# Traffic Demand Estimations Considering Route Trajectory Reconstruction in Congested Networks
## 1 Introduction  
With the accelerated development of urbanization in developing countries, such as China, car ownership has increased substantially, triggering a surge in urban traffic. It is difficult for limited traffic routes to meet the rapid growth in urban traffic demand, resulting in disordered and congested urban traffic. However, car ownership is not proportional to urban congestion. In other words, urban congestion can be alleviated through rational planning of urban road networks and effective formulation of traffic control policies.  
Origin-destination (OD) demand, which describes the distribution characteristics of traffic travel space, is an important input parameter for long-term urban traffic planning and short-term traffic management. OD demand is helpful in traffic network design (with respect to traffic bottleneck identification, road network capacity assessment, etc.) and traffic demand management (with respect to road congestion pricing, traffic control, etc.) in congested networks [1]. Therefore, accurately estimating OD demand can help ascertain traffic characteristics of current road networks, facilitating alleviation of traffic congestion in a more targeted and purposeful way during traffic planning and urban planning [2].  
In recent years, transportation scholars have increasingly focused on OD demand estimation [3], especially regarding new data sources, methods, and theories associated with the theoretical and practical research of transportation planning. Existing studies can be categorized as OD demand estimation for either non-congested or congested networks (depending on the application's scope) and as static or dynamic OD demand estimation (depending on whether time variations are considered). Maximum entropy theory has been employed to estimate traffic demand for non-congested networks based on observing link flow [4]. [PERSON] [5] further estimated OD demand based on the Bayesian method. [PERSON] [6] observed link flow and route flow at the same time, and estimated traffic demand using the maximum likelihood method. The Kalman filtering method has been dynamically used to predict the OD demand for rail transit [7]. Some scholars determined traffic demand based on the generalized least square method by observing information such as link flow, route flow, speed, and entrance lane flow at intersections [8; 9]. [PERSON] et al. used maximum entropy theory to estimate traffic demand on congested networks based on observing vehicle density at links [10]. Many scholars observed variables such as link flow, speed, and density to estimate traffic demand based on the generalized least square method [11; 12; 13]. Many OD demand estimation models use other theoretical frameworks, including OD demand estimation under supervised learning, sub-network OD demand estimation [14], OD demand estimation based on mobile phone location data [15], OD demand estimation based on bus card data [16], and multi-target OD demand estimation models [17].  
The main weaknesses of current OD demand estimation research are as follows. (1) Existing studies ignore congestion characteristics in the observed travel data of road networks of various types. (2) The existing traffic demand estimation literature usually only includes road traffic data location and time information for origin and destination, lacking route trajectory reconstruction research. (3) Although road detection equipment can monitor a large amount of route travel time data, the existing Bayesian traffic demand estimation method fails to integrate the route travel time. This paper further reconstructs route trajectory data and establishes a Bayesian traffic demand estimation model with route trajectory reconstruction in congested networks by analyzing the propagation mechanism of congested traffic parameters and transforming the multi-source observed variables to a uniform format. Next, an iterative algorithm designed to solve the model is presented. Finally, numerical experiments are employed to test the model and algorithm.