HW #7 17.2-3 17.5-1 17.5-9 Due Day: Nov 23.

Slides:

Advertisements

Similar presentations

Waiting Line Management

Advertisements

Lecture 10 Queueing Theory. There are a few basic elements common to almost all queueing theory application. Customers arrive, they wait for service in.

Many useful applications, especially in queueing systems, inventory management, and reliability analysis. A connection between discrete time Markov chains.

E&CE 418: Tutorial-4 Instructor: Prof. Xuemin (Sherman) Shen

Chapter Queueing Notation

INDR 343 Problem Session

Review of Probability Distributions

Readings Readings Chapter 11, Sections 1, 2, 3, 5 Waiting Line Models.

Lecture 13 – Continuous-Time Markov Chains

Operations research Quiz.

1 Waiting Lines Also Known as Queuing Theory. 2 Have you ever been to the grocery store and had to wait in line? Or maybe you had to wait at the bank.

Chap. 20, page 1051 Queuing Theory Arrival process Service process Queue Discipline Method to join queue IE 417, Chap 20, Jan 99.

Model Antrian By : Render, ect. Outline  Characteristics of a Waiting-Line System.  Arrival characteristics.  Waiting-Line characteristics.  Service.

1.(10%) Let two independent, exponentially distributed random variables and denote the service time and the inter-arrival time of a system with parameters.

Waiting Lines and Queuing Theory Models

HW # Due Day: Nov 23.

Queueing Theory (2). Home Work 12-9 and Due Day: October 31 (Monday) 2005.

Queuing Systems Chapter 17.

Multiple server queues In particular, we look at M/M/k Need to find steady state probabilities.

EMGT 501 Fall 2005 Midterm Exam SOLUTIONS.

EMGT 501 HW # Due Day: Sep 12.

Queueing Theory: Part I

Lec13, Ch.6, pp : Gap acceptance and Queuing Theory (Objectives)

CEE 320 Spring 2007 Queuing CEE 320 Steve Muench.

1 Overview of Queueing Systems Michalis Faloutsos Archana Yordanos The web.

Queuing. Elements of Waiting Lines  Population –Source of customers Infinite or finite.

Model Antrian By : Render, ect. M/M/1 Example 2 Five copy machines break down at UM St. Louis per eight hour day on average. The average service time.

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3  Terminology: The characteristics of a queuing system is captured by five parameters:

Lecture 14 – Queuing Systems

MNG221 - Management Science –

Solutions Queueing Theory 1

Queuing Theory (Waiting Line Models)

Introduction to Management Science

Queuing Theory Summary of results. 2 Notations Typical performance characteristics of queuing models are: L : Ave. number of customers in the system L.

The Poisson Process. A stochastic process { N ( t ), t ≥ 0} is said to be a counting process if N ( t ) represents the total number of “events” that occur.

Copyright ©: Nahrstedt, Angrave, Abdelzaher, Caccamo1 Queueing Systems.

1 1 © 2003 Thomson  /South-Western Slide Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

1 Queuing Analysis Overview What is queuing analysis? - to study how people behave in waiting in line so that we could provide a solution with minimizing.

Ch 6 Tech Notes OBJECTIVES

Structure of a Waiting Line System Queuing theory is the study of waiting lines Four characteristics of a queuing system: –The manner in which customers.

Queueing Theory What is a queue? Examples of queues: Grocery store checkout Fast food (McDonalds – vs- Wendy’s) Hospital Emergency rooms Machines waiting.

1 Systems Analysis Methods Dr. Jerrell T. Stracener, SAE Fellow SMU EMIS 5300/7300 NTU SY-521-N NTU SY-521-N SMU EMIS 5300/7300 Queuing Modeling and Analysis.

Queuing Theory. Introduction Queuing is the study of waiting lines, or queues. The objective of queuing analysis is to design systems that enable organizations.

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3  Mean inter-arrival time = 1/Ri = 1/R  Probability that the time between two arrivals.

1 1 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole.

Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies,

1 1 Slide © 2009 South-Western, a part of Cengage Learning Slides by John Loucks St. Edward’s University.

Structure of a Waiting Line System Queuing theory is the study of waiting lines Four characteristics of a queuing system: –The manner in which customers.

1 Ardavan Asef-Vaziri Sep-09Operations Management: Waiting Lines3 Example: The arrival rate to a GAP store is 6 customers per hour and has Poisson distribution.

Copyright ©: Nahrstedt, Angrave, Abdelzaher, Caccamo1 Queueing Systems.

1 1 Slide Chapter 12 Waiting Line Models n The Structure of a Waiting Line System n Queuing Systems n Queuing System Input Characteristics n Queuing System.

© 2015 McGraw-Hill Education. All rights reserved. Chapter 17 Queueing Theory.

1 BIS 3106: Business Process Management (BPM) Lecture Nine: Quantitative Process Analysis (2) Makerere University School of Computing and Informatics Technology.

Queueing Theory/Waiting Line: Models and Analysis Navneet Vidyarthi

Simulation of single server queuing systems

Topic VI. Multiple-Channel Queuing Model (Limited queue length system)

Abu Bashar Queuing Theory. What is queuing ?? Queues or waiting lines arise when the demand for a service facility exceeds the capacity of that facility,

Chapter 2 Simulation Examples. Simulation steps using Simulation Table 1.Determine the characteristics of each of the inputs to the simulation (probability.

Managerial Decision Making Chapter 13 Queuing Models.

Models of Traffic Flow 1.

Birth-Death Process Birth – arrival of a customer to the system

Introduction Notation Little’s Law aka Little’s Result

Solutions Queueing Theory 1

System Performance: Queuing

Solutions Queueing Theory 1

Mitchell Jareo MAT4340 – Operations Research Dr. Bauldry

Introduction to Queueing Theory

Solutions Queueing Theory 1

Topic IV. Single Channel Systems (Limited queue length system)

Queuing Theory III.

Presentation transcript:

HW #7 17.2-3 17.5-1 17.5-9 Due Day: Nov 23

17.2-3 Mom-and-Pop’s Grocery Store has a small adjacent parking lot with three parking spaces reserved for the store’s customers. During store hours, cars enter the lot and use one of the spaces at a mean rate of 2 per hour. For n = 0, 1, 2, 3, the probability Pn that exactly n spaces currently are being used is P0 = 0.2, P1 = 0.3, P2 = 0.3, P3 = 0.2. (a) Describe how this parking lot can be interpreted as being a queueing system. In particular, identify the customers and the servers. What is the service being provided? What constitutes a service time? What is the queue capacity? (b) Determine the basic measures of performance - L, Lq, W, and Wq - for this queueing system. (c) Use the results from part (b) to determine the average length of time that a car remains in a parking space.

17.2-3 (a) A parking lot is a queueing system for providing cars with parking opportunities. The parking spaces are servers. The service time is the amount of time a car spends in a system. The queue capacity is 0.

(b) (c)

17.5-1 Consider the birth-and-death process with all and for n = 3, 4, … (a) Display the rate diagram. (b) Calculate P0, P1, P2, P3, and Pn for n = 4, 5, ... (c) Calculate L, Lq, W, and Wq.

17.5-1 (a) 3 2 1 . . . 1 2 3 4 2 2 2 2

(b)

(c)

17.5-9 A certain small grocery store has a single checkout stand with a full-time cashier. Customers arrive at the stand “randomly” (i.e., a Poisson input process) at a mean rate of 30 per hour. When there is only one customer at the stand, she is processed by the cashier alone, with an expected service time of 1.5 minutes. However, the stock boy has been given standard instructions that whenever there is more than one customer at the stand, he is to help the cashier by bagging the groceries. This help reduces the expected time required to process a customer to 1 minute. In both cases, the service-time distribution is exponential. (a) Construct the rate diagram for this queueing system. (b) What is the steady-state probability distribution of the number of customers at the checkout stand? (c) Derive L for this system. (Hint: Refer to the derivation of L for the M/M/1 model at the beginning of Sec. 17.6.) Use this information to determine Lq, W, and Wq.

17.5-9 (a) . . . 1 2 3

(b)

(c)