CHAPTER 3 CALL CENTER QUEUING MODEL WITH LOGNORMAL SERVICE TIME DISTRIBUTION

Size: px
Start display at page:

Download "CHAPTER 3 CALL CENTER QUEUING MODEL WITH LOGNORMAL SERVICE TIME DISTRIBUTION"

Transcription

1 31 CHAPTER 3 CALL CENTER QUEUING MODEL WITH LOGNORMAL SERVICE TIME DISTRIBUTION 3.1 INTRODUCTION In this chapter, construction of queuing model with non-exponential service time distribution, performance measures of the call center, simulation experiment and results are presented. 3.2 MODEL CONSTRUCTION In the present work, queuing model with lognormal service time distribution is constructed to study the performance measures of call center. It is denoted by M/G/s+M with lognormal service time distribution. The basic assumptions behind the M/G/s+M queuing model with lognormal service time distribution of call center are as given below Inter arrival time of calls follows exponential distribution with the parameter 1 Service time of calls follows lognormal distribution with the parameters and The number of servers is s Abandonment time of calls follows exponential distribution with the parameter 2

2 PERFORMANCE MEASURES The call center queuing model involves large and complex model that incorporate many primitives for the call center management. The call center managers are very much interested in evaluating the performance measures of the call center. In order to measure the performance of the call center, the analysis of various performance measures is very much needed to the management of call centers. The commonly encountered performance measures in call center include service level, agent s utilization, abandoned calls, average waiting time, average queue length etc. Among the various performance measures of the call center, the important modeling primitives of complex call center queuing model in evaluating the performance measures appear to be abandoned calls and agent s utilization. These two primitives play an important role in the management of call center industry Abandoned Calls A call that is not served immediately hangs up. Otherwise, it joins the queue from which it will abandon if experiencing waiting time is greater than its patience time. This call is called abandoned calls. In industry, each abandoned calls represents a missed opportunity not only to provide a customer with excellent service but also to generate additional revenue. When trying to manage a large call center in heavy traffic, the call center management should consider the effect of abandoned calls in call center. The major drawback of call center queuing model is the ignorance of abandonment. Due to lack of understanding of abandonment behaviour, most modeler ignores the abandonment. This leads to many diffuiculties in the management of call center.

3 Agent s Utilization Agent s utilization is one of the important primitives of call center management. To improve the quality of service in call center, the agent s utilization is always maintained at maximum level. Due to ignorance of agent s utilization in call center, the call center faces over staffing or under staffing problem. To analyse the staffing problem in call center, agent s utilization plays an important role in call center management. 3.4 SIMULATION EXPERIMENT AND ANALYTICAL METHOD Experimental Setup The value of the parameter 1 of exponential inter arrival time of calls of call center queuing model is assumed as one. The value of the parameter 2 of exponential abandonment time distribution of calls of call center queuing model is assumed as one. The values of parameters and of lognormal service time distribution of calls of the call center queuing model are allowed to vary in their intervals (, ) and (, ) respectively. The numbers of servers are assumed as four. The service discipline of model is First-Come and First-Served Simulation Procedure For analysising the abandoned calls and agent s utilization, the approach taken to the simulation experiment was based on the terminology employed by EXTEND simulation software. This software has graphical structure to design through which users can understand the relationship between various modules of simulation model. The modification is also done easily in each module.

4 34 The simulation model for queuing model M/G/s+M is constructed with the help of hierarchical blocks that are used to design the structure of simulation model. The hierarchical blocks are Generate call type, Queue call type and Answer call type. In Generate call type hierarchical block, the inbound calls are generated, based on the assumed distribution and routed to agents for service. If the agent is busy, then calls are placed in the waiting line which is called as queue. The Queue call type hierarchical block transfers the calls from queue to agent whenever agent is free. If waiting time is more than patience time of call, then this call becomes abandoned call which is allowed leave the block through alternative connects. The Answer call type hierarchical block allows the agents to process the calls. The processing time of the calls is based on the assumed distribution in this block. Based on the values of parameters, the mean of exponential distribution for inter arrival and abandonment time distribution, mean and standard deviation of lognormal service time distribution are calculated and are used as input values to the simulation experiment for the model of call center queuing model M/G/s+M. The formulae for calculating the mean and standard deviation of lognormal distribution are Mean = e 2 2 Standard deviation = e e ( 1) The simulation experiment was carried out by fixing the mean of inter-arrival and abandonment time of calls as one time unit, number of servers as 4 and by varying the mean and standard deviation of lognormal service time distribution for the values of and in their intervals. The simulation experiment of the queuing model M/G/s+M was carried out for replications. Each replication has processed calls at 1 time unit

5 35 in four parallel servers. The results obtained from simulation experiment are the percentage of agent s utilization and abandoned calls for the model Analytical Procedure For the validation of the model, the analytical method is applied to find the agent s utilization. The formula for finding the agent s utilization of E ( s) queuing model is 1 where arrival rate of customer is 1, E(s) is the s mean of service time and s is the number of servers. 3.5 RESULTS BASED ON THE ANALYSIS OF AGENT S UTILIZATION The results are obtained from simulation experiment in terms of abandoned calls and agent s utilization for various input values of the model. The agent s utilization of the queuing model is analysed with the help of simulation method by fixing the parameters value of exponential inter arrival time and abandonment time distribution and allowing the parameters values of lognormal service time distribution in their range. In this section, the agent s utilizations for some of the values of parameters of the model are presented Variations of Percentage of Agent s Utilization with ( ) when = -7 Figure 3.1 shows the variations of percentage of agent s utilization for both analytical and simulation methods when value of is positive and the value of is taken as -7. When value of is greater than 4.5, the percentage of agent s utilization will be more than per cent. When value of

6 36 is from 3.5 to 4.5, the percentage of agent s utilization is increased from 1 per cent to per cent. When value of is less than 3.5, the percentage of agent s utilization will be less than 1 per cent Percentages of Agent's Utilization A nalytic al method S imulation method Figure 3.1 Variations of percentage of agent s utilization with sigma when = -7 The value of parameters of lognormal distribution is allowed to vary in their intervals. Due to this variation of value of parameters of service time distribution, the variance and mean of lognormal service time is changed. Since simulation experiment is done with help of variance and mean of service time distribution as input, the percentage of agent s utilization of call center is increased from per cent to per cent. Therefore, the performance measures of call center are varied from per cent to per cent in all the graphs.

7 Variations of Percentage of Agent s Utilization with when = - 4 It is observed from figure 3.2 that the variations of percentage of agent s utilization are changed from per cent to per cent for both analytical and simulation method when value of is positive and the value of is taken as -4. When the values of is greater than 3.5, the percentage of agent s utilization will be more than per cent. When values of is changed from 2.5 to 3.5, the percentage of agent s utilization is changed from 1 per cent to per cent. When value of is less than 2.5, the percentage of agent s utilization will be less than 1 per cent. Percentages of Agent's Utilization A nalytical method S imulation method Figure 3.2 Variations of percentage of agent s utilization with sigma when = - 4

8 Variations of Percentage of Agent s Utilization with when = - 3 The variations of the percentage of agent s utilization with sigma when = -3 is shown in figure 3.3 for both analytical and simulation method. It is increased from per cent to per cent when is positive values and the value of is taken as -3. When the value of is greater than 3.4, the percentage of agent s utilization will be more than per cent. When value of is changed from 2.5 to 3.4, the percentage of agent s utilization varies from 1 per cent to per cent. When value of is less than 2.5, the percentage of agent s utilization will be less than 1 per cent. Percentages of Agent's Utilization A nalytic al method S imulation method Figure 3.3 Variations of percentage of agent s utilization with sigma when = -3

9 Variations of Percentage of Agent s Utilization with when = -2 Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.4 Variations of percentage of agent s utilization with sigma when = -2 Figure 3.4 presents the variations of percentage of agent s utilization which are increased from per cent to per cent for both analytical and simulation method when value of moves in positive direction and the value of is taken as -2. When value of is greater than 3, the percentage of agent s utilization will be more than per cent. When value of ranges from 1.5 to 3, the percentage of agent s utilization will change from 1 per cent to per cent. When value of is less than 1.5, the percentage of agent s utilization will be less than 1 per cent.

10 3.5.5 Variations of Percentage of Agent s Utilization with when = -1 It is observed from Figure 3.5 that the variations of percentage of agent s utilization increase from per cent to per cent for both analytical and simulation method when value of is in the positive direction and the value of is taken as -1. Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.5 Variations of percentage of agent s utilization with sigma when = -1 When value of is greater than 2.5, the percentage of agent s utilization will be more than per cent. When value of moves from 1 to 2.5, the percentage of agent s utilization will be from 1 per cent to per cent. When value of is less than 1, the percentage of agent s utilization is less than 1 per cent.

11 Variations of Percentage of Agent s Utilization with When = The variations of percentage of agent s utilization are illustrated in figure 3.6 for both analytical and simulation method when the value of increases in positive direction and the value of is assumed as. The variation starts from 1 per cent to per cent. When value of is greater than 2, the percentage of agent s utilization will be more than per cent. When assumes the values from to 2, the percentage of agent s utilization will vary from 1 per cent to per cent. Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.6 Variations of percentage of agent s utilization with sigma when =

12 Variations of Percentage of Agent s Utilization with when = 1 Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.7 Variations of percentage of agent s utilization with sigma when = 1 From Figure 3.7, it is explored that the variations of percentage of agent s utilization has a growth from 3 per cent to per cent for both analytical and simulation method when value of is positive and the value of is taken as 1. When value of is greater than 1.5, the percentage of agent s utilization will be than per cent. When value of varies from to 1.5, the percentage of agent s utilization will lie from 3 per cent to per cent Variations of Percentage of Agent s Utilization with when = 2 It is observed from Figure 3.8 that the variations of percentage of agent s utilization range from per cent to per cent for both analytical

13 43 and simulation method when value of are positive and the value of is taken as 2. Figure 3.8 also shows that for the analytical method, the percentage of agent s utilization remains at per cent. 11 Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.8 Variations of percentage of agent s utilization with sigma when = Variations of Percentage of Agent s Utilization with when = 3 It is observed from Figure 3.9 that the variations of percentage of agent s utilization are increased from 98 per cent to per cent for both analytical and simulation method when value of is positive and the value of is assumed as 3. The percentage of agent s utilization goes near to per cent for positive value of

14 44 11 Percentages of Agent's Utilization Analytic al method S imulation method Figure 3.9 Variations of percentage of agent s utilization with sigma when = 3 Due to the variations of value of parameters in lognormal service time distribution of the queuing model M/G/s+M, the percentage of agent s utilization varies from per cent per cent 3.6 RESULTS BASED ON THE ANALYSIS OF ABANDONED CALLS The analysis of abandoned calls in call center is a very complex task because of the non availability of systematic method or procedures. Hence in this study, the simulation method is applied to analyse the call center. For this analysis, the variations of percentage of abandoned calls are obtained for various values

15 Variations of Percentages of Abandoned Calls with when µ =3 It is observed from Figure 3.1 that the variations of percentage of abandoned calls range from 51 per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as 3. It is seen that the value of percentage of abandoned calls increases with an increase value of. Percentage of Abandoned Calls Figure 3.1 Variations of percentages of abandoned calls with sigma when µ =3

16 Variations of Percentages of Abandoned Calls with when µ = 2 Percentage of Abandoned Calls Figure 3.11 Variations of percentages of abandoned calls with sigma when µ = 2 It is evident from Figure 3.11 that the variations of percentage of abandoned calls slope from 9 per cent to per cent when (sigma) value is allowed to vary in positive direction and the value of µ is assumed as 2.

17 Variations of Percentage of Abandoned Calls with when µ = 1 Percentage of Abandoned Calls Figure 3.12 Variations of percentage of abandoned calls with sigma when µ = 1 It is depicted from Figure 3.12 that the variations of percentage of abandoned calls shows an upward trend from per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as 1. When the value of is less than 1.5, the percentage of abandoned calls is less than 1 per cent Variations of Percentage of Abandoned Calls with when µ = Figure 3.13 exhibits that the variations of percentage of abandoned calls witness a positive trend ranging from per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as

18 48. Moreover, when value of is less than 2, the percentage of abandoned calls will be less than 1 per cent. Percentage of Abandoned Calls Figure 3.13 Variations of percentage of abandoned calls with sigma when µ = Variations of Percentage of Abandoned Calls with when µ = -1 Figure 3.14 reveals that the variations of percentage of abandoned calls experience a positive trend varying from per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as -1. Further, when value of is less than 2.5, the percentage of abandoned calls would be less than 1 per cent. The percentage of abandoned calls gradually increase when is greater than 2.5.

19 49 Percentage of Abandoned Calls Figure 3.14 Variations of percentage of abandoned calls with sigma when µ = Variations of Percentage of Abandoned Calls with when µ = -2 It is understood from Figure 3.15 that the curve on the variations of percentage of abandoned calls slope up from per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as -2. It is added that when the value of is less than 2.7, the percentage of abandoned calls will be less than 1 per cent. The curve rises smoothly when is greater than 2.7

20 5 Percentage of Abandoned Calls Figure 3.15 Variations of percentage of abandoned calls with sigma when µ = Variations of Percentage of Abandoned Calls with when µ = -3 Percentage of Abandoned Calls Figure 3.16 Variations of percentage of abandoned calls with sigma when µ = -3

21 51 Figure 3.16 shows that the variations of percentage of abandoned calls vary from per cent to per cent when (sigma) value is met the positive values and the value of µ is assumed as -3. It is seen that the percentage of abandoned calls is less than 1 per cent when value of ranges from to Variations of Percentages of Abandoned Calls with when µ = -4 Percentage of Abandoned Calls Figure 3.17 Variations of percentage of abandoned calls with sigma when µ = -4 Figure 3.17 finds that the variations of percentage of abandoned calls vary between per cent and per cent when (sigma) value is witnessed at an upward trend and the value of µ is assumed as -4. Further, when value of is less than 3.5, the percentage of abandoned calls will be below 1 per cent.

22 Variations of Percentage of Abandoned Calls with when µ = -7 Figure 3.18 presents that the variations of percentage of abandoned calls slope up from per cent to per cent when (sigma) value is allowed in positive direction and the value of µ is assumed as -7. While the value of is below to 4, the percentage of abandoned calls will be less than 1 per cent. Percentage of Abandoned Calls Figure 3.18 Variations of percentages of abandoned calls with sigma when µ = -7 Due to the variations of value of parameters in lognormal service time distribution of the queuing model M/G/s+M, the percentage of abandoned calls varies from per cent per cent

Basic Queuing Relationships

Basic Queuing Relationships Queueing Theory Basic Queuing Relationships Resident items Waiting items Residence time Single server Utilisation System Utilisation Little s formulae are the most important equation in queuing theory

More information

Waiting Times Chapter 7

Waiting Times Chapter 7 Waiting Times Chapter 7 1 Learning Objectives Interarrival and Service Times and their variability Obtaining the average time spent in the queue Pooling of server capacities Priority rules Where are the

More information

CALL CENTER PERFORMANCE EVALUATION USING QUEUEING NETWORK AND SIMULATION

CALL CENTER PERFORMANCE EVALUATION USING QUEUEING NETWORK AND SIMULATION CALL CENTER PERFORMANCE EVALUATION USING QUEUEING NETWORK AND SIMULATION MA 597 Assignment K.Anjaneyulu, Roll no: 06212303 1. Introduction A call center may be defined as a service unit where a group of

More information

Assignment #2 for Computer Networks

Assignment #2 for Computer Networks Assignment # for Computer Networks Savvas C. Nikiforou Department of Computer Science and Engineering University of South Florida Tampa, FL 6 Abstract The purpose of this assignment is to compare the queueing

More information

Rule-based Traffic Management for Inbound Call Centers

Rule-based Traffic Management for Inbound Call Centers Vrije Universiteit Amsterdam Research Paper Business Analytics Rule-based Traffic Management for Inbound Call Centers Auteur: Tim Steinkuhler Supervisor: Prof. Dr. Ger Koole October 7, 2014 Contents Preface

More information

Lecture 3 APPLICATION OF SIMULATION IN SERVICE OPERATIONS MANAGEMENT

Lecture 3 APPLICATION OF SIMULATION IN SERVICE OPERATIONS MANAGEMENT Lecture 3 APPLICATION OF SIMULATION IN SERVICE OPERATIONS MANAGEMENT Learning Objective To discuss application of simulation in services 1. SIMULATION Simulation is a powerful technique for solving a wide

More information

AS-D1 SIMULATION: A KEY TO CALL CENTER MANAGEMENT. Rupesh Chokshi Project Manager

AS-D1 SIMULATION: A KEY TO CALL CENTER MANAGEMENT. Rupesh Chokshi Project Manager AS-D1 SIMULATION: A KEY TO CALL CENTER MANAGEMENT Rupesh Chokshi Project Manager AT&T Laboratories Room 3J-325 101 Crawfords Corner Road Holmdel, NJ 07733, U.S.A. Phone: 732-332-5118 Fax: 732-949-9112

More information

Service Management Capacity Planning and Queuing Models

Service Management Capacity Planning and Queuing Models Service Management Capacity Planning and Queuing Models Univ.-Prof. Dr.-Ing. Wolfgang Maass Chair in Economics Information and Service Systems (ISS) Saarland University, Saarbrücken, Germany WS 2011/2012

More information

Scheduling Policies, Batch Sizes, and Manufacturing Lead Times

Scheduling Policies, Batch Sizes, and Manufacturing Lead Times To appear in IIE Transactions Scheduling Policies, Batch Sizes, and Manufacturing Lead Times Saifallah Benjaafar and Mehdi Sheikhzadeh Department of Mechanical Engineering University of Minnesota Minneapolis,

More information

Conclusions and Suggestions for Future Research

Conclusions and Suggestions for Future Research 6 Conclusions and Suggestions for Future Research In this thesis dynamic inbound contact centers with heterogeneous agents and retrials of impatient customers were analysed. The term dynamic characterises

More information

Outline. Simulation examples will be given in queuing, inventory, reliability and network analysis.

Outline. Simulation examples will be given in queuing, inventory, reliability and network analysis. Simulation Examples Today I ll present several examples of simulations that can be performed by devising a simulation table either manually or with a spreadsheet. This will provide insight into the methodology

More information

Process simulation. Enn Õunapuu enn.ounapuu@ttu.ee

Process simulation. Enn Õunapuu enn.ounapuu@ttu.ee Process simulation Enn Õunapuu enn.ounapuu@ttu.ee Content Problem How? Example Simulation Definition Modeling and simulation functionality allows for preexecution what-if modeling and simulation. Postexecution

More information

Simple Queuing Theory Tools You Can Use in Healthcare

Simple Queuing Theory Tools You Can Use in Healthcare Simple Queuing Theory Tools You Can Use in Healthcare Jeff Johnson Management Engineering Project Director North Colorado Medical Center Abstract Much has been written about queuing theory and its powerful

More information

UNITY CALL CENTER REPORTING. Version 1.0

UNITY CALL CENTER REPORTING. Version 1.0 UNITY CALL CENTER REPORTING Version 1.0 Contents Introduction... 3 Accessing the Reports... 3 Abandoned Call Report... 4 Settings:... 4 Report:... 5 Agent Activity Detail Report... 6 Settings:... 6 Report:...

More information

Performance Analysis of a Distributed System under Time-Varying Workload and Processor Failures

Performance Analysis of a Distributed System under Time-Varying Workload and Processor Failures Performance Analysis of a Distributed System under Time-Varying Workload and Processor Failures Helen Karatza Department of Informatics, Aristotle University 5 Thessaloniki, Greece Email: karatza@csd.auth.gr

More information

Queuing Formulas. 1 Notation 2. 2 Basic Queueing Formulas 2

Queuing Formulas. 1 Notation 2. 2 Basic Queueing Formulas 2 Queuing Formulas Contents 1 Notation 2 2 Basic Queueing Formulas 2 3 Single-Server Queues 3 3.1 Formulas...................................... 3 3.2 Some additional useful facts...........................

More information

ENGINEERING SOLUTION OF A BASIC CALL-CENTER MODEL

ENGINEERING SOLUTION OF A BASIC CALL-CENTER MODEL ENGINEERING SOLUTION OF A BASIC CALL-CENTER MODEL by Ward Whitt Department of Industrial Engineering and Operations Research Columbia University, New York, NY 10027 Abstract An algorithm is developed to

More information

Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I

Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA - Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting

More information

Chapter 10. Verification and Validation of Simulation Models Prof. Dr. Mesut Güneş Ch. 10 Verification and Validation of Simulation Models

Chapter 10. Verification and Validation of Simulation Models Prof. Dr. Mesut Güneş Ch. 10 Verification and Validation of Simulation Models Chapter 10 Verification and Validation of Simulation Models 10.1 Contents Model-Building, Verification, and Validation Verification of Simulation Models Calibration and Validation 10.2 Purpose & Overview

More information

THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT. Roger Klungle AAA Michigan. Introduction

THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT. Roger Klungle AAA Michigan. Introduction THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT Roger Klungle AAA Michigan Introduction With recent advances in technology and the changing nature of business, call center management has become a rapidly

More information

Modelling the performance of computer mirroring with difference queues

Modelling the performance of computer mirroring with difference queues Modelling the performance of computer mirroring with difference queues Przemyslaw Pochec Faculty of Computer Science University of New Brunswick, Fredericton, Canada E3A 5A3 email pochec@unb.ca ABSTRACT

More information

Service Level Variability of Inbound Call Centers

Service Level Variability of Inbound Call Centers Service Level Variability of Inbound Call Centers Alex Roubos, Ger Koole & Raik Stolletz Department of Mathematics, VU University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands Chair

More information

PARTIAL CROSS TRAINING IN CALL CENTERS WITH UNCERTAIN ARRIVALS AND GLOBAL SERVICE LEVEL AGREEMENTS. D. J. Medeiros

PARTIAL CROSS TRAINING IN CALL CENTERS WITH UNCERTAIN ARRIVALS AND GLOBAL SERVICE LEVEL AGREEMENTS. D. J. Medeiros Proceedings of the 07 Winter Simulation Conference S. G. Henderson, B. Biller, M.-H. Hsieh, J. Shortle, J. D. Tew, and R. R. Barton, eds. PARTIAL CROSS TRAINING IN CALL CENTERS WITH UNCERTAIN ARRIVALS

More information

DISCRETE EVENT SIMULATION COURSE INSTRUCTOR DR. J. BOOKBINDER PROJECT REPORT. Simulation Study of an Inbound Call Center SACHIN JAYASWAL

DISCRETE EVENT SIMULATION COURSE INSTRUCTOR DR. J. BOOKBINDER PROJECT REPORT. Simulation Study of an Inbound Call Center SACHIN JAYASWAL DISCRETE EVENT SIMULATION MSCI 632 SPRING 5 COURSE INSTRUCTOR DR. J. BOOKBINDER PROJECT REPORT Simulation Study of an Inbound Call Center Submitted by SACHIN JAYASWAL & GAURAV CHHABRA Table of Contents

More information

IST 301. Class Exercise: Simulating Business Processes

IST 301. Class Exercise: Simulating Business Processes IST 301 Class Exercise: Simulating Business Processes Learning Objectives: To use simulation to analyze and design business processes. To implement scenario and sensitivity analysis As-Is Process The As-Is

More information

UNIT 2 QUEUING THEORY

UNIT 2 QUEUING THEORY UNIT 2 QUEUING THEORY LESSON 24 Learning Objective: Apply formulae to find solution that will predict the behaviour of the single server model II. Apply formulae to find solution that will predict the

More information

LECTURE - 1 INTRODUCTION TO QUEUING SYSTEM

LECTURE - 1 INTRODUCTION TO QUEUING SYSTEM LECTURE - 1 INTRODUCTION TO QUEUING SYSTEM Learning objective To introduce features of queuing system 9.1 Queue or Waiting lines Customers waiting to get service from server are represented by queue and

More information

LECTURE 16. Readings: Section 5.1. Lecture outline. Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process

LECTURE 16. Readings: Section 5.1. Lecture outline. Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process LECTURE 16 Readings: Section 5.1 Lecture outline Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process Number of successes Distribution of interarrival times The

More information

AS-D2 THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT. Dr. Roger Klungle Manager, Business Operations Analysis

AS-D2 THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT. Dr. Roger Klungle Manager, Business Operations Analysis AS-D2 THE ROLE OF SIMULATION IN CALL CENTER MANAGEMENT Dr. Roger Klungle Manager, Business Operations Analysis AAA Michigan 1 Auto Club Drive Dearborn, MI 48126 U.S.A. Phone: (313) 336-9946 Fax: (313)

More information

Cumulative Diagrams: An Example

Cumulative Diagrams: An Example Cumulative Diagrams: An Example Consider Figure 1 in which the functions (t) and (t) denote, respectively, the demand rate and the service rate (or capacity ) over time at the runway system of an airport

More information

Performance Analysis, Autumn 2010

Performance Analysis, Autumn 2010 Performance Analysis, Autumn 2010 Bengt Jonsson November 16, 2010 Kendall Notation Queueing process described by A/B/X /Y /Z, where Example A is the arrival distribution B is the service pattern X the

More information

Network Design Performance Evaluation, and Simulation #6

Network Design Performance Evaluation, and Simulation #6 Network Design Performance Evaluation, and Simulation #6 1 Network Design Problem Goal Given QoS metric, e.g., Average delay Loss probability Characterization of the traffic, e.g., Average interarrival

More information

Simulation of Call Center With.

Simulation of Call Center With. Chapter 4 4.1 INTRODUCTION A call center is a facility designed to support the delivery of some interactive service via telephone communications; typically an office space with multiple workstations manned

More information

Prescriptive Analytics. A business guide

Prescriptive Analytics. A business guide Prescriptive Analytics A business guide May 2014 Contents 3 The Business Value of Prescriptive Analytics 4 What is Prescriptive Analytics? 6 Prescriptive Analytics Methods 7 Integration 8 Business Applications

More information

Recent Advances in Web System Performance Modeling with Queueing Networks. Author: Nikola Janevski Class: CS 736 Software Performance Engineering

Recent Advances in Web System Performance Modeling with Queueing Networks. Author: Nikola Janevski Class: CS 736 Software Performance Engineering Recent Advances in Web System Performance Modeling with Queueing Networks Author: Nikola Janevski Class: CS 736 Software Performance Engineering 1 How are Web systems different Many users Multi-tier architecture

More information

MTAT.03.231 Business Process Management (BPM) Lecture 6 Quantitative Process Analysis (Queuing & Simulation)

MTAT.03.231 Business Process Management (BPM) Lecture 6 Quantitative Process Analysis (Queuing & Simulation) MTAT.03.231 Business Process Management (BPM) Lecture 6 Quantitative Process Analysis (Queuing & Simulation) Marlon Dumas marlon.dumas ät ut. ee Business Process Analysis 2 Process Analysis Techniques

More information

1 st year / 2014-2015/ Principles of Industrial Eng. Chapter -3 -/ Dr. May G. Kassir. Chapter Three

1 st year / 2014-2015/ Principles of Industrial Eng. Chapter -3 -/ Dr. May G. Kassir. Chapter Three Chapter Three Scheduling, Sequencing and Dispatching 3-1- SCHEDULING Scheduling can be defined as prescribing of when and where each operation necessary to manufacture the product is to be performed. It

More information

OPTIMUM TOUR SCHEDULING OF IT HELP DESK AGENTS

OPTIMUM TOUR SCHEDULING OF IT HELP DESK AGENTS OPTIMUM TOUR SCHEDULING OF IT HELP DESK AGENTS Hesham K. Alfares Systems Engineering Department College of Computer Sciences and Engineering King Fahd University of Petroleum & Minerals Saudi Arabia hesham@ccse.kfupm.edu.sa

More information

Forecasting and Planning a Multi-Skilled Workforce: What You Need To Know

Forecasting and Planning a Multi-Skilled Workforce: What You Need To Know Welcome Forecasting and Planning a Multi-Skilled Workforce: What You Need To Know Presented by: Skills Scheduling What is it? Scheduling that takes into account the fact that employees may have one or

More information

Keywords: Dynamic Load Balancing, Process Migration, Load Indices, Threshold Level, Response Time, Process Age.

Keywords: Dynamic Load Balancing, Process Migration, Load Indices, Threshold Level, Response Time, Process Age. Volume 3, Issue 10, October 2013 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Load Measurement

More information

A Contact Center Crystal Ball:

A Contact Center Crystal Ball: A Contact Center Crystal Ball: Marrying the Analyses of Service, Cost, Revenue, and Now, Customer Experience Ric Kosiba, Ph.D. Vice President Interactive Intelligence, Inc. Table of Contents Introduction...

More information

Load Balancing and Switch Scheduling

Load Balancing and Switch Scheduling EE384Y Project Final Report Load Balancing and Switch Scheduling Xiangheng Liu Department of Electrical Engineering Stanford University, Stanford CA 94305 Email: liuxh@systems.stanford.edu Abstract Load

More information

Glossary TASKE Call Center Management Tools Version 7.0. A caller terminates the call before an agent can answer.

Glossary TASKE Call Center Management Tools Version 7.0. A caller terminates the call before an agent can answer. Glossary of Terms Term Abandoned Call ABSBH Account Code ACD ACD Call ACD Call Center ACD Queue ACD Record ACD Search Agent Agent Group Agent Identifier Agent Report Definition A caller terminates the

More information

Aachen Summer Simulation Seminar 2014

Aachen Summer Simulation Seminar 2014 Aachen Summer Simulation Seminar 2014 Lecture 07 Input Modelling + Experimentation + Output Analysis Peer-Olaf Siebers pos@cs.nott.ac.uk Motivation 1. Input modelling Improve the understanding about how

More information

NOVEL PRIORITISED EGPRS MEDIUM ACCESS REGIME FOR REDUCED FILE TRANSFER DELAY DURING CONGESTED PERIODS

NOVEL PRIORITISED EGPRS MEDIUM ACCESS REGIME FOR REDUCED FILE TRANSFER DELAY DURING CONGESTED PERIODS NOVEL PRIORITISED EGPRS MEDIUM ACCESS REGIME FOR REDUCED FILE TRANSFER DELAY DURING CONGESTED PERIODS D. Todinca, P. Perry and J. Murphy Dublin City University, Ireland ABSTRACT The goal of this paper

More information

Performance Analysis of Computer Systems

Performance Analysis of Computer Systems Performance Analysis of Computer Systems Introduction to Queuing Theory Holger Brunst (holger.brunst@tu-dresden.de) Matthias S. Mueller (matthias.mueller@tu-dresden.de) Summary of Previous Lecture Simulation

More information

Drop Call Probability in Established Cellular Networks: from data Analysis to Modelling

Drop Call Probability in Established Cellular Networks: from data Analysis to Modelling Drop Call Probability in Established Cellular Networks: from data Analysis to Modelling G. Boggia, P. Camarda, A. D Alconzo, A. De Biasi and M. Siviero DEE - Politecnico di Bari, Via E. Orabona, 4-7125

More information

Robust Staff Level Optimisation in Call Centres

Robust Staff Level Optimisation in Call Centres Robust Staff Level Optimisation in Call Centres Sam Clarke Jesus College University of Oxford A thesis submitted for the degree of M.Sc. Mathematical Modelling and Scientific Computing Trinity 2007 Abstract

More information

A TUTORIAL ON MODELLING CALL CENTRES USING DISCRETE EVENT SIMULATION

A TUTORIAL ON MODELLING CALL CENTRES USING DISCRETE EVENT SIMULATION A TUTORIAL ON MODELLING CALL CENTRES USING DISCRETE EVENT SIMULATION Benny Mathew Manoj K. Nambiar Innovation Lab Performance Engineering Innovation Lab Performance Engineering Tata Consultancy Services

More information

Time series Forecasting using Holt-Winters Exponential Smoothing

Time series Forecasting using Holt-Winters Exponential Smoothing Time series Forecasting using Holt-Winters Exponential Smoothing Prajakta S. Kalekar(04329008) Kanwal Rekhi School of Information Technology Under the guidance of Prof. Bernard December 6, 2004 Abstract

More information

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4 4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

More information

Fluid Approximation of a Priority Call Center With Time-Varying Arrivals

Fluid Approximation of a Priority Call Center With Time-Varying Arrivals Fluid Approximation of a Priority Call Center With Time-Varying Arrivals Ahmad D. Ridley, Ph.D. William Massey, Ph.D. Michael Fu, Ph.D. In this paper, we model a call center as a preemptive-resume priority

More information

1. Implementation of a testbed for testing Energy Efficiency by server consolidation using Vmware

1. Implementation of a testbed for testing Energy Efficiency by server consolidation using Vmware 1. Implementation of a testbed for testing Energy Efficiency by server consolidation using Vmware Cloud Data centers used by service providers for offering Cloud Computing services are one of the major

More information

Overview of Monte Carlo Simulation, Probability Review and Introduction to Matlab

Overview of Monte Carlo Simulation, Probability Review and Introduction to Matlab Monte Carlo Simulation: IEOR E4703 Fall 2004 c 2004 by Martin Haugh Overview of Monte Carlo Simulation, Probability Review and Introduction to Matlab 1 Overview of Monte Carlo Simulation 1.1 Why use simulation?

More information

RESOURCE POOLING AND STAFFING IN CALL CENTERS WITH SKILL-BASED ROUTING

RESOURCE POOLING AND STAFFING IN CALL CENTERS WITH SKILL-BASED ROUTING RESOURCE POOLING AND STAFFING IN CALL CENTERS WITH SKILL-BASED ROUTING by Rodney B. Wallace IBM and The George Washington University rodney.wallace@us.ibm.com Ward Whitt Columbia University ward.whitt@columbia.edu

More information

Minimize Wait Time and Improve the Waiting Experience

Minimize Wait Time and Improve the Waiting Experience Improving the Customer Experience Minimize Wait Time and Improve the Waiting Experience www.lavi.com (888) 285-8605 Overview Waiting lines easily become the source of tension between customers and businesses

More information

Discrete-Event Simulation

Discrete-Event Simulation Discrete-Event Simulation Prateek Sharma Abstract: Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the

More information

A Content-Based Load Balancing Algorithm for Metadata Servers in Cluster File Systems*

A Content-Based Load Balancing Algorithm for Metadata Servers in Cluster File Systems* A Content-Based Load Balancing Algorithm for Metadata Servers in Cluster File Systems* Junho Jang, Saeyoung Han, Sungyong Park, and Jihoon Yang Department of Computer Science and Interdisciplinary Program

More information

A SIMULATION STUDY FOR DYNAMIC FLEXIBLE JOB SHOP SCHEDULING WITH SEQUENCE-DEPENDENT SETUP TIMES

A SIMULATION STUDY FOR DYNAMIC FLEXIBLE JOB SHOP SCHEDULING WITH SEQUENCE-DEPENDENT SETUP TIMES A SIMULATION STUDY FOR DYNAMIC FLEXIBLE JOB SHOP SCHEDULING WITH SEQUENCE-DEPENDENT SETUP TIMES by Zakaria Yahia Abdelrasol Abdelgawad A Thesis Submitted to the Faculty of Engineering at Cairo University

More information

An Overview of Routing and Staffing Algorithms in Multi-Skill Customer Contact Centers. Submitted version

An Overview of Routing and Staffing Algorithms in Multi-Skill Customer Contact Centers. Submitted version An Overview of Routing and Staffing Algorithms in Multi-Skill Customer Contact Centers Ger Koole & Auke Pot Department of Mathematics, Vrije Universiteit Amsterdam, The Netherlands Submitted version 6th

More information

The problem with waiting time

The problem with waiting time The problem with waiting time Why the only way to real optimization of any process requires discrete event simulation Bill Nordgren, MS CIM, FlexSim Software Products Over the years there have been many

More information

Variance and Standard Deviation. Variance = ( X X mean ) 2. Symbols. Created 2007 By Michael Worthington Elizabeth City State University

Variance and Standard Deviation. Variance = ( X X mean ) 2. Symbols. Created 2007 By Michael Worthington Elizabeth City State University Variance and Standard Deviation Created 2 By Michael Worthington Elizabeth City State University Variance = ( mean ) 2 The mean ( average) is between the largest and the least observations Subtracting

More information

Quantitative Analysis of Cloud-based Streaming Services

Quantitative Analysis of Cloud-based Streaming Services of Cloud-based Streaming Services Fang Yu 1, Yat-Wah Wan 2 and Rua-Huan Tsaih 1 1. Department of Management Information Systems National Chengchi University, Taipei, Taiwan 2. Graduate Institute of Logistics

More information

This paper describes an interactive spreadsheet-based tool that can be used to generate data representative

This paper describes an interactive spreadsheet-based tool that can be used to generate data representative Vol. 8, No. 2, January 2008, pp. 55 64 issn 1532-0545 08 0802 0055 informs I N F O R M S Transactions on Education An Interactive Spreadsheet-Based Tool to Support Teaching Design of Experiments S. T.

More information

Simulation Software 1

Simulation Software 1 Simulation Software 1 Introduction The features that should be programmed in simulation are: Generating random numbers from the uniform distribution Generating random variates from any distribution Advancing

More information

The Effects of Start Prices on the Performance of the Certainty Equivalent Pricing Policy

The Effects of Start Prices on the Performance of the Certainty Equivalent Pricing Policy BMI Paper The Effects of Start Prices on the Performance of the Certainty Equivalent Pricing Policy Faculty of Sciences VU University Amsterdam De Boelelaan 1081 1081 HV Amsterdam Netherlands Author: R.D.R.

More information

Accurate Forecasting: The Heart of Call Center Success

Accurate Forecasting: The Heart of Call Center Success Accurate Forecasting: The Heart of Call Center Success Accurate Forecasting: The Heart of Call Center Success Page 2 Overview In times of economic crisis and dwindling profits, it is more important than

More information

8. Time Series and Prediction

8. Time Series and Prediction 8. Time Series and Prediction Definition: A time series is given by a sequence of the values of a variable observed at sequential points in time. e.g. daily maximum temperature, end of day share prices,

More information

Veri cation and Validation of Simulation Models

Veri cation and Validation of Simulation Models of of Simulation Models mpressive slide presentations Faculty of Math and CS - UBB 1st Semester 2010-2011 Other mportant Validate nput- Hypothesis Type Error Con dence nterval Using Historical nput of

More information

Proceedings of the 2010 Winter Simulation Conference B. Johansson, S. Jain, J. Montoya-Torres, J. Hugan, and E. Yücesan, eds.

Proceedings of the 2010 Winter Simulation Conference B. Johansson, S. Jain, J. Montoya-Torres, J. Hugan, and E. Yücesan, eds. Proceedings of the 2010 Winter Simulation Conference B. Johansson, S. Jain, J. Montoya-Torres, J. Hugan, and E. Yücesan, eds. DOES THE ERLANG C MODEL FIT IN REAL CALL CENTERS? Thomas R. Robbins D. J. Medeiros

More information

Examining Self-Similarity Network Traffic intervals

Examining Self-Similarity Network Traffic intervals Examining Self-Similarity Network Traffic intervals Hengky Susanto Byung-Guk Kim Computer Science Department University of Massachusetts at Lowell {hsusanto, kim}@cs.uml.edu Abstract Many studies have

More information

Chapter 3 RANDOM VARIATE GENERATION

Chapter 3 RANDOM VARIATE GENERATION Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.

More information

PROCESS FLOW IMPROVEMENT PROPOSAL OF A BATCH MANUFACTURING SYSTEM USING ARENA SIMULATION MODELING

PROCESS FLOW IMPROVEMENT PROPOSAL OF A BATCH MANUFACTURING SYSTEM USING ARENA SIMULATION MODELING PROCESS FLOW IMPROVEMENT PROPOSAL OF A BATCH MANUFACTURING SYSTEM USING ARENA SIMULATION MODELING Chowdury M. L. RAHMAN 1 Shafayet Ullah SABUJ 2 Abstract: Simulation is frequently the technique of choice

More information

Using Fuzzy Logic Control to Provide Intelligent Traffic Management Service for High-Speed Networks ABSTRACT:

Using Fuzzy Logic Control to Provide Intelligent Traffic Management Service for High-Speed Networks ABSTRACT: Using Fuzzy Logic Control to Provide Intelligent Traffic Management Service for High-Speed Networks ABSTRACT: In view of the fast-growing Internet traffic, this paper propose a distributed traffic management

More information

OPTIMIZED PERFORMANCE EVALUATIONS OF CLOUD COMPUTING SERVERS

OPTIMIZED PERFORMANCE EVALUATIONS OF CLOUD COMPUTING SERVERS OPTIMIZED PERFORMANCE EVALUATIONS OF CLOUD COMPUTING SERVERS K. Sarathkumar Computer Science Department, Saveetha School of Engineering Saveetha University, Chennai Abstract: The Cloud computing is one

More information

Creating operational shift schedules for third-level IT support: challenges, models and case study

Creating operational shift schedules for third-level IT support: challenges, models and case study 242 Int. J. Services Operations and Informatics, Vol. 3, Nos. 3/4, 2008 Creating operational shift schedules for third-level IT support: challenges, models and case study Segev Wasserkrug*, Shai Taub,

More information

Internet Traffic Variability (Long Range Dependency Effects) Dheeraj Reddy CS8803 Fall 2003

Internet Traffic Variability (Long Range Dependency Effects) Dheeraj Reddy CS8803 Fall 2003 Internet Traffic Variability (Long Range Dependency Effects) Dheeraj Reddy CS8803 Fall 2003 Self-similarity and its evolution in Computer Network Measurements Prior models used Poisson-like models Origins

More information

APPENDIX 1 USER LEVEL IMPLEMENTATION OF PPATPAN IN LINUX SYSTEM

APPENDIX 1 USER LEVEL IMPLEMENTATION OF PPATPAN IN LINUX SYSTEM 152 APPENDIX 1 USER LEVEL IMPLEMENTATION OF PPATPAN IN LINUX SYSTEM A1.1 INTRODUCTION PPATPAN is implemented in a test bed with five Linux system arranged in a multihop topology. The system is implemented

More information

Arena 9.0 Basic Modules based on Arena Online Help

Arena 9.0 Basic Modules based on Arena Online Help Arena 9.0 Basic Modules based on Arena Online Help Create This module is intended as the starting point for entities in a simulation model. Entities are created using a schedule or based on a time between

More information

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random

More information

How Useful Is Old Information?

How Useful Is Old Information? 6 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 11, NO. 1, JANUARY 2000 How Useful Is Old Information? Michael Mitzenmacher AbstractÐWe consider the problem of load balancing in dynamic distributed

More information

Lecture 8 Performance Measurements and Metrics. Performance Metrics. Outline. Performance Metrics. Performance Metrics Performance Measurements

Lecture 8 Performance Measurements and Metrics. Performance Metrics. Outline. Performance Metrics. Performance Metrics Performance Measurements Outline Lecture 8 Performance Measurements and Metrics Performance Metrics Performance Measurements Kurose-Ross: 1.2-1.4 (Hassan-Jain: Chapter 3 Performance Measurement of TCP/IP Networks ) 2010-02-17

More information

Accurate Forecasting: The Heart of Call Center Success

Accurate Forecasting: The Heart of Call Center Success Accurate Forecasting: The Heart of Call Center Success Accurate Forecasting: The Heart of Call Center Success Page 2 Overview In times of economic crisis and dwindling profits, it is more important than

More information

Simulation Tools Evaluation using Theoretical Manufacturing Model

Simulation Tools Evaluation using Theoretical Manufacturing Model Acta Polytechnica Hungarica Vol. 10, No. 2, 2013 Simulation Tools Evaluation using Theoretical Manufacturing Model Pavol Semanco, David Marton Faculty of Manufacturing Technologies with seat in Presov

More information

ITEE Journal. Information Technology & Electrical Engineering International Journal of Information Technology and Electrical Engineering

ITEE Journal. Information Technology & Electrical Engineering International Journal of Information Technology and Electrical Engineering Performance Analysis of Short Term Scheduling Algorithms 1 Muhammad Usman, 2 Aamir Iqbal, 3 Ehsan Ahmed, 4 Shaukat Ghani, 5 Muhammad Adnan Khan 1,2,3,4 Federal Urdu University of Arts, Science and Technology,

More information

Web Server Software Architectures

Web Server Software Architectures Web Server Software Architectures Author: Daniel A. Menascé Presenter: Noshaba Bakht Web Site performance and scalability 1.workload characteristics. 2.security mechanisms. 3. Web cluster architectures.

More information

Deployment of express checkout lines at supermarkets

Deployment of express checkout lines at supermarkets Deployment of express checkout lines at supermarkets Maarten Schimmel Research paper Business Analytics April, 213 Supervisor: René Bekker Faculty of Sciences VU University Amsterdam De Boelelaan 181 181

More information

Chapter 5: CPU Scheduling. Operating System Concepts 8 th Edition,

Chapter 5: CPU Scheduling. Operating System Concepts 8 th Edition, Chapter 5: CPU Scheduling, Silberschatz, Galvin and Gagne 2009 Objectives To introduce CPU scheduling, which is the basis for multiprogrammed operating systems To describe various scheduling algorithms

More information

Optimizing Stochastic Supply Chains via Simulation: What is an Appropriate Simulation Run Length?

Optimizing Stochastic Supply Chains via Simulation: What is an Appropriate Simulation Run Length? Optimizing Stochastic Supply Chains via Simulation: What is an Appropriate Simulation Run Length? Arreola-Risa A 1, Fortuny-Santos J 2, Vintró-Sánchez C 3 Abstract The most common solution strategy for

More information

Exploiting Simulation for Call Centre Optimization

Exploiting Simulation for Call Centre Optimization , June 30 - July 2, 2010, London, U.K. Exploiting Simulation for Centre Optimization Salman khtar and Muhammad Latif bstract The global trend in developed economies from manufacturing towards services

More information

User s Guide for ContactCenters Simulation Library

User s Guide for ContactCenters Simulation Library User s Guide for ContactCenters Simulation Library Generic Simulator for Blend and Multi-skill Call Centers Version: March 17, 2014 Eric Buist This document introduces a generic simulator for blend and

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

System Simulation - Modeling and Analysis

System Simulation - Modeling and Analysis System Simulation - Modeling and Analysis Jason R. W. Merrick Jill Hardin Department of Statistical Sciences & Operations Research Virginia Commonwealth University Table of Contents 1 Simulation Modeling

More information

Quantile-Quantile Plot (QQ-plot) and the Normal Probability Plot. Section 6-6 : Normal Probability Plot. MAT 2377 (Winter 2012)

Quantile-Quantile Plot (QQ-plot) and the Normal Probability Plot. Section 6-6 : Normal Probability Plot. MAT 2377 (Winter 2012) MAT 2377 (Winter 2012) Quantile-Quantile Plot (QQ-plot) and the Normal Probability Plot Section 6-6 : Normal Probability Plot Goal : To verify the underlying assumption of normality, we want to compare

More information

A MANAGER-FRIENDLY PLATFORM FOR SIMULATION MODELING AND ANALYSIS OF CALL CENTER QUEUEING SYSTEMS. Robert Saltzman Vijay Mehrotra

A MANAGER-FRIENDLY PLATFORM FOR SIMULATION MODELING AND ANALYSIS OF CALL CENTER QUEUEING SYSTEMS. Robert Saltzman Vijay Mehrotra Proceedings of the 2004 Winter Simulation Conference R.G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters, eds. A MANAGER-FRIENDLY PLATFORM FOR SIMULATION MODELING AND ANALYSIS OF CALL CENTER QUEUEING

More information

Appendix: Simple Methods for Shift Scheduling in Multi-Skill Call Centers

Appendix: Simple Methods for Shift Scheduling in Multi-Skill Call Centers MSOM.1070.0172 Appendix: Simple Methods for Shift Scheduling in Multi-Skill Call Centers In Bhulai et al. (2006) we presented a method for computing optimal schedules, separately, after the optimal staffing

More information

EXAM IN COURSE [EKSAMEN I EMNE] TTM4110 Dependability and Performance with Discrete event Simulation [Pålitelighet og ytelse med simulering]

EXAM IN COURSE [EKSAMEN I EMNE] TTM4110 Dependability and Performance with Discrete event Simulation [Pålitelighet og ytelse med simulering] Norwegian University of Science and Technology Department of Telematics Page 1 of 20 Contact during exam [Faglig kontakt under eksamen]: Poul E. Heegaard (94321 / 99286858) EXAM IN COURSE [EKSAMEN I EMNE]

More information

Part 1 : 07/27/10 21:30:31

Part 1 : 07/27/10 21:30:31 Question 1 - CIA 593 III-64 - Forecasting Techniques What coefficient of correlation results from the following data? X Y 1 10 2 8 3 6 4 4 5 2 A. 0 B. 1 C. Cannot be determined from the data given. D.

More information

Introduction to Scheduling 1

Introduction to Scheduling 1 CPU Scheduling Basic Concepts Scheduling Criteria Scheduling Algorithms FCFS, SJF, RR Exponential Averaging Multi-level Queue Scheduling Performance Evaluation Scheduling Terminology Scheduling Terminology

More information

Addressing Arrival Rate Uncertainty in Call Center Workforce Management

Addressing Arrival Rate Uncertainty in Call Center Workforce Management 1 Addressing Arrival Rate Uncertainty in Call Center Workforce Management Thomas R. Robbins Penn State University Abstract Workforce management is a critical component of call center operations. Since

More information