Customers arrive at a check-out counter in a supermarket in a Poisson fashion at a rate of 8 customers per hour. The supermarket has one cashier only. Thecheck-out time is exponentially distributed with a mean of 3.204 minutes. Assume the queue discipline is first in first out (FIFO). Use Arena to simulate the system,run one replication for 10,000,000 minutes (10 million minutes), use minutes as the base time unit. Choose the nearest answer for the following.Note: No need to upload your Arena ModelThe server utilizationChoose. +The average time in the queue;Choose.The probability that the server is idleChoose.The average number of cars in the queue; Choose.The average number of cars in the system Choose.The average time in systemChoose.

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Customers arrive at a check-out counter in a supermarket in a Poisson fashion at a rate of 8 customers per hour. The supermarket has one cashier only. The check-out time is exponentially distributed with a mean of 3.204 minutes. Assume the queue discipline is first in first out (FIFO). Use Arena to simulate the system run one replication for 10,000,000 minutes (10 milion minutes), use minutes as the base time unit Choose the nearest answer for the following. Note: No need to upload your Arena Model The server utilization Choose The average time in the queue Choose. The probability that the server is idle Choose. The average number of cars in the queue Choose. * The average number of cars in the system Choose. The average time in system Choose

Customers arrive at a check-out counter in a supermarket in a Poisson fashion at a rate of 8 customers per hour. The supermarket has one cashier only. The check-out time is exponentially distributed with a mean of 3.204 minutes. Assume the queue discipline is first in first out (FIFO). Use Arena to simulate the system run one replication for 10,000,000 minutes (10 milion minutes), use minutes as the base time unit Choose the nearest answer for the following. Note: No need to upload your Arena Model The server utilization Choose The average time in the queue Choose. The probability that the server is idle Choose. The average number of cars in the queue Choose. * The average number of cars in the system Choose. The average time in system Choose

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.
In the machine-repair model, assume that there are 2 repairman (each working at the same rate) and 3 machines. (a) Draw a rate diagram and determine the steady-state distribution if ! = 4 and µ = 8 . (b) Evaluate the expected total cost per hour if each repairman costs $10 per hour and broken machines cost $5 per hour
A computer system queues up batch jobs and processes them on an FCFS basis. Between 2 and 5 P.M., jobs arrive at an average rate of 30 per hour and require an average of 1.2 minutes of computer time. Assume the arrival process is Poisson and the processing times are exponentially distributed.a. What is the expected number of jobs in the system and in the queue in the steady state?b. What are the expected flow time and the time in the queue in the steady state?c. What is the probability that the system is empty?d. What is the probability that the queue is empty?e. What is the probability that the flow time of a job exceeds 10 minutes?
Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?
Moore’s television repair service receives an average of six TV sets per 8-hour day to be repaired. The service manager would like to be able to tell customers that they can expect 1-day service. What average repair time per set will the repair shop have to achieve to provide 1-day service, on average? (Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.)
All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has two screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival rate is 4.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. The facility manager's goal is to limit the average number of passengers waiting in line to 8 or fewer. How many screening stations must be…
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