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At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.(USE MODEL 1)
a. What is the average length of the waiting line?
b. What is the average time that a vehicle must wait to get through the system?
c. What is the utilization of the inspector?
d. What is the probability that when you arrive there will be three or more vehicles ahead of you?
A teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrival process. Calculate the average utilization of the teller. How many customers are in the b..
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