The 2003 International Conference on Information Systems and Engineering (ISE/SCS 2003) July 20 - 25, 2003
Multimodal Transportation Networks : Object Modelling and the K-Multimodal Shortest Path Hicham Mouncif and Azedine Boulmakoul, R. Laurini* LIST Lab. Computer Sciences Department Mohammedia Faculty of Sciences and Technology (FSTM), B.P. 146 Mohammedia, Morocco. {
[email protected],
[email protected] } * LIRIS, INSA de Lyon, 20 Avenue Albert Einstein, F-69621 Villeurbanne Cedex, France. Keywords: Object-Oriented modelling, multimodal transportation networks, multimodal routing, UML. ABSTRACT The objective of this paper is to develop, implement and test a solution to the problem of long-run planning of transit on multimodal network. It presents the general results found, and algorithm used along this work. The aim is to provide a tool to detect facilities of using different modes of transport through multimodal network. Routings may include distinct combination of rail, and route. Geographic Information Systems (GIS) was invaluable in the costeffective construction and maintenance of this work and subsequent validation of mode sequences and paths selections. Attention is paid to multimodal path operator as well as to the use of GIS-transit planning.
1. INTRODUCTION In recent years, railway servicing planning, and modernisation of trains was remarkable and added important gains, with regard to the use of travellers of this transportation means of transport. Trains are used to cross short and long distances, such as TGV train in France for instance. The growth of traffic by private cars is due to evolution of socio-economic context, and to the road network planning. Transportation modelling activities have traditionally paid that movement through transportation networks is a hard task, especially when considering configuration of several means of travel. In fact, movements of people and goods don’t occur solely on the basis of a single mode. Multimodal movements involve contribution of each of these modes to overall movement patterns of people and goods, while intermodal movements are those in which two or more different transportation modes are linked in order to move people or/and goods from origin place to destination place. Trip chains for passenger travel may include several modes. A work trip commute might involve driving an auto to a rail or bus stop, with possibility of additional transfers within or among modes to complete the trip. In this work we present in a unifying framework both algorithmic approaches that we have been proposed to solve multimodal shortest path problem, and also a multimodal network modelling with some consideration of the path operator. More precisely, section 2 develops
multimodal transit network modelling, section 3 presents a main component of the network solver. We accurately consider the evaluation path operator. Section 4 is devoted to the integration of GIS component within multimodal operators analysis, and a conclusion is formulated in section 5.
2. MULTIMODAL NETWORK MODEL The research [14] presents a strategy to design multimodal network based on the concept of hierarchical network levels. In road networks and public transport networks a hierarchy of functionally different network levels can easily be distinguished. For private cars, network levels as street, arterials and freeways can be distinguished, and for public transport local bus, metro, and long distance train are well known network levels. The first step to model multimodal transit networks is to derive a model witch captures all possible transit modalities and the interconnections among them. 2.1. Data Model of Multimodal Transit Network Three levels of abstraction are defined in [7] to manage network oriented-data : Physical level(i.e. spatial coordinates), logical level (i.e, graph modelling the transportation network), and applicative level(i.e., structuring a graph taking into account depending modelling application). Each data model has its own facilities to represent relationships between objects. Since graphs are a special concept for representing such relationships, few graph data models (Mainguenaud and Simatic [8]) have been proposed particularly in Geographical Information System context. In many cases, it is helpful to view such relationships as graph structures. Then many queries can directly be mapped to wellknown graph problems for which efficient algorithms exist. The graph data model [6] used in this work is based on the merge of graph theory concepts and object-oriented paradigm. Components of data model are described by logical view (see figures 1-3), it also represents relationships between classes. Nodes and edges may carry geometric information. A node (for generic topology) is the smallest identified location in space, it plays many different roles in a transport network. A link is an important component of the multimodal transit system, it represents
both type of road and mode of transport between two nodes. Introduction of the HyperNode (with respect to HyperLink) allows definition of node (with respect to a link) as an abstraction of a sub-network. Strategy implementation is the use of special data structures for the representation of graphs [8] that allow efficient traversal. Graph operations are implemented on the basis of efficient graph algorithms. 2.1.1. Main Classes This network modelling is used to elaborate different levels of details following the importance of the nodes and the links. The principals classes predefined are: node, link and network. For each of them we give its form using C++ class syntax. a) Nodes The class node is given as follows: Template class Node { T * Label; Node() //constructor { Label = new T; } ~Node() //destructor { delete[] Label; } }; The use of template class T is very interesting in routing problem, for example class T may represent a set of constraints that are assigned a class Node. Figure 1 gives an example of node abstraction.
Node
City Bus S tation
Road Intersection
Link
Figure 1. Node may represents several elements of the multimodal network. b) Links The class link is defined to model, rail, road and transport mode. It is given as follows :
Template class Link { Node* Initial_Node; Node* Terminal_Node; Link{ Initial_Node = new Node; Terminal_Node = new Node; } ~Link (){} };
Link
Mode of Transportation
Train
Type of Link
RailWay
Car
HighWay
Figure 2. Link representation. c) Networks A graph is an efficient concept to model network oriented data. A graph as defined in literature is a binary relation between the set of nodes and the set of edges. Then, class network is defined as follows : Template Network() { list *ListNodes; list *ListLinks; Network { ListNodes = new list; ListLinks = new list; } ~Network(){} }; 2.1.2. Abstraction Levels As a multimodal network is modelled with hierarchical structure, we can add an abstraction level in order to take into account network-oriented data as well as object type hierarchies that are also part of functional modelling. In particular, HyperNode class (in respect of HyperLink class) are considered to allow definition of a node (in respect of an link) as an abstraction of sub-network. In that respect,
the approach presented in [6] describes a strategy to manage several levels of abstraction. a) HyperNode The class HyperNode inherit from the class node. This class may have several associated sub-networks. Template class HyperNode : public Node { list * ListNetworks; HyperNode{ ListNetworks = new list; } ~HyperNode(){} }; b) HyperLink
the most important operators in a geographical Information System. The evaluation of path is performed with a path operator. The specification of the path operator that we consider is this evaluation that corresponds to the detection of a multimodal shortest path between an origin and a destination. This path can be a direct link (i.e, a successor in a graph) or a more complex path (i.e, a transitive closure of a graph).
Develop/Undevelop Operator NetSolver
Graph Weight
Path Operator
Class HyperLink is a subclass of class link. It has a unique associated sub-network. K-MSP-Algorithm
Template class HyperLink : public Link { Network* *Net; HyperLink { Net = new ; } ~HyperNode(){} };
3. K-MULTIMODAL SHORTEST PATH OPERATOR A Geographical Information System must provide an opportunity to manage network facilities. Hence, network solver modelling must take into account several levels of interaction as well as the manipulation of network-oriented data, we have Basic component directly linked to abstraction concept in data model, elementary operators correspond to graph manipulations and sub-graphs, and high level operators correspond to the GIS user interface. B. Langou and M. Mainguenaud, in studies [3] defined two operators directly linked to concepts of abstraction in data model : the DEVELOP operator and the UNDEVELOP operator. The DEVELOP operator provides more specific details by merging a sub-network associated with an HypredNode or with an HyperLink. On the other hand we have the conversion operator UNDEVELOP operator that provides a more restricted graph by replacement of subnetwork by HyperNode or HyperLink. The main operator considered at high level is the evaluation path operator, between an origin and a destination. Path operator can be classified into categories of network-oriented operators based on graph manipulation. Many current researches [2], [3], and [7] consider that path evaluation operator is one of
Node
Link
TransMode
UniModal
TransModal
Figure 3. Network Solver Model. 3.1. Information Models of Multimodal Network Multimodal transit networks contain several hierarchical levels. Our goal is to find a feasible path such that its cost and time is the minimum (the shortest path), that browses different levels of multimodal transit network. In multimodal network one has to select between continuing with current mode or changing it. A link connecting two nodes is associated with many attributes cost travel, time travel, nature link (travel mode, road type), which is incurred when selecting it to be part of a travel between two given places. N=(V, E) is a multimodal network, where V is a set of vertices, E represents a set of Links. In multimodal network we have two distinct types of arc, one is called transfer arc, it represents a change of mode or modal transfer, and travel arc that connects two nodes by only one travel mode. M is the set of modes. The main modes of travel considered over multimodal transit network are presented in the following table :
Transport mode in a city
Transport mode between cities P: Private vehicle P: Private vehicle T: Train M: Metro A: AutoCar B: Bus Table 1. Main modes of travel. Private vehicle mode can be a common mode between different levels of the network. Otherwise, change from one network level to another is transparent for a private car, but for public transport travellers such a transfer is quite noticeable. 3.2. Multimodal Viable Path Few researches have been introduced The definition of viable path in multimodal transit (Battista et al. [1], A. Lozano, G. Storchi.[5]). Pallottino and Scutellà [10] considered the number of modal transfers in a path as an attribute in the multicriteria shortest path. Miller and Storm [9] created a modal transfer arc to represent each modal change. A characteristic of viable path is the use of distinct modes of transportation. Then, the viable path is a path that respect a set of constraint on its sequences of used modes. Each user assigns his personal attribute to O-D paths in multimodal network, he can give the maximum of generalised cost, modes of transport used, i.e., a user can choose modes he prefers to reach his destination, and a number of modal transfer that he is able to establish. A. Lozano and G. Storchi [5] have given a definition for viable path in urban network. Hence, private and metro modes considered as a constrained modes at city’s level, and train mode at cities level. A O-D path is considered viable if it uses only one consecutive sequence of metro mode, or only one consecutive sequence of private mode with initial node O. In the same way, one defines a viable path at a higher level (between cities), private mode is a common mode between network levels, so we say that a viable path is a path that contains only one consecutive sequence of train mode.
3.3. Design of the K-Multimodal Path Algorithm The ranking of shortest paths is considered as a generalisation of the well known shortest path problem [11], since several paths must be listed by nondecreasing order of their cots. The algorithm that we present is a modified version of the K-shortest path algorithm to which one integrated multimodal viable path concepts defined above, and a generalised cost, in order to define an efficient solution for multimodal shortest path problem. For more details about K-shortest paths, the reader can reviews the studies [12],[15]. The labels functions are composed of the following elements:
Γ(i) is the set of successor nodes to node i. Max_transfer is the maximum number of transfer modal given by the user. h is the number of transfer modal in the current path. X is the set of nodes with h modal transfers. Y is the set of nodes with h+ 1 modal transfers. Λir is a generalized cost assigns to node i. lastlabelik is the cost of the last shortest path with h modal transfers from the origin O to node i. Modeik is the set of modes used in the current path from the origin O to node i.
Algorithm {Λi1, Λi2, …, ΛiK }←{∞, ∞, …, ∞}; for all node i∈V; Λir is unused for all i∈N and r∈{1,..,K}; Λs1← 0; X← {s}; Modes1← O; Do { while X≠∅ { i← node of X; X← X\{i}; For each k∈{1,…,K} such that Λik is unused and finite { If(Λik
