1 Introduction                                     1  (2)
2 Characterization of Inbound Call Centers         3  (18)
  2.1 What is an Inbound Call Center?              3  (2)
  2.2 Performance Measures and Objective           5  (7)
  Functions
    2.2.1 Technical Performance Measures           5  (3)
    2.2.2 Economic Performance Measures            8  (3)
    2.2.3 Objective Functions for Operational      11 (1)
    Planning
  2.3 Operational Personnel Planning in Inbound    12 (9)
  Call Centers
    2.3.1 Main Tasks of Operational Personnel      12 (1)
    Planning
    2.3.2 Call Forecasting                         13 (2)
    2.3.3 Weekly Personnel Scheduling              15 (7)
      2.3.3.1 Current Planning Process in          15 (1)
      Practice
      2.3.3.2 Agent Requirements Planning          16 (2)
      2.3.3.3 Shift Scheduling and Rostering       18 (1)
      2.3.3.4 A Simultaneous Planning Approach     19 (2)
3 Classification of Queueing Models of Inbound     21 (26)
Call Centers
  3.1 Characteristics of Queueing Models of        21 (1)
  Call Centers
  3.2 Classification by Customers and Agents       22 (6)
    3.2.1 Arrival Process                          22 (1)
    3.2.2 Waiting Behavior                         23 (1)
    3.2.3 Distribution of Service Time             24 (2)
    3.2.4 Homogeneity of Customers and Agents      26 (2)
  3.3 Routing Decisions in Call Centers            28 (4)
    3.3.1 Overview                                 28 (1)
    3.3.2 Customer Selection                       29 (2)
    3.3.3 Agent Selection                          31 (1)
  3.4 Limitation of the Waiting Room               32 (5)
  3.5 Review of the Literature                     37 (10)
    3.5.1 Overview                                 37 (1)
    3.5.2 Homogeneous Customers and Agents         37 (3)
    Homogeneous
    3.5.3 Heterogeneous Customers and              40 (8)
    Heterogeneous Agents
      3.5.3.1 Introduction of the M-Design         40 (1)
      3.5.3.2 The M-Design with Priority-Based     40 (3)
      Routing Policies
      3.5.3.3 Special Cases of the M-Design        43 (4)
      with Priority-Based Routing Policies
4 Queueing Models of Call Centers with             47 (50)
Homogeneous Customers and Homogeneous Agents
  4.1 Common Features                              47 (1)
  4.2 The M/M/c and M/M/c/K Queueing Models
  with Patient Customers   4Q
    4 .2.l Description and Derivation of           48 (5)
    Performance Measures for the M/M/c/K
    Queueing Model
    4.2.2 Description and Derivation of            53 (2)
    Performance Measures for the M/M/c/oo
    Queueing Model
    4.2.3 Numerical Results                        55 (19)
      4.2.3.1 Impact of the Number of Trunks       55 (13)
      4.2.3.2 Economies of Scale   6l
      4.2.3.3 Impact of Talk Time                  68 (2)
      4.2.3.4 Optimal Number of Agents and         70 (4)
      Trunks in Large Call Center
  4.3 An M/M/c/K Queueing Model with Impatient     74 (23)
  Customers
    4.3.1 Model Description and Derivation of      74 (8)
    Performance Measures
    4.3.2 Numerical Results                        82 (15)
      4.3.2.1 Impact of Customer Impatience:       82 (5)
      Reneging
      4.3.2.2 Impact of Customer Impatience:       87
      Balking
      4.3.2.3 Impact of Customer Impatience:       80 (10)
      Dependencies between Reneging and Balking
      4.3.2.4 Optimal Number of Agents and the     90 (7)
      Impact of the Number of Trunks
    4.4 Management Implications of the
    Numerical Results 96
5 Queueing Model of a Call Center with two         97 (68)
Classes of Customers and Skill-Based Routing
  5.1 Description of the Queueing System           97 (4)
  5.2 Description of the State Space               101(5)
    5.2.1 Representation of the States             101(2)
    5.2.2 Division and Size of the State Space     103(3)
  5.3 Steady-State Equations                       106(10)
    5.3.1 Steady-State Equations for States        108(3)
    with Waiting A- and B-Customers
    5.3.2 Steady-State Equations for States        111(2)
    with Waiting A- and without Waiting
    B-Customers
    5.3.3 Steady-State Equations for States        113(1)
    with Waiting B- and without Waiting
    A-Customers
    5.3.4 Steady-State Equations for States        114(2)
    without Waiting Customers
  5.4 Determination of Performance Measures        116(12)
    5.4.1 Solution of the Steady-State Equations   116(3)
    5.4.2 Derivation of Technical Performance      119(5)
    Measures
    5.4.3 Validation of the Derivation for         124(4)
    Special Cases
  5.5 Numerical Results                            128(35)
    5.5.1 Impact of Flexible Agents: Effects of    129(16)
    Priority-Based Customer Selection and
    Pooling
      5.5.1.1 Impact of Priority-Based Customer    129(5)
      Selection
      5.5.1.2 Comparison of Call Centers with      134(7)
      Completely Crosstrained or Completely
      Specialized Agents
      5.5.1.3 Advantages of Adding Generalists     141(4)
      Instead of Specialists
    5.5.2 Impact of the Processing Times of        145(4)
    Generalists
    5.5.3 Impact of the Allocation of Trunks       149(5)
    5.5.4 Impact of the Allocation of a Fixed      154(17)
    Number of Agents
      5.5.4.1 Identically Distributed              154(5)
      Processing Times for Specialists and
      Generalists
      5.5.4.2 Different Processing Times for       159(4)
      Generalists and Specialists
  5.6 Management Implications of the Numerical     163(2)
  Results
6 Conclusions and Suggestions for Further          165(2)
Research
A Algorithms for Call Center Models with           167(12)
Homogeneous Customers and Agents
  A.1 Computations for the M/M/c/K Model with      167(3)
  Patient Customers
  A.2 Computations for the M/M/c/oo Model with     170(1)
  Patient Customers
  A.3 Computations for the M/M/c/K Model with      171(8)
  Impatient Customers
    A.3.1 Computation of Steady-State              171(2)
    Probabilities
    A.3.2 Computation of the Waiting Time          173(6)
    Distributions
B Appendix for the Queueing Model of a Call        179(24)
Center with two Classes of Customers and
Skill-Based Routing
  B.1 Derivation of the Number of States           179(3)
  B.2 Derivation of the Remaining Steady-State     182(11)
  Equations
    B.2.1 Steady-State Equations for States        182(3)
    with Waiting A- and without Waiting
    B-Customers
    B.2.2 Steady-State Equations for States        185(3)
    with Waiting B- and without Waiting
    A-Customers
    B.2.3 Steady-State Equations for States        188(5)
    without Waiting Customers
  B.3 Algorithms Used for Performance Analysis     193(10)
    B.3.1 Description of Data Structures and       193(7)
    Algorithms
    B.3.2 Behavior of the Algorithm                200(3)
Glossary of Notation                               203(2)
List of Figures                                    205(6)
List of Tables                                     211(2)
References                                         213