he following novel speed-density model is proposed as an Improvement to existing macroscopic traffic models: fork sa fork >a) Where: T, -space mean speed (kmhr), k - density (vehkm), wy-free flow speed (km/hr). ky-jam density and a is a density parameter of the road section Assuming a jam density of 50 vehem, analyse the provided data and answer the following questions: a) Given the type of field data collected, what type of speed data has been collected in the traffic survey and what does "average speed" mean? Clearty Justify your answer based on definitions of speed provided in the lecture material. (2 marks) For the remainder of the question, assess conditions for BOTH northbound and southbound directions of travel. b) Using the fundamental relationships of traffic flow and linear regression (use Microsoft Excel Assuming that al density data collected is less than density parameter derive the speed-density relationship for the novel model presented above. (12 marks) Are the derived models a good fit for the observed data? Use a statistical measure to justify your answer. (4 marks) IL Calculate the value of 'w' and 2 (4 marks) IV. For each direction, how many data points did not meet the criteria k >a"? Do you think this makes the model invald? Justify your answer (4 marks) C) Based on the results of part b) determine the mathematical relationship (present the equations) between speed and flow as well as the relationship between flow and density for both directions (12 marks) Calculate the capacity of Wilson Road for both directions. What does the density parameter "a" signity in the novel model? 18 marks) e) Provide a brief discussion on the advantages and disadvantages of the novel model in describing traffic flow along a road section. Compare win the Greenshields and Greenberg models?