Weight Estimation using AHP In this section weight estimation using AHP is provided, where first dependency matrix is created based on saaty’s scale. Referring to matrix A1, every attribute is compared with others, ex. DT (Distance) first compared with itself so value is 1, then DT is compared with TT (Travel Time) as in this case TT is moderately important than DT is value will be 1/3, when DT is compared with PCU (Traffic Volume), in this case DT is moderately important than PCU thus its value will be 3.Accordingly weight estimation is carried out by knowing the importance of individual attribute in real transportation network.
A1=■(■(■(DT@TT@PCU)@RW@NI)@PR@ENR)[■(■(1&1/3&3@3&1&3@1/3&1/3&1)&■(4&4&■(4&3)@5&5&■(5&2)@2&2&■(3&1/3))@■(1/4&1/5&1/2@1/4&1/5&1/2@■(1/4@1/3)&■(1/5@1/2)&■(1/3@3))&■(1&2&■(3&1/3)@1/2&1&■(1/3&1/4)@■(1/3@3)&■(3@4)&■(■(1@5)&■(1/5@1))))] …show more content…
Dijkstra's algorithm solves the single-source shortest-path problem when all edges have non-negative weights. Let G= {V, E} be a directed weighted graph with V having the set of vertices. The special vertex s in V, where s is the source and let for any edge e in E, Edge Cost(e) be the length of edge e. For the weighted directed graph its adjacency matrix A = 〖(a_ij)〗_(n × n) is defined as follows: a_ij={ █(w_ij,& (V_i,V_j )∈E@ ∞,&(V_i,V_j )∉E)┤ i,j = 1,2,…n (4) where w_ij denotes the weight of arc < V_i,V_j >,∞ denotes that there is no edge between V_i and V_j [12].
The main steps of the Dijkstra’s algorithm are as follows [12],
Use adjacency matrix C to store network information. C_ij denotes the weight of arc . If there is no arc between V_i and V_j , then C_ij is set to ∞. d_(i )is defined as the weight from the source points to node v_(i ). Initialize starting point as d_(s ) = 0 and D_(i ) = si.
Select V_(p ), then we …show more content…
Conclusion: A useful routing system should have the capability to support the driver effectively in deciding on an optimum route to his/her preference. In this research paper, shortest path over specified zones using individual traffic attribute criteria’s like travel distance, travel time, traffic volume(PCU), road width, number of intersections, parking on road, encroachment are considered and also AHP is modeled to obtain the optimal path by considering above mentioned traffic attributes over specified zones. Using this model optimal path between various zones of Nagpur city is found out. An example for source zone no.4 to destination zone no.69 is illustrated in the paper. For the present case study, the Consistency Ratio obtained for AHP is 0.0729 which is much less than 0.1, thus optimal paths obtained using AHP for specified origin & destination zones are valid. From the experimental results for optimal path over specified zones, it is observed that in most cases the optimal path is prominently obtained for travel distance or travel time as evaluation criteria. This methodology paves the way for more intelligent traffic system.
5.1 CONCLUDING
A1=■(■(■(DT@TT@PCU)@RW@NI)@PR@ENR)[■(■(1&1/3&3@3&1&3@1/3&1/3&1)&■(4&4&■(4&3)@5&5&■(5&2)@2&2&■(3&1/3))@■(1/4&1/5&1/2@1/4&1/5&1/2@■(1/4@1/3)&■(1/5@1/2)&■(1/3@3))&■(1&2&■(3&1/3)@1/2&1&■(1/3&1/4)@■(1/3@3)&■(3@4)&■(■(1@5)&■(1/5@1))))] …show more content…
Dijkstra's algorithm solves the single-source shortest-path problem when all edges have non-negative weights. Let G= {V, E} be a directed weighted graph with V having the set of vertices. The special vertex s in V, where s is the source and let for any edge e in E, Edge Cost(e) be the length of edge e. For the weighted directed graph its adjacency matrix A = 〖(a_ij)〗_(n × n) is defined as follows: a_ij={ █(w_ij,& (V_i,V_j )∈E@ ∞,&(V_i,V_j )∉E)┤ i,j = 1,2,…n (4) where w_ij denotes the weight of arc < V_i,V_j >,∞ denotes that there is no edge between V_i and V_j [12].
The main steps of the Dijkstra’s algorithm are as follows [12],
Use adjacency matrix C to store network information. C_ij denotes the weight of arc . If there is no arc between V_i and V_j , then C_ij is set to ∞. d_(i )is defined as the weight from the source points to node v_(i ). Initialize starting point as d_(s ) = 0 and D_(i ) = si.
Select V_(p ), then we …show more content…
Conclusion: A useful routing system should have the capability to support the driver effectively in deciding on an optimum route to his/her preference. In this research paper, shortest path over specified zones using individual traffic attribute criteria’s like travel distance, travel time, traffic volume(PCU), road width, number of intersections, parking on road, encroachment are considered and also AHP is modeled to obtain the optimal path by considering above mentioned traffic attributes over specified zones. Using this model optimal path between various zones of Nagpur city is found out. An example for source zone no.4 to destination zone no.69 is illustrated in the paper. For the present case study, the Consistency Ratio obtained for AHP is 0.0729 which is much less than 0.1, thus optimal paths obtained using AHP for specified origin & destination zones are valid. From the experimental results for optimal path over specified zones, it is observed that in most cases the optimal path is prominently obtained for travel distance or travel time as evaluation criteria. This methodology paves the way for more intelligent traffic system.
5.1 CONCLUDING