probabilities of no customer in 5 mins. Concept introduction : 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

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Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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: probabilities of exactly one customer in a min.

Concept introduction: 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: probabilities of exactly two customers in 2mins.

Concept introduction: 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: probability of at least two customers in 10 mins.

Concept introduction: 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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Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of (a) no customers in 20 minutes; (b) exactlyone customer in 5 minutes; (c) exactly 12 customers in a hour; and (d) fewer than threecustomers in 10 minutes.

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.a. How many customers would you expect to see, on average, at the coffee urn?b. How long would you expect it to take to get a cup of coffee?c. What percentage of time is the urn being used?d. What is the probability that three or more people are in the cafeteria?e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constanttime of 15 seconds, how does this change your answers to (a) and (b)?

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee urn? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria? e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?

Answer 2

Question

100%

Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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: probabilities of exactly one customer in a min.

Concept introduction: 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: probabilities of exactly two customers in 2mins.

Concept introduction: 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: probability of at least two customers in 10 mins.

Concept introduction: 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.

Expert Solution & Answer

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Answer 3

Question

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Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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: probabilities of exactly one customer in a min.

Concept introduction: 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: probabilities of exactly two customers in 2mins.

Concept introduction: 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: probability of at least two customers in 10 mins.

Concept introduction: 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.

Expert Solution & Answer

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Answer 4

Question

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Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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: probabilities of exactly one customer in a min.

Concept introduction: 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: probabilities of exactly two customers in 2mins.

Concept introduction: 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: probability of at least two customers in 10 mins.

Concept introduction: 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

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Answer 6

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Answer 7

Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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: probabilities of exactly one customer in a min.

Concept introduction: 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: probabilities of exactly two customers in 2mins.

Concept introduction: 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: probability of at least two customers in 10 mins.

Concept introduction: 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

Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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

Chapter 7.3, Problem 11P

a)

Summary Introduction

Interpretation: probabilities of no customer in 5 mins.

Concept introduction: 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

b)

Summary Introduction

Interpretation: probabilities of exactly one customer in a min.

Concept introduction: 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

b)

Summary Introduction

Interpretation: probabilities of exactly one customer in a min.

Concept introduction: 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

c)

Summary Introduction

Interpretation: probabilities of exactly two customers in 2mins.

Concept introduction: 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

c)

Summary Introduction

Interpretation: probabilities of exactly two customers in 2mins.

Concept introduction: 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

d)

Summary Introduction

Interpretation: probability of at least two customers in 10 mins.

Concept introduction: 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 15

d)

Summary Introduction

Interpretation: probability of at least two customers in 10 mins.

Concept introduction: 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 16

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Answer 18

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Answer 19

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

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Chapter 7 Solutions