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

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

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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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.
12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and isconstant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following:a. The average number of customers waiting in lineb. The average time customers spend in the systemc. The average number in the system
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?
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.
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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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?
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.)