This paper offers an integrative behavioral-based physics-inspired approach to model and control traffic congestion in an efficient manner While existing physics-based approaches commonly assign density and traffic flow states with the Fundamental Diagram, this paper specifies the flow-density relation using past traffic behavior (intent) recorded over a time sliding window with constant horizon length. With this approach, traffic coordination trends can be consistently learned and incorporated into traffic planning. This is integrated with mass conservation law (continuity) to model traffic coordination as a probabilistic process and obtain traffic feasibility conditions using linear temporal logic. By spatial discretization of a network of inter-connected roads (NOIR), the NOIR is represented by a graph with inlet boundary nodes, outlet boundary nodes, and interior nodes. The paper offers a boundary control approach to manage congestion through the inlet boundary nodes. More specifically, model predictive control (MPC) is applied to control traffic congestion through the boundary of the traffic network. Therefore, the optimal boundary in flow is assigned as the solution of a constrained quadratic programming problem with equality and inequality constrained. The simulation results shows that the proposed MPC boundary controller can successfully control the traffic through the inlet boundary nodes where traffic reaches the steady state condition.