Problem 4: Traffic Assignment (25 marks) Upgrades to North Haverbrook Station and Springtown Union Station will require long term closure of the metro system in Springtown. This will create congestion throughout the network but in particular for road network connecting these two stations, as presented in Figure 4. The time period of most concern is during the AM Peak where there is a significant amount of traffic travelling from North Haverbrook Station to Springtown Union Station. Of particular concern are Highway 201 and Main Street, where significant queuing is present. 1 Meway 2011 B Not Hancock Highway 201 3 3 Street 2 Evergreen Parade Mal Street Centre Street 6 Eser Son Enon Balon 7 3Street F Sycamore Avenue E 5 DANIE Map of focussed study area Schematic network drawing of focussed study area Figure 4: Maps of Origin - Destination pair Table 10 presents the labelling of the volumes and travel time for each link as well as the link cost functions. Table 10: Link cost functions (x, represents the link volume on link A) Link Link Cost (travel Link Link Volume Travel time) Function Time (minutes) X4 500 1 = (200) 1 X. t = +2 1 2 3 t1 ta X2 N X2 + 3 3 w *3 ts t = +4 250 24 4 X4 t4 t4 = + 2 1200) 5 X's ts ts = Xs 1400 + 1 6 X6 ts Is = = 400) +1 7 X tz ty = (160) + 2 Answer the following questions to determine the traffic assignment from North Haverbrook Station and Springtown Union Station. a) How many routes are there to travel from North Haverbrook Station to Springtown Union Station? Identify each route using link labels. (2 marks) b) Consider "free flow" traffic conditions, where link travel times are unaffected by link traffic volume, which route would travellers use and why? Present a calculation to justify your solution. What does this finding indicate about the design of the road network between North Haverbrook Station and Springtown Union Station? (5 marks) c) The current link volumes of the road network are presented in Table 11. Table 11: Current link volumes (prior to closure of the Link Volume Link (vehicles/time period) 1 1144 2 1144 4 477 656 W N 3 5 6 477 179 7 179 What is the current Origin to Destination demand? Also are the current traffic conditions in a state of "User Equilibrium". Justify your assessment using route travel time calculations (complete your route travel time calculations to an accuracy of 2 decimal places). (5 marks) d) Assume that during the station closure phase that there is an Origin to Destination demand of 3000 trips for the time period being assessed, and using the principle of *User Equilibrium", determine the equilibrium conditions between North Haverbrook Station and Springtown Union Station. i. Clearly present all demand conservation equations and route travel time equilibrium equations. (5 marks) ii. Solve the system of equations and present link volumes, link travel times and route travel times under equilibrium conditions. How much additional travel time will travellers be faced with as a result of the closure? What impact will the new traffic assignment forecasts have on the queuing issues described? (8 marks) Problem 4: Traffic Assignment (25 marks) Upgrades to North Haverbrook Station and Springtown Union Station will require long term closure of the metro system in Springtown. This will create congestion throughout the network but in particular for road network connecting these two stations, as presented in Figure 4. The time period of most concern is during the AM Peak where there is a significant amount of traffic travelling from North Haverbrook Station to Springtown Union Station. Of particular concern are Highway 201 and Main Street, where significant queuing is present. 1 Meway 2011 B Not Hancock Highway 201 3 3 Street 2 Evergreen Parade Mal Street Centre Street 6 Eser Son Enon Balon 7 3Street F Sycamore Avenue E 5 DANIE Map of focussed study area Schematic network drawing of focussed study area Figure 4: Maps of Origin - Destination pair Table 10 presents the labelling of the volumes and travel time for each link as well as the link cost functions. Table 10: Link cost functions (x, represents the link volume on link A) Link Link Cost (travel Link Link Volume Travel time) Function Time (minutes) X4 500 1 = (200) 1 X. t = +2 1 2 3 t1 ta X2 N X2 + 3 3 w *3 ts t = +4 250 24 4 X4 t4 t4 = + 2 1200) 5 X's ts ts = Xs 1400 + 1 6 X6 ts Is = = 400) +1 7 X tz ty = (160) + 2 Answer the following questions to determine the traffic assignment from North Haverbrook Station and Springtown Union Station. a) How many routes are there to travel from North Haverbrook Station to Springtown Union Station? Identify each route using link labels. (2 marks) b) Consider "free flow" traffic conditions, where link travel times are unaffected by link traffic volume, which route would travellers use and why? Present a calculation to justify your solution. What does this finding indicate about the design of the road network between North Haverbrook Station and Springtown Union Station? (5 marks) c) The current link volumes of the road network are presented in Table 11. Table 11: Current link volumes (prior to closure of the Link Volume Link (vehicles/time period) 1 1144 2 1144 4 477 656 W N 3 5 6 477 179 7 179 What is the current Origin to Destination demand? Also are the current traffic conditions in a state of "User Equilibrium". Justify your assessment using route travel time calculations (complete your route travel time calculations to an accuracy of 2 decimal places). (5 marks) d) Assume that during the station closure phase that there is an Origin to Destination demand of 3000 trips for the time period being assessed, and using the principle of *User Equilibrium", determine the equilibrium conditions between North Haverbrook Station and Springtown Union Station. i. Clearly present all demand conservation equations and route travel time equilibrium equations. (5 marks) ii. Solve the system of equations and present link volumes, link travel times and route travel times under equilibrium conditions. How much additional travel time will travellers be faced with as a result of the closure? What impact will the new traffic assignment forecasts have on the queuing issues described? (8 marks)