We switch to employ­ ing fuzzy arrival rates and fuzzy service rates to model the fuzzy queuing system in part three in Chapters 11 and 12. Two other items relating to fuzzy sets, needed in Chapters 13-17, are also in Chapter 2: (1) how we plan to handle the maximum/minimum of a fuzzy set;

1 Introduction.- 1.1 Introduction.- 1.2 Fuzzy Probabilities.- 1.3 Fuzzy Arrival/Service Rates.- 1.4 Optimization Models.- 1.5 Notation.- 1.6 References.- 2 Fuzzy Sets.- 2.1 Introduction.- 2.2 Fuzzy Sets.- 2.3 Fuzzy Arithmetic.- 2.4 Fuzzy Functions.- 2.5 Finding the Min/Max of a Fuzzy Number.- 2.6 Ordering/Ranking Fuzzy Numbers.- 2.7 References.- 3 Fuzzy Probabilities/Arrival Rates.- 3.1 Introduction.- 3.2 Fuzzy Probabilities from Confidence Intervals.- 3.3 Fuzzy Arrival/Service Rates.- 3.4 Fuzzy Numbers from Expert Opinion.- 3.5 Restricted Fuzzy Arithmetic.- 3.6 Computations.- 3.7 Figures.- 3.8 References.- 4 Fuzzy Markov Chains.- 4.1 Introduction.- 4.2 Fuzzy Regular Markov Chains.- 4.3 Fuzzy Absorbing Markov Chains.- 4.4 Other Fuzzy Markov Chains.- 4.5 References.- 5 Fuzzy Queuing Theory.- 5.1 Introduction.- 5.2 Queuing Theory.- 5.3 Fuzzy Queuing Theory.- 6 Computations: One Sever.- 6.1 Introduction.- 6.2 Calculations.- 6.3 References.- 7 Example: One Sever.- 7.1 Introduction.- 7.2 Computations.- 7.3 References.- 8 Computations: Two Servers.- 8.1 Introduction.- 8.2 Calculations.- 9 Example: Two Servers.- 9.1 Introduction.- 9.2 Computations.- 9.3 References.- 10 Computations: Three or More Servers.- 10.1 References.- 11 Fuzzy Arrival/Service Rates.- 11.1 Introduction.- 11.2 Fuzzy Steady State Probabilities.- 11.3 Fuzzy System Parameters.- 11.4 References.- 12 Example: Fuzzy Arrival/Service Rates.- 12.1 Introduction.- 12.2 One Server.- 12.3 Two Servers.- 12.4 Three or More Servers.- 12.5 References.- 13 Optimization: Without Revenue/Costs.- 13.1 Introduction.- 13.2 Fuzzy Probabilities.- 13.3 Fuzzy Arrival/Service Rates.- 13.4 References.- 14 Optimization: With Revenue/Costs.- 14.1 Introduction.- 14.2 Fuzzy Probabilities.- 14.3 Fuzzy Arrival/Service Rates.- 14.4 References.- 15 Burstiness.- 15.1 Introduction.- 15.2 Fuzzy Probabilities.- 15.3 Fuzzy Arrival/Service Rates.- 15.4 References.- 16 Long Tailed Distributions.- 16.1 Introduction.- 16.2 Fuzzy Probabilities.- 16.3 Fuzzy Arrival/Service Rates.- 16.4 References.- 17 Putting It All Together.- 17.1 Introduction.- 17.2 Fuzzy Probabilities.- 17.3 Fuzzy Arrival/Service Rates.- 18 Summary and Future Research.- 18.1 Introduction.- 18.2 Fuzzy Probabilities.- 18.3 Fuzzy arrival/Service Rate.- 18.4 Future Research.- 18.5 References.- 19 Computational Algorithms.- 19.1 Introduction.- 19.2 Computations: Fuzzy Probabilities.- 19.3 Computations: Fuzzy Arrivals and Service Rates.- 19.4 References.- List of Figures.- List of Tables.

This book presents important applications of soft computing and fuzziness to the growing field of web planning. A new method of using fuzzy numbers to model uncertain probabilities and how these can be used to model a fuzzy queuing system is demonstrated, as well as a method of modeling fuzzy queuing systems employing fuzzy arrival rates and fuzzy service rates. All the computations needed to get to the fuzzy numbers for system performance are described starting for the one server case to more than three servers. A variety of optimization models are discussed with applications to the average response times, server utilization, server and queue costs, as well as to phenomena identified with web sites such as "burstiness" and "long tailed distributions".