International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 2, Issue 12, December 2012) 369 Game Theoretic Model for Collision Free Geometric Path and Evasion of Network Congestion in a Dynamic Environment Seema Purohit 1 , Shruti Mantri 2 1 Department of Mathematics and MCA, Kirti M. Doongursee College and NMITD 2 Department of Computer Science, University of Mumbai and Kirti M. Doongursee College Abstract—In this paper, the researchers have made an attempt to address the problem of traffic network congestion to speed up the disaster response activity during a disaster. A dynamic environment is made up of static and moving obstacles. Each moving vehicle acts as a dynamic obstacle for other moving vehicle. There by increasing the network congestion. It is shown that the game theoretic model effectively helps to construct a navigation graph for each moving vehicle and computes collision free geometric path in a 2-D and 3-D work space. In this study (i) the problem of Network congestion is addressed by using the concept of Multi-Agents where, the transportation network is depicted as a non-deterministic, non-cooperative n – person game and (ii) the computation of collision free geometric path by using a 2 player non-deterministic game which detects the dynamic obstacles based on the observation made by the object sensor, computes all the possible geometric paths and selects the optimal path for the vehicle to travel in a 2-D and 3-D workspace (iii) Cooperative game theory model to resolve traffic congestion at a merge using the concepts of Time- Divison Multiple Access(TDMA) data slot that propagates through the a transportation channel Keywords— traffic congestion, obstacles, collision, game theory, multi-agents, navigation graph, action space, geometric path, TDMA. I. INTRODUCTION A. Natural Disaster An emergency is a deviation from planned or expected behaviour or course of events that endangers or adversely affects people, property, or the environment. Disaster is characterized by the scope of an emergency. An emergency becomes a disaster when it exceeds the capability of the local resources to manage it. Natural disasters include those unplanned events that occur as a result of natural processes such as earthquakes, tornadoes, tsunami, freezes, extreme heat or cold, floods, drought, or insect infestation…etc. A flood is an overflow of an expanse of water that submerges land. Floods are the major disaster affecting many countries in the world year after year. It is an inevitable natural phenomenon occurring from time to time, which not only damages the lives, natural resources and environment, but also causes the loss of economy and health. Every year Mumbai is affected by floods during monsoons. Greater Mumbai is greatly diversified and practically has every type of flood risk [15]. B. Disaster Management Disaster Management is skillful handling of crisis, danger or an unexpected situation demanding instant action which can be handled under a controlled situation in case of a juncture. It is a cycle of activities beginning with planning the Disaster Management plan, mitigating the vulnerability and negative impacts of disasters, preparedness in responding to operations, responding and providing relief in emergency situations such as search and rescue, etc. To speed up the response activity the emergency responder’s vehicles need to reach the disaster site as fast as possible. The emergency responders thus need to take the fastest route to reach to the disaster site. C. Geometric Path Geometric Path is a geometrical methods used for computing a collision or obstacle free path connecting the initial and final point in 2D and 3D environments [1]. Given a mapping and a description of the obstacles they provide a geometric description of the path in the workspace. Advantages of using geometrical descriptions are obstacles can be represented by arbitrary polygons, arbitrary motion angles. Also it is possible to find optimal paths for circular objects using topological abstractions. Successful attempts are made to reduce the computation time needed to find an optimal collision-free path for robot motions (Ziyad Aljarboua, 2009) [3] D. Importance of Geometric Path in Disaster Management System During the disaster response phase, response activities are designed to provide disaster assistance for victims. Disaster response activities can be facilitated by providing the best route and closest facility required at the time of emergencies. Best Route means the shortest/fastest geometrical path to be identified among different alternate paths available in different situations. For example, while people are affected during disaster, they need to be rescued by any means. So the selection of the quickest and shortest route to the disaster site, hospital or shelter is very important at that moment.