Game-theoretic Patrol Strategies for Transit Systems:the TRUSTS System and its Mobile AppSamantha Luber, Zhengyu Yin, Francesco Delle Fave, Albert Xin Jiang, Milind Tambe and John Sullivan*University of Southern California, *Los Angeles Sheriff’s DepartmentThe TRUSTS System The Fare Evasion ProblemFare evasion costs proof-of-payment transit systems significant losses in revenue. In2007 alone, the Los Angeles Metro system, using proof-of-payment, suffered anestimated revenue loss of $5.6 million due to fare evasion.To address this shortcoming, the Los Angeles Sheriff’s Department (LASD) periodicallypatrols the Metro system in order to prevent and deter fare evasion.However, patrolling a transit system presents a number of challenges. For instance,resource limitations prevent officers from verifying all passengers. As a consequence,such officers periodically inspect a subset of the passengers based on a patrol strategy.Randomization is another challenge. The complexity of a transit system makes itimpossible for human schedulers to manually produce randomized patrol strategies,while taking into account all of the system’s scheduling constraints. As a result, thepatrol schedules often become predictable, making it easier for people to avoid buyingtheir ticket.Against this background, the intelligent deployment of effective patrol strategies is akey challenge to deter fare evasion and maximize revenue in transit systems.Furthermore, since potential fare evaders can exploit knowledge about the patrolstrategy to avoid inspection, a randomized patrol strategy is needed for effectiveness.MDP TRUSTS Real World EvaluationAcknowledgements: We thank the Los Angeles Sheriff’sDepartment for their exceptional collaboration.Future WorkThe Mobile Application10h00 to 10h1511h00 to 11h20Officers of the LASD patrol one line of the Metro System. They perform eithertrain or ticket checks, depending on a large number of spatial and temporalconstraints (e.g., time of the day, trains schedule and station location as shown inthe figure). To model this problem a compact representation is used. A transitiongraph is defined encoding all the possible constraints of the problem (see Figure).The transition graph is used to define a zero-sum Bayesian Stackelberg game. Onedefender (the LASD) patrols the metro line by choosing a specific path of thetransition graph. There exists then multiple types of attacker (the fare evaders),one for each possible path. Each type can choose whether to buy his ticket or not.The game is solved using linear programming.Patrol schedules are derived by sampling the defender’s mixed strategy (variablesxij in the algorithm), obtained after solving the LP.The schedules generated using TRUSTS have been tested by the LASD in severallines of the LA Metro system. Results showed one key problem: the scheduleswere not robust to the execution uncertainty related to patrolling a public transitsystem.To address this shortcoming, the TRUSTS’s schedules are transformed into plans.The key idea is to generalize the transition graph into an MDP (see Figure below),i.e., the outcome of each action becomes stochastic (each action might lead to aspecific state or it might end up in another one). In so doing, the element ofexecution uncertainty is incorporated within the model. For instance, train orstation checks can be delayed for some time due to the officer having to deal withsome other problem.The solution of the MDP TRUSTS linear program is a mixed strategy for the defender. A pure strategy can then be generated by sampling the mixed strategy. However, a pure strategy now does not correspond to a simple schedule anymore. Rather itcorresponds to a plan: a mapping from states to actions, where each state represents a station of a metro line and a time slot. To visualize these plans, we developed a mobile application. The application is essentially a software tool which allows each patrolofficer to visualize its schedule and to record data related to each patrol shift. As shown in the figures, the application consists of three views.The resulting MDP is used to define a zero-sum Bayesian Stackelberg game. Thegame is defined similarly to the original TRUSTS formulation. One defender (theLASD) patrols the metro line by choosing a specific policy of the MDP. There existsthen multiple type of attacker (the fare evaders), one for each possible route. Theattacker can choose whether to buy or not his ticket. The game is solved usinglinear programming (a network flow).Schedule View: it is used to visualize the plan foreach patrol officer.Reporting View: it is used to submit all theinformation collected during a patrol shift.Summary View: it is used to submit thecollected information to a central databaseEach action specifies:• Type of action• Start / End timeSelect a new stationSelect the violationtypeReal world tests of the application have started on January 2013. Thus far, three tests have been run on the LA metrosystem (on the red line). Each test was conducted together with a team of three officers of the LASD. Further tests areplanned on the blue, green and expo line and will start in the middle of May.Thus far, both the MDP TRUSTS system and the mobile app have shown great potential to be used in several otherpublic transit system in the United States (e.g., in Chicago or Washington).The use of the mobile application opens up several different possibilities for research. The key reason is that theinformation collected within each shift is recorded by the reporting view. This data can then be used to improve thequality of the schedules. For instance, data about each evader that has been caught could be used to learn its behavior.Similarly, data about each execution interruption could be used to learn the uncertainty model related to the MDP.References A. Jiang, Z. Yin, C. Zhang, S. Kraus, M. Tambe Game-Theoretic Randomization for Security Patrolling withDynamic Execution Uncertainty. In AAMAS, 2013. Yin, Z., Jiang, A. X., Johnson, M. P., Tambe, M., Kiekintveld, C., Leyton-Brown, K., Sandholm, T., and Sullivan, J. 2012.TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems. In IAAI, 2012.