Answer Happy

Bus riders begin to line up (queue) to board a bus 5 minutes before the departure time. For the first two minutes, passengers arrive at the rate of 5 per minute and then at the rate of 10 per minute of the remaining 3 minutes. Boarding starts 2 ½ minutes before the departure. It takes each passenger an average of 3 seconds to board. Assume that the system can be modelled as a deterministic queuing system. 6.a (5 marks) Sketch the queuing diagram for the queuing system. Clearly label axes, and the arrivals and services, indicating the appropriate arrival and service rates. 6.b (4 marks) What is the maximum length of the queue? 6.c (4 marks) When will the queue clear? 6.d (4 marks) What is the longest any passenger will wait in the queue? 6.e (3 marks) Clearly show your answers to Q6.b), Q6.c) and Q6.d) on your sketch in Q6.a).