Spectral analysis for performance evaluation in a bus network

This paper deals with the performance evaluation of a public transportation system in terms of waiting times at various connection points. The behaviour of a bus network is studied in the framework of Discrete Event Systems (DES). Two possible operating modes of buses can be observed at each connection stop: periodic and non-periodic mode. Two complementary tools, Petri nets and (max, +) algebra, are used to describe the network by a non-stationary linear state model. This one can be solved after solving the structural conflicts associated to the graphical representation. From the characteristic matrix of the mathematical model, we determine eigenvalues and eigenvectors that we use to evaluate the connection times of passengers. This work is finally illustrated with a numerical example.

[1]  Michael R. Bussieck,et al.  Discrete optimization in public rail transport , 1997, Math. Program..

[2]  B. Schutter,et al.  On max-algebraic models for transportation networks , 1998 .

[3]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[4]  J. Boimond,et al.  TIMETABLE SYNTHESIS USING (MAX,+) ALGEBRA , 2006 .

[5]  A. Nait-Sidi-Moh,et al.  A (max, plus) modelling approach for the evaluation of travelling times in a public transportation system , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[6]  Jürgen Lind,et al.  Using a multi-agent approach to optimise the train coupling and sharing system , 2001, Eur. J. Oper. Res..

[7]  Yi Deng,et al.  Performance analysis of traffic networks based on Stochastic Timed Petri Net models , 1999, Proceedings Fifth IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'99) (Cat. No.PR00434).

[8]  Marie-Ange Manier,et al.  Control of an electroplating line in the max and min algebras , 1999, Int. J. Syst. Sci..

[9]  E. Castelain,et al.  Regulation of a public transport network with consideration of the passenger flow: modeling of the system with high-level Petri nets , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[10]  Pierre Borne,et al.  Traffic control in transportation systems , 2005 .

[11]  Bruno Gaujal.  Parallelisme et simulation des systemes a evenements discrets , 1994 .

[12]  Ahmed Nait-Sidi-Moh,et al.  Petri net with conflicts and (max, plus) algebra for transportation systems , 2006 .

[13]  Loo Hay Lee,et al.  Hybrid Genetic Algorithm in Solving Vehicle Routing Problems with Time Window Constraints (APORS) , 2000 .

[14]  Ricardo Calle Saiz,et al.  Commission des Communautés Européennes , 1980 .

[15]  Simona Sacone,et al.  Hybrid modelling of transportation systems by means of Petri nets , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[16]  Matthew G. Karlaftis,et al.  DECISION SUPPORT SYSTEMS FOR PLANNING BUS OPERATIONS DURING MEGA EVENTS: THE ATHENS 2004 SUMMER OLYMPICS , 2006 .

[17]  A. El Moudni,et al.  MAX-PLUS ALGEBRA MODELING FOR A PUBLIC TRANSPORT SYSTEM , 2005 .

[18]  S. Gaubert.  Theorie des systemes lineaires dans les dioides , 1992 .

[19]  Didier Dubois,et al.  A linear-system-theoretic view of discrete-event processes , 1983 .

[20]  J. Quadrat,et al.  A linear-system-theoretic view of discrete-event processes , 1983, The 22nd IEEE Conference on Decision and Control.