Game theory project: Train Queuing Model Jonathan Ang, Poh Jer Lin, Quek Yu Han, Ryan Goh Introduction In Singapore at least, the train seat is a prized, invaluable commodity. Many commuters share a common desire for physical comfort during the long rides they suffer and the least embarrassing or objectionable way to obtain physical comfort on the train (other than leaning against the wall) would be to get a seat and sit down. Depending on the time of the day and the train station in question, the probability of getting a seat on a train varies widely, though it is generally very low, negligible even. On several occasions, a person may find himself in a quandary: whether or not he should take the first train he sees (where he will definitely not get a seat immediately after boarding) or if he should wait until a tr ain with empty seats arrives. There are two conflicting factors that will influence the person’s decision: time and comfort . The importance of these two factors varies from individual to individual: for instance, a businessman rushing to seal a deal will place far more importance on time than comfort while a tired student looking to replenish lost sleep on the train will place more importance on comfort than time. A special situation also arises at certain train stations, namely the stations situated near the termini of each line. At such stations, commuters see king comfort have the option of taking the train going the opposite direction to have a guaranteed seat when the train returns to the station. Whether or not this choice is viable depends on the number of stops between the current station and the terminus, as well as how crowded the trains going in the opposite direction are. Thus, in this study, we have modeled games after these dilemmas to determine the best course ofaction for any given commuter. A variable kdescribes the commuter’s preference for comfort/saved time, and through calculations, we can determine if the commuter would be better off boarding t he first train or waiting for a train with seats, and if the commuter should wait, we can determine how long (in terms of number of trains) the commuter should wait to enjoy the maximum payoff. Model This model is based on a dynamic game. It involves a queuing system, whereby passengers on the train platform decide whether to board the train or not according to the order in which they reached
