utilization of employees. Concept introduction : The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

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Answer 1

Question

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

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Customers send emails to a help desk that has three employees who answer theemails (and this is their only responsibility). Customer requests arrive accordingto a Poisson process with a rate of 30 per hour. It takes on average 4 minutes towrite a response email; the standard deviation of this service times is 2 minutes.b. What is the average time an email spends waiting before an employee startsworking on it? What is the average time to complete the emails requests (fromthe time the email is sent to when it is answered)?

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Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.5 hours per call. Requests for copier repairs come in at a mean rate of 2.1 per eight-hour day (assume Poisson). a. Determine the average number of customers awaiting repairs. (Round your answer to 2 decimal places.) Number of customers b. Determine system utilization. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.) System utilization % c. Determine the amount of time during an eight-hour day that the repairman is not out on a call. (Use your rounded answer from Part b. Round your answer to 2 decimal places.) Amount of time hours d. Determine the probability of two or more customers in the system. (Do not round intermediate calculations. Round your answer to…

Answer 2

Question

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

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Answer 3

Question

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

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Answer 4

Question

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

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Answer 5

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 6

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 7

Chapter 7.5, Problem 24P

a)

Summary Introduction

Interpretation: utilization of employees.

Concept introduction: The M/M/1 queue assumes poisonarrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 8

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 9

b)

Summary Introduction

interpretation: the average time an email spends waiting before an employee starts working on it.

concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 10

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 11

c)

Summary Introduction

Interpretation:average number of emails in the system waiting to be worked on.

Concept introduction: The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 12

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 13

D)

Summary Introduction

Interpretation:options available to decrease customers waiting.

Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 7.1 - Prob. 1P Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 10P

Solution Summary: The author explains that the M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in an FCFS fashion.

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