Analyze the complexities involved in optimizing traffic flow in urban environments through the design and implementation of intelligent transportation systems $($ITS$).$ Explore the underlying theories of traffic flow dynamics, including congestion theory, queuing theory, and traffic signal optimization algorithms. Discuss the challenges of integrating emerging technologies like connected and autonomous vehicles $($CAVs$)$ into existing traffic management systems, addressing issues such as cybersecurity, infrastructure compatibility, and public acceptance. Evaluate the potential benefits and drawbacks of ITS solutions in enhancing safety, efficiency, and environmental sustainability in urban transportation networks.