A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 7. Find the average time a person seeking information spends at the desk. 8. Find the expected time a person spends just waiting in line to have a question answered. 9. What is the probability there are exactly 2 people in the system? 10. What is the probability there are more than 4 people in the system?

A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 7. Find the average time a person seeking information spends at the desk. 8. Find the expected time a person spends just waiting in line to have a question answered. 9. What is the probability there are exactly 2 people in the system? 10. What is the probability there are more than 4 people in the system?

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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A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. 3. Find the proportion of the time that the employee is busy. 4. Find the average number of people receiving and waiting to receive information. 5. Find the average number of people waiting in line to get information.
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes you answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the proportion of the time that the employee is busy Find the average number of people receiving and waiting to receive some information
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes you answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the probability that the employee is idle?
A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes you answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the average number of people waiting in line to get some information Find the average time a person seeking information spends in the system Find the expected time a person spends just waiting in line to have a question answered (time in queue) Assume that the information desk employee in problem 1 earn $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of the time spent waiting in line. Find the total expected costs over an 8-hour day
new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Find the probability that the employee is idle. Find the proportion of the time that the employee is busy. Find the average number of people receiving and waiting to receive some information. Find the average number of people waiting in line to get some information. Find the average time a person seeking information spends in the system. Find the expected time a person spends just waiting in line to have a question answered (time in the queue).
Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system.(a) What is the average utilization of the cashier?(b) What is the average number of customers in the system?(c) What is the average number of customers in the line?(d) What is the average time spent in the system?(e) What is the average time spent in line?(f) The owner feels that if there are more than 5 customers at the cashier(waiting in the line and being served), we induce ill-will in our customers, and they will not return. What is the probability that there willbe more than 5 customers in the system?(g) Should the retail store consider creating a second
At a fashion retailer, there are 3 cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It has been estimated that the arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 17 minutes. Suppose that customers form a single line. What is the average length of the line (i.e., average number of customers in the waiting line)? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
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.)
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 arrivalprocess. Because of the range of possible transactions, the time taken to serve eachcustomer may be assumed to follow an exponential distribution with a mean timeof 7 minutes. Customers wait in a single queue to get their banking done and nocustomer leaves without service.a. Calculate the average utilization of the teller.b. Calculate how long customers spend on average to complete their transactionsat the bank (time in queue plus service time). What percentage of that time isspent queueing?
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.)
12-12 From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the average number of cars in line. average time a car waits before it is washed. average time a car spends in the service system. utilization rate of the car wash. probability that no cars are in the system.
The Universal Manufacturing Company produces a particular product in an assembly-line operation. One of themachines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, onaverage, according to an exponential distribution. Themachine operator can process an average of 10 parts perhour (Poisson distributed). Determine the average numberof parts waiting to be worked on, the percentage of timethe operator is working, and the percentage of time themachine is idle.