CMA Intermediate · Operations Management and Strategic Management · Scheduling and Queuing Models
At a toll plaza lane modelled as M/M/1, vehicles arrive at an average of 40 per hour and the booth serves an average of 50 per hour. What is the traffic intensity (utilisation factor) and the average number of vehicles in the system?
Utilisation is 40/50 = 0.8 and the average number of vehicles in the system is 40/(50-40) = 4. The figure 3.2 is the average number waiting in the queue only, which excludes the vehicle currently being served.
- A0.8 and 4Correct
- B0.8 and 3.2
- C1.25 and 4
- D0.8 and 5
Explanation
Traffic intensity rho = lambda/mu = 40/50 = 0.8. Average number in system Ls = lambda/(mu - lambda) = 40/10 = 4. Using rho/(1-rho) = 0.8/0.2 = 4 confirms it. The value 3.2 is the average queue length Lq = rho x Ls, not the number in the system.
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