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Nowadays, the development of “smart cities” with a high level of quality of life is becoming a prior challenge to be addressed. In this paper, promoting the model shift in railway transportation using tram network towards more reliable, greener and in general more sustainable transportation modes in a potential world class university is proposed. “Smart mobility” in a smart city will significantly contribute to achieving the goal of a university becoming a world class university. In order to have a regular and reliable rail system on campus, we optimize the route among major stations on campus, using shortest path problem Dijkstra algorithm in conjunction with a computer software called LINDO to arrive at the optimal route. In particular, it is observed that the shortest path from the main entrance gate (Canaan land entrance gate) to the Electrical Engineering Department is of distance 0.805 km.

One of the major advantages of rail transit, particularly Trams, is that it can provide a highly efficient and very attractive mode of public transit to provide access to and from hostels and places on university campuses [

S/N | Notation | Proposed stations |
---|---|---|

1 | A | CANAAN LAND ENTRANCE |

2 | B | CANAAN RESTAURANT |

3 | C | DOMINION Book STORE |

4 | D | COVENANT UNIVERSITY GATE |

5 | E | CU MAIN ROUND ABOUT |

6 | F | CHAPEL PARKING LOT |

7 | G | EAGLE SQUARE(HOSTEL) |

8 | H | CFMB |

9 | I | WORD OF FAITH BIBLE INSTITUTE |

10 | J | GREEN PASTURE |

11 | K | ALDC |

12 | L | CU CENTRE FOR LEANING AND RESEARCH |

13 | M | STAFF QUARTERS(FAITH AVENUE) |

14 | N | GUEST HOUSE |

15 | O | CAMP HOUSE |

16 | P | MECHANCIAL ENGINEERING |

17 | Q | CENTRE FOR DEVELOPMENT STUDIES |

18 | R | CAFE 2 |

19 | S | CIVIL ENGINEERING |

20 | T | YOUTH CHAPEL |

21 | U | ELECTRRICAL ENGINEERING DEPARTMENT |

to node. The main advantage of this work is the fact that a simple algorithm, such as Dijkstra algorithm, can be applied, with some assumptions, to estimate the shortest part of a proposed tramway in a potential world class university. Tramway transit system is very new in universities in sub-Saharan Africa countries. Tram system will soon be the transit mode of choice among many sub-Saharan Universities of lower to medium population density. Tram systems are very safe in pedestrian environments ~ far safer than automobiles―while providing convenient surface access to the public. Some of the advantages of this would be lower cost and greater flexibility, reduction in carbon dioxide emission and convenience, especially during rainy season. Also, the following are other benefits of this transportation system; extension of rail network to areas currently not served by campus shuttle cars, reduction in cost of transportation within the covenant university, reduction in carbon monoxide in the air, making the university cleaner and always quite, making the university accessible and socially vibrant [

The Data collected are shown in

S/N | ROUTES | Distance between two points (in meters) x10 |
---|---|---|

1 | A---C | 250 |

2 | A---B | 270 |

3 | A---D | 2000 |

4 | B---C | 1800 |

5 | B---I | 1800 |

6 | D---C | 750 |

7 | D---E | 2700 |

8 | C---I | 2000 |

9 | C---H | 290 |

10 | E---C | 450 |

11 | E---F | 1200 |

12 | G---H | 1300 |

13 | F---C | 500 |

14 | F---G | 7000 |

15 | H---K | 500 |

16 | H---J | 2500 |

17 | H---1 | 2500 |

18 | I---J | 2000 |

19 | J---O | 220 |

20 | K---J | 2200 |

21 | K---M | 900 |

22 | L---M | 1500 |

23 | L---K | 10000 |

24 | L---G | 350 |

25 | L---Q | 400 |

26 | M---N | 300 |

27 | M---P | 450 |

28 | N---O | 3200 |

29 | N---J | 2000 |

30 | O---T | 3200 |

31 | J---O | 270 |

32 | P---O | 2600 |

33 | P---S | 150 |

34 | Q---R | 700 |

35 | Q---P | 1000 |

36 | Q---M | 550 |

37 | R---S | 400 |

38 | R---U | 550 |

39 | S---T | 450 |

40 | S---U | 500 |

41 | T---U | 270 |

The following assumptions are claimed in this work:

1) There is no waiting time at the stations.

2) The shortest distance in this work means shortest time costing.

3) One-way travel condition is considered.

Dijkstra’s algorithm gives shortest distance between a source vertex and a target vertex in a weighted graph. Let the node at which we are starting be called the initial node (node A). Let the distance of node B be the distance from the initial node A to B. Dijkstra’s algorithm will assign some initial distance values and will try to improve them step by step. The procedure is as follows (Nilesh More, 2014):

1) Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes.

2) Set the initial node as current. Mark all other nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.

3) For the current node, consider all of its unvisited neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 5, and the edge connecting it with a neighbour B has length 4, then the distance to B (through A) will be 5 + 4 = 9. If B was previously marked with a distance greater than 9 then change it to 9. Otherwise, keep the current value.

4) When we are done considering all of the neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.

5) If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.

6) Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new “current node”, and go back to Step 3.

Let node A be the initial node. Let the distance between the nodes be as shown in

By interpretation, starting from Canaan land entrance gate, the rail path should go through Covenant University gate, then pass through CU main round about, then the Chapel parking lot, then CU Centre for learning and research, then through the centre for development studies, then finally through café 2 to the Electrical Engineering department.

From

B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A | 270_{A} | 250_{A} | 2000_{A} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |

C | 270_{A} | 250_{A} | 2000_{A} | ∞ | ∞ | ∞ | 540_{C} | 2250_{C} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |

B | 270_{A} | 2000_{A} | ∞ | ∞ | ∞ | 540_{C} | 2070_{B} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |

H | 2000_{A} | ∞ | ∞ | ∞ | 540_{C} | 2070_{B} | 3040_{H} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ||

D | 2000_{A} | 4700_{D} | ∞ | ∞ | 2070_{B} | 3040_{H} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |||

I | 4700_{D} | ∞ | ∞ | 2070_{B} | 3040_{H} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ||||

J | 4700_{D} | ∞ | ∞ | 3040_{H} | ∞ | ∞ | ∞ | ∞ | 3310_{J} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | |||||

O | 4700_{D} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | 3310_{J} | ∞ | ∞ | ∞ | ∞ | 6500_{O} | ∞ | ||||||

E | 4700_{D} | 5900_{E} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | 6500_{O} | ∞ | |||||||

F | 5900_{E} | 12900_{F} | ∞ | 6400_{F} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | 6500_{O} | ∞ | ||||||||

T | 12900_{F} | ∞ | 6400_{F} | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | 6500_{O} | ∞ | |||||||||

L | 6750_{L} | 16400_{L} | 6400_{F} | 7900_{L} | ∞ | ∞ | 6800_{L} | ∞ | ∞ | ∞ | ||||||||||

G | 6750_{L} | 16400_{L} | 7900_{L} | ∞ | ∞ | 6800_{L} | ∞ | ∞ | ∞ | |||||||||||

Q | 16400_{L} | 7350_{Q} | ∞ | 7800_{Q} | 6800_{L} | 7500_{Q} | ∞ | ∞ | ||||||||||||

M | 16400_{L} | 7350_{Q} | 7650_{M} | 7800_{M} | 7500_{Q} | ∞ | ∞ | |||||||||||||

R | 16400_{L} | 7650_{M} | 7800_{M} | 7500_{Q} | 7900_{R} | 8150_{R} | ||||||||||||||

N | 16400_{L} | 7650_{M} | 7800_{M} | 7900_{R} | 8150_{R} | |||||||||||||||

P | 16400_{L} | 7800_{M} | 7900_{R} | 8150_{R} | ||||||||||||||||

S | 16400_{L} | 7900_{R} | 8150_{R} | |||||||||||||||||

U | 16400_{L} | |||||||||||||||||||

K | 16400_{L} |

The actual shortest distance, therefore, is 805 meters. That is 0.805 km from Canaan land entrance gate to the Electrical Engineering department. From

From (3) above, the initial distance between the starting node A to C, D and B are 25 m, 200 m and 27 m respectively.

From (4): the shortest distance of I from A is 207 m and it is through B.

From (5): the shortest distance of H from A is 54 m and it is through C.

From (6): the shortest distance of E from A is 470 m and it is through D.

From (7): the shortest distance of F from A is 470 m and it is through E.

From (8): the shortest distance of L from A is 470 m and it is through F.

From (9): the shortest distance of J from A is 470 m and it is through H.

From (10): the shortest distance of O from A is 470 m and it is through J.

From (11): the shortest distance of S from A is 470 m and it is through K.

From (12): the shortest distance of Q from A is 680 m and it is through L, the shortest distance of G from A is 675 m and it is through L. the shortest distance of K from A is 1640 m and it is through L.

From (13): the shortest distance of P from A is 780 m and it is through M the shortest distance of O from A is 765 m and it is through M.

From (14): the shortest distance of T from A is 651 m and it is through O.

From (15): the shortest distance of M from A is 735 m and it is through Q the shortest distance of R from A is 750 m and it is through Q.

From (16):the shortest distance of U from A is 805 m and it is through R.

Analysis of the shortest path of a proposed tramway for a potential world class University is carried out in this paper using the Dijkstra Algorithm. Covenant University is used as a case study. Some important spots on the campus are identified as the tramway stations. The Canaan land gate is using as the starting point, which represents the initial node A on the weighted graph in

M. C.Agarana,N. C.Omoregbe,M. O.Ogunpeju, (2016) Application of Dijkstra Algorithm to Proposed Tramway of a Potential World Class University. Applied Mathematics,07,496-503. doi: 10.4236/am.2016.76045