Example - KCR

1. Example - KCR

2. Example - KCR weeds out Trouble makers • During the Ching Ming holiday, KCR, which runs train service from Hung Hom through Kowloon Tong to Lo We, imposed a fine of $100 for each passenger who did not use the appropriate ticket to Lo Wu Terminus and had to back his/her way out against the flow of the large crowd in order to purchase the appropriate ticket. What is the impact of these trouble makers on the average waiting time of the customers? The following is a qualitative analysis using queueing models. We consider two cases:

3. Example KCR - case 1 Everyone uses the right ticket: Let  be the arrival rate of passengers to the Lo Wu terminus exit and ms = 1.0 be the service time, the time required for each passenger to pass the exit. We assume 2 = 0. Then  =  ms = (1.0) = ,

4. Example KCR - case 2 One out of one hunderd is a trouble maker: Suppose the service time is X. X now has a distribution: P(X=1.0) = 0.99; P(X=10.0) = 0.01; that is, a passenger not possessing the appropriate ticket who squeezes his/her way out of the crowd occupies a service time equal to 10 times a normal passenger’s time. ms = E(X) = (0.99)(1.0) + (0.01))10.0) = 1.09

5. Example KCR: case 2 Under this situation, the average waiting time for a passenger is twice as long (or 100% longer) as the first case!