The average length of time that elapses between request and completion of letter. Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

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Answer 1

Question

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

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A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.

CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 5 hours. The standard deviation of the interarrival times is 5 hours. Executing each job takes on average 3 hours on the supercomputer and the standard deviation of the processing time is 4.5 hours. How long does a customer have to wait to have a job completed?

An emergency room (ER) at a Prisma Health Hospital has 10 total beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9 and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’ of this queueing system. The amount of time required for an ER doctor to treat a patient is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any calculations that were used to determine Wq for each number of servers that you considered until you meet the target metric.

Answer 2

Question

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

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Answer 3

Question

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

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Answer 4

Question

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Expert Solution & Answer

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Answer 5

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 6

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 7

Chapter 12.5, Problem 21P

a)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 8

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 9

b)

Summary Introduction

To determine: The average length of time that elapses between request and completion of letter if two typists are grouped into typing pool.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 10

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 11

c)

Summary Introduction

To determine: The results of Part (a) and Part (b).

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 12

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 13

d)

Summary Introduction

To determine: The probability that more than 0.2 days will elapse between request and completion of letter.

Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 12.3 - Prob. 1P Ch. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3P Ch. 12.3 - Prob. 4P Ch. 12.4 - Prob. 5P Ch. 12.4 - Prob. 6P Ch. 12.4 - Prob. 7P Ch. 12.4 - Prob. 8P Ch. 12.5 - Prob. 9P Ch. 12.5 - Prob. 10P

Solution Summary: The author explains that queueing theory is the mathematical model that can be used for the decision-making process regarding resources required to provide a service.

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