A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 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 customers ?? 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 ??

A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 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 customers ?? 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 ??

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.4: Important Queueing Relationships

Problem 6P

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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
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?
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 4.0 per hour. It will take Benny an average of 11 minutes to give a haircut. Based on these figures, find the following:a. The average number of customers waiting. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.) b. The average time a customer waits. (Round your answer to 2 decimal places.) c. The average time a customer is in the shop. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) d. The average utilization of Benny’s time. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)
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?
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?
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…
A fast-food restaurant has one drive-through window.On average, 40 customers arrive per hour at thewindow. It takes an average of one minute to serve acustomer. Assume that interarrival and service timesare exponentially distributed.a. On average, how many customers are waiting in line?b. On average, how long does a customer spend at therestaurant (from time of arrival to time service iscompleted)?c. What fraction of the time are more than three carsin line? (Here, the line includes the car, if any,being serviced.)
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?
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following a The average number of customers waiting b. The average time a customer waits.