Please Hwlp!!!!!!! b. What is the average total time it takes for a vehicle to get through the system?Note: Round your answer to 2 decimal places.Average timeminutesc. What is the utilization of the inspector?Note: Round your answer to 1 decimal place.Utilization%d. What is the probability that when you arrive there will be three or more vehicles ahead of you?Note: Round your answer to 1 decimal place.Probability% At a border inspection station, vehicles arrive at the rate of 12 per hour in a Poisson distribution. For simplicity in this problem, assumethat there is only one lane and one inspector, who can inspect vehicles at the rate of 18 per hour in an exponentially distributedfashion.a. What is the average length of the waiting line?Note: Round your answer to 2 decimal places.Average lengthcustomersb. What is the average total time it takes for a vehicle to get through the system?Note: Round your answer to 2 decimal places.Average timeminutesc. What is the utilization of the inspector?Note: Round your answer to 1 decimal place.Utilization%

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Answered: b. What is the average total time it…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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At a border inspection station, vehicles arrive at the rate of 8 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 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
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 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average total time it takes for a vehicle to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there are only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.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 vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup andis constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poissondistributed.A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?
Western National Bank wants to provide a drive-through window for its customers. Management estimates that customers will arrive in their cars at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of 20 per hour. Assuming Poisson arrivals and exponential service, find the following: Capacity utilization of the teller. Average number of cars in the waiting line Average number in the system. Average waiting time in line. Average waiting time in the system, including service.
Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.
The vehicles are entering the parking area of the a mall.There is only one ticket line to get and pay a parkingticket. Each ticket purchase takes an average of 18seconds. The average arrival rate is 3 vehicles/minute.Find the average length of queue, average waiting timein queue and average time spent by the vehicles in thesystem assuming M/M/1 queuing.

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