Problem 1 At the California border inspection station, vehicles arrive at the ra

Question

Problem 1 At the California border inspection station, vehicles arrive at the rate of 36 per hour following a Poisson distribution. For simplicity, assume that there is only one lane and one inspector, who can consider vehicles at the rate of 40 per minute also according to a Poisson distribution. What is the average length of the waiting line? What is the average time that a vehicle must wait to get through the system? What is the utilization of the inspector? What is the probability that when you arrive there will be three or more vehicles ahead of you? a. b. Problem 2 The California border inspection station discussed in the prior question, is considering the addition of a second inspector. The vehicles would wait in one lane and then be directed to the first available inspector. Arrival rates would remain the same (36 per hour) and the new inspector would process vehicles at the same rate as the first (40 per hour) a. What would be the average length of the waiting line? b.What would be the average time that a vehicle must wait to get through the system? What proportion of the time would the inspection station be empty? What is the average utilization of each inspector?

Explanation / Answer

Problem 1 At the California border inspection station, vehicles arrive at the rate of 36 per hour following a Poisson distribution. For simplicity, assume that there is only one lane and one inspector, who can consider vehicles at the rate of 40 per minute also according to a Poisson distribution. What is the average length of the waiting line? What is the average time that a vehicle must wait to get through the system? What is the utilization of the inspector? What is the probability that when you arrive there will be three or more vehicles ahead of you? a. b. Problem 2 The California border inspection station discussed in the prior question, is considering the addition of a second inspector. The vehicles would wait in one lane and then be directed to the first available inspector. Arrival rates would remain the same (36 per hour) and the new inspector would process vehicles at the same rate as the first (40 per hour) a. What would be the average length of the waiting line? b.What would be the average time that a vehicle must wait to get through the system? What proportion of the time would the inspection station be empty? What is the average utilization of each inspector?

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.