A vending machine dispenses hot chocolate or coffee. Service time is 45 seconds per cup and is constant. Customers arrive at a mean rate of 59 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers

A vending machine dispenses hot chocolate or coffee. Service time is 45 seconds per cup and is constant. Customers arrive at a mean rate of 59 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers

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 vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 76 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers
In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions. a. What is λ? b. What is μ? c. Find probability of no units in the system. d. Find average number of units in the system. e. Find average time in the waiting line. f. Find average time in the system. g. Find probability that there is one person waiting. h. Find probability an arrival will have to wait. Please show a corrct solution and answer. Thank you.
Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation.a. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? How long would a customer expect to spend in the camera department (total time)?b. What is the utilization of the clerk?c. What is the probability that there are more than two people in the camera department (excluding the clerk)?d. Another clerk has been hired for the camera department who also takes an average of six minutes to serve each arrival. How long would a customer expect to spend in the department now?
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Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ?customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places).
A car wash takes a constant time of 5.2 minutes in its automated car wash cycle. Autos arrive following a poisson distribution at the rate of 8 per hour. The owner wants to know: (a) the average waiting time in line. (b) the average length of the line. (c) the average utilization rate. (d) the average time in the system. (e) the average number of customers in the system.
Customers enter the camera department of a store at the average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. a. As a casual observer, how many people would you expect to see in the camera de- partment (excluding the clerk)? How long would a customer expect to spend in the camera department (total time)? b. What is the utilization of the clerk? c. What is the probability that there are more than two people in the camera department (excluding the clerk)? d. Another clerk has been hired for the camera department who also takes an average of six minutes to serve each arrival. How long would a customer expect to spend in the department now?
One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 1.5 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)
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The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?