Figure Q1.1 shows a section of a road network around a major city consisting of 16...

 

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Figure Q1.1 shows a section of a road network around a major city consisting of 16 nodes and 22 links. The travel time on each link (in minutes) is as depicted. a) Find the route with the shortest path from Node 9 to Node 16 using Dijkstra algorithm by hand. Show all your work including a tabular summary of the steps and the final results. (20%) b) Determine the route with the shortest time from Node 1 to Node 15 assuming System Optimum conditions apply. Use a suitable optimization software such as Matlab for this problem. Make sure to state the software used and include all the input data. (15%) c) Assuming the coordinates of the nodes (junctions) of the network are as shown in Table Q1.1, use a suitable mapping software to show the shortest path determined in b) on a UK map. (5%). In your asnwers, clearly show all the appropriate steps you took to arrive at your answers in a) and b). The inputs and outputs from the software used in c) should also be documented in your report. Provide high quality diagrams to depict your results in order to get top marks. T -2- -2.2- -2.4- -2.6- -2.8- -3- 1 52 Table Q1.1 Label A B C D E F G H 1 J K L M B N O P +9 6 I 52.15 Figure Q1.1. Network location details. 52.05 10 Node 10 12 12: 3 52.1 15 +1476 11 9 13 3 Latitude Longitude 1 52.12451 -3.00213 2 52.20418 -2.83707 3 52.23237 4 52.31293 5 52.37877 -2.73078 -2.70422 -2.25051 -2.0487 -2.16201 6 52.33584 7 52.2136 8 52.0472 -2.13908 10 52.05959 11 52.17402 9 52.05348 -2.50342 -2.71982 -2.71543 -2.56183 -2.26662 12 52.10258 13 52.18896 14 52.16797 -2.24258 -2.22291 15 52.23092 16 52.35659 -2.23348 *2 T 52.2 *12 15 L 52.25 10 1 52.3 6 2 +162 L 52.35 1 52.4 Figure Q1.1 shows a section of a road network around a major city consisting of 16 nodes and 22 links. The travel time on each link (in minutes) is as depicted. a) Find the route with the shortest path from Node 9 to Node 16 using Dijkstra algorithm by hand. Show all your work including a tabular summary of the steps and the final results. (20%) b) Determine the route with the shortest time from Node 1 to Node 15 assuming System Optimum conditions apply. Use a suitable optimization software such as Matlab for this problem. Make sure to state the software used and include all the input data. (15%) c) Assuming the coordinates of the nodes (junctions) of the network are as shown in Table Q1.1, use a suitable mapping software to show the shortest path determined in b) on a UK map. (5%). In your asnwers, clearly show all the appropriate steps you took to arrive at your answers in a) and b). The inputs and outputs from the software used in c) should also be documented in your report. Provide high quality diagrams to depict your results in order to get top marks. T -2- -2.2- -2.4- -2.6- -2.8- -3- 1 52 Table Q1.1 Label A B C D E F G H 1 J K L M B N O P +9 6 I 52.15 Figure Q1.1. Network location details. 52.05 10 Node 10 12 12: 3 52.1 15 +1476 11 9 13 3 Latitude Longitude 1 52.12451 -3.00213 2 52.20418 -2.83707 3 52.23237 4 52.31293 5 52.37877 -2.73078 -2.70422 -2.25051 -2.0487 -2.16201 6 52.33584 7 52.2136 8 52.0472 -2.13908 10 52.05959 11 52.17402 9 52.05348 -2.50342 -2.71982 -2.71543 -2.56183 -2.26662 12 52.10258 13 52.18896 14 52.16797 -2.24258 -2.22291 15 52.23092 16 52.35659 -2.23348 *2 T 52.2 *12 15 L 52.25 10 1 52.3 6 2 +162 L 52.35 1 52.4

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