Question 1

A camera is located 3km away from the entrance gate of a port tocount the number of incoming trucks. Trucks that have passed thecamera but have not passed the gate are considered to be in thequeueing system, in which some trucks are waiting to be serviced bythe gate and the other trucks are being serviced by the gate. Iftruck A passes the camera before truck B, it will pass the gate nolater than truck B (first-come-first serve). If truck A passes thecamera later than truck B, it will pass the gate no earlier thantruck B. Suppose the port does not work at mid-night, and the gateopens at 7:00am. The cumulative numbers of trucks that have passedthe camera and the gate at different times of a day are shown inthe table below. For brevity, assume trucks pass the camera and thegate only at 6:00, 6:10, 6:20, etc. That is, suppose that in thetable below 5 trucks passed the camera exactly at 6:10, and 10trucks pass the gate exactly at 7:10.

Table Q1-1. Cumulative numbers of trucks that have passed thecamera and the gate

Time	6:00	6:10	6:20	6:30	6:40	6:50
#camera	0	5	10	25	44	50
#gate	0	0	0	0	0	0
Time	7:00	7:10	7:20	7:30	7:40	7:50
#camera	60	62	81	88	95	105
#gate	0	10	20	35	55	75
Time	8:00	8:10	8:20	8:30	8:40	8:50
#camera	110	112	115	130	132	139
#gate	95	110	111	115	125	139

Q1.1: Calculate the average flow rate per hour of the system forthe three hours from 6:00am to 8:59:59am.

Q1.2: (You can use software tools, e.g., Microsoft Excel, tohelp answer this question.) Calculate the average flow time of allflow units.

Q1.3: (You can use software tools, e.g., Microsoft Excel, tohelp answer this question.) Calculate the average inventory of thesystem from 6:00am to 8:59:59am, that is, the average number oftrucks in the system at 6:00:01, 6:10:01, 6:20:01, 6:30:01,6:40:01, … 8:40:01, 8:50:01.