Refer to the Journal of Transportation Engineering (May 2013) investigation of railroad track allocation at a railway station with 11 tracks, Exercise 2.16 (p. 40). A simple algorithm designed to minimize waiting time and bottlenecks is one in which engineers randomly assign one of the 11 tracks to a train entering the station.
a. What is the probability that track #7 is assigned to an entering train?
b. Unknown to the engineer, tracks #2, #5, and #10 will have maintenance problems. What is the probability that one of these problematic tracks is assigned to an entering train?
(Reference Exercise 2.16)
Railway track allocation. One of the problems faced by transportation engineers is the assignment of tracks to trains at a busy railroad station. Overused and/or underused tracks cause increases in maintenance costs and inefficient allocation of resources. The Journal of Transportation Engineering (May 2013) investigated the optimization of track allocation at a Chinese railway station with 11 tracks. Using a new algorithm designed to minimize waiting time and bottlenecks, engineers assigned tracks to 53 trains in a single day as shown in the accompanying table. Construct a Pareto diagram for the data. Use the diagram to help the engineers determine if the allocation of tracks to trains is evenly distributed and, if not, which tracks are underutilized and over utilized.
Track Assigned ............ Number of Trains
Track # 1 .................... 3
Track # 2 .................... 4
Track # 3 .................... 4
Track # 4 .................... 4
Track # 5 .................... 7
Track # 6 .................... 5
Track # 7 .................... 5
Track # 8 .................... 7
Track # 9 .................... 4
Track # 10 .................. 5
Track # 11 .................. 5
Total ........................ 53