To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 14 Chapter 14 Waiting Lines and Queuing Theory Models

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Learning Objectives Students will be able to Describe the trade-off curves for cost-of-waiting time and cost-of- service. Understand the three parts of a queuing system: the calling population, the queue itself, and the service facility. Describe the basic queuing system configurations. Understand the assumptions of the common models dealt with in this chapter Analyze a variety of operating characteristics of waiting lines.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter Outline 14.1 Introduction 14.2 Waiting Line Costs 14.3 Characteristics of a Queuing System 14.4 Single-Channel Queuing Model with Poisson Arrivals and Exponential Service Times 14.5 Multiple-Channel Queuing Model with Poisson Arrivals and Exponential service Times 14.6 Constant Service Time Model 14.7 Finite Population Model

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter Outline – cont Some General Operating Characteristics Relationships 14.9 More Complex Queuing Models and the Use of Simulation

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Queuing Costs and Service Levels Cost of Operating Service Facility Service Level Total Expected Cost Cost of Providing Service Cost of Waiting Time O ptimal Service Level

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Waiting Line Cost Analysis Three Rivers Shipping Number of Stevedore Teams $1,000 35,00029,000$15,000$10,000 $6,000$12,00018,000 $24,000 $41,000$32,000$33,000$34,000 Average waiting time per ship Total ship hours lost Est. cost per hour of idle ship time Value of ships' lost time Stevedore teams salary Total Expected Cost Avg. number of ships arriving per shift

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Characteristics of a Waiting Line System Calling Population Unlimited Limited

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Characteristics of a Waiting Line System - cont. Arrival Characteristics Arrival rate distribution Poisson other Pattern of arrivals random scheduled Behavior of arrivals join the queue, and wait till served balk; refuse to join the line renege; leave the line

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 14-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Characteristics of a Waiting Line System- cont. Waiting Line Characteristics Length of the queue limited unlimited Service priority/Queue discipline FIFO other

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Characteristics of a Waiting Line System - cont. Service Facility Characteristics Number of channels single multiple Number of phases in service system single multiple Service time distribution negative exponential other

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Poisson Distribution for Arrival Times X P(X) P(X), = X P(X) P(X), = 4

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Basic Queuing System Configurations Single Channel, Single Phase Queue Service facility Facility 1 Facility 2 Single Channel, Multi-Phase Queue Service Facility

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Basic Queuing System Configurations Service facility 1 Service facility 2 Service facility 3 Multi-Channel, Single Phase Queue Multi-Channel, Multiphase Phase Queue Type 1 Service Facility Type 2 Service Facility

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Exponential Distribution for Service Times Probability (for Intervals of 1 Minute) Average Service Time of 1 Hour Average Service Time of 20 Minutes X

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Assumptions: M/M/1 Model 1. Queue discipline: FIFO 2. No balking or reneging 3. Independent arrivals; constant rate over time 4. Arrivals: Poisson distributed 5. Service times: negative exponential 6. Average service rate > average arrival rate

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Performance Measures of Queuing Systems Average time each customer spends in the queue Average length of the queue Average time each customer spends in the system Average number of customers in the system Probability that the service facility will be idle Utilization factor for the system Probability of a specific number of customers in the system

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Equations: M/M/1

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Equations: M/M/m

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Equations: M/D/1

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Equations Finite Population Model

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ General Operating Characteristics