes consumers more aware of the transport network's operating circumstances and suggests routes to take. In [30], a heuristic assignment methodology is suggested for determining the optimal system architecture. It tries to reduce transportation network congestion as a whole. In [31], a heuristic task is created to examine online information that might result in non-equilibrium line flows. The study in [31] is expanded in [32] to address the stringent capacity of lines. As an assessment tool, the evaluated transit assignment models have received minimal attention in the BNDP literature. In [33; 34; 35], a path-generating algorithm's set of path configurations is evaluated using the TRUST analysis process. TRUST employs basic principles to allocate demand across O/Ds in the network where similar trajectories are addressed differently. Even though they are longer, users prioritize direct paths (i.e., without transfers). The user is always supposed to take a group of paths within a certain span of the shortest route and has the least number of feasible transfers to reach his/her destination. Numerous studies, such as [36; 37; 38; 39], decided to follow the exact protocol: consumers would select the route set with the fewest feasible transfer numbers and then choose the first bus to arrive in that set. Similarly, references [40; 41; 42; 43; 44; 45] used all-or-nothing assignment algorithms to capture line flows in which each user is allocated the shortest way in total travel time. In [46; 47; 48; 49; 50; 51], when just in-vehicle periods are analyzed to establish served passengers' preferences, more lenient assumptions are utilized. They do not address waiting periods in their goal functions. In contrast, passenger assignment was performed in [52; 53] using multiple path assignments and the frequency-sharing approach. If accessible, it is believed that all customers would use no more than two lines.