System utilization rate. Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

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Answer 1

Question

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

d)

Summary Introduction

To determine: The observations based on the results from part c.

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Students have asked these similar questions

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.

Determining the Number of ServersIn the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 40 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential).If the cost for a parts clerk is $30 per hour and the cost for a mechanic is $60 per hour, determine the optimum number of clerks to staff the counter. (Because of the high arrival rate, an infinite source may be assumed.)

In an M/M/1 queueing system, the arrival rate is 3 customers per hour and the service rate is 5 customers per hour. a. What is the utilization? (round your answer to 3 decimal places) b. What is the expected number of customers in the system (L)? (round your answer to 3 decimal places) c. What is the expected waiting time in the system (W)? (express the waiting time in hours, round your answer to 3 decimal places) d. What is the expected number of customers in the queue (Lq)? (round your answer to 3 decimal places) e. What is the expected waiting time in the queue (Wq)? (express the waiting time in hours, round your answer to 3 decimal places)

Answer 2

Question

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

d)

Summary Introduction

To determine: The observations based on the results from part c.

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Answer 3

Question

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

d)

Summary Introduction

To determine: The observations based on the results from part c.

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Answer 4

Question

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

d)

Summary Introduction

To determine: The observations based on the results from part c.

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Answer 5

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

d)

Summary Introduction

To determine: The observations based on the results from part c.

Answer 6

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

Answer 7

Chapter 18, Problem 17P

a)

Summary Introduction

To determine: System utilization rate.

Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.

Answer 8

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

Answer 9

b)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

Answer 10

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

Answer 11

c)

Summary Introduction

To determine: The average customer waiting for service for each class and waiting in each class on average.

Answer 12

d)

Summary Introduction

To determine: The observations based on the results from part c.

Answer 13

d)

Summary Introduction

To determine: The observations based on the results from part c.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 18.1 - Prob. 1.1RQ Ch. 18.1 - Prob. 1.2RQ Ch. 18 - Prob. 1DRQ Ch. 18 - Why do waiting lines form even though a service...Ch. 18 - Prob. 3DRQ Ch. 18 - Prob. 4DRQ Ch. 18 - What approaches do supermarkets use to offset...Ch. 18 - Prob. 6DRQ Ch. 18 - Prob. 7DRQ Ch. 18 - Prob. 8DRQ

Solution Summary: The author calculates the system utilization rate by adding all the total customer hours for each class and the result is divided with number of servers and customer process per hour.

Concept explainers

To determine: The average customer waiting for service for each class and waiting in each class on average.

To determine: The average customer waiting for service for each class and waiting in each class on average.

To determine: The observations based on the results from part c.

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Chapter 18 Solutions