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Best Route Finding Based on Cost in Multimodal Network With Care of Networks Constraints
Definition:
In this part different component of a multi modal network and their constraints are considered.
A multi modal network is a collection of arcs and nodes as a graph G = (N, A).
Node in a multi modal network is a place that traveler can decide to continue his route in the same mode or change the mode (Lozano and Storchi, 1999).
Arc in a multi modal network have two types:
Travel arc is a connection of two nodes in the same mode. Transfer arc is a representation of transfer between two nodes in different modes (Lozano and Storchi, 1999).
A route from an origin (a) to a destination (b) (a, b ε N) is a continuous and finite collection of nodes and arcs that connects the origin and destination node.
The best route, through the collection of selective route, is the route that has minimum time of journey or cost and some other constraints such as number of changing mode. So a function as a cost function (c: A-->r) should transform a collection of arcs to a route from the origin to the destination.
Assigning the cost function is based on type of networks and their expense. For example in a bus network since travelers use a bus line only need a ticket but if we want to change the bus line it is needed to pay another ticket.
So it is not possible to link directly a cost to a traverse arc. In this situation, the determination of cost of journey must be taken with care of changing the modes of transportation. The final route is, hence, divided into parts named sub-route that has only nodes of the same mode and each line has a start and end node. The final route is a combination of these sub-routes and the connection of end of one sub-route to start of other in a transfer arc.
The transfer arc can be a walking route or even time of waiting for changing the mode. As such, the total cost for a route is the cost of travel arc in addition to transfer arc. Because of the time and cost of changing the modes of transportation, user usually enters the maximum number of changing modes as a constraint to the system.
Algorithm theory:
In a route finding application from the origin to the destination, many of the existing theory routes are not feasible due to insufficient consideration of especial conditions of the mode of transportation. In such a situation an assessment test is needed to check the feasibility of selected route.
Some of such conditions are:
- nonexistence of loop in a route
- possibility of car travel in a route with care of route direction
- Not using the privately-own care if the last used mode is not a car.
- Not using metro mode once more after changing the mode one time.
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