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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Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) services 5 customers/hr, on average. Assume an M/M/s queue system. Dean Smith suggests that the average time in the QUEUE should be 4 minutes or less. How fast must each service worker work to achieve 4 minutes on average in the Queue? That is, what is the service rate necessary to get to this goal? Please provide an answer to 2 decimal places.

The check-out area of a grocery store has the average customer interarrival time = 2 minutes, the average processing time of each cashier = 6 minutes, and in total 4 cashiers. The average waiting time for each customer is 8 minutes. What is the average number of customers in the system (including waiting and using the service)? a 3 b 7 c 6 d 4

In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the utilization? Note: Round your answer to 3 decimal places. What is the expected number of customers in the system (L)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the system (W)? Note: Express the waiting time in hours, round your answer to 3 decimal places. What is the expected number of customers in the queue(Lq)? Note: Round your answer to 3 decimal places. What is the expected waiting time in the queue(Wq)?

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