The El Farol Bar Problem for next generation systems

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32 CHAPTER 3. ANALYSIS AND EXTENSION OF THE STOCHASTIC ALGORITHM N /M 60/100 60/100 60/100 iterations 5000 4 · 10 4 2 · 10 6 µ 0.01 0.01 0.001 average 59.133400 58.161900 n/a yet std 0.999281 1.673139 n/a yet time 6 sec 5 min 2 weeks... Table 3.4: Behaviour of the ‘modified budget’ algorithm for budget=10 and staying at home=6. financial difficulties they do not attend bars. For values of this ratio much less than 1 the algorithm settles down almost instantly. If the budget is large the results are similar to the original ‘partial information’ algorithm (Table: 3.5 and Figure: 3.6). frequency 0 200 400 600 budget 10 100 10 10 10 waiting 0 0 3 10 6 average 59.385200 59.287200 59.292000 48.981200 58.165750 std 2.916301 1.132950 1.861538 7.423848 4.851578 Table 3.5: Simulation results for budget algorithms. Histogram of attendances in budget with b=10 35 40 45 50 attendances 55 60 65 70 frequency 0 200 400 600 800 1000 Histogram of attendances in modified budget with b=10,w=6 40 50 attendances 60 70 Figure 3.5: histograms for budget algorithms (b = 10, w = 0/6). Although budget algorithms are a variation of the partial information algorithm, their histograms (figure: 3.5) are quite different. Especially the first which has a wider distribution than the original one.
3.3. BUDGET ALGORITHMS 33 probabities for each agent probabities for each agent probabities for each agent 1.0 0.8 0.6 0.4 0.2 0.0 0 1000 2000 3000 4000 5000 time (iterations) 1.0 0.8 0.6 0.4 0.2 0.0 0 1.0 1000 2000 time (iterations) 3000 4000 0.8 0.6 0.4 0.2 0.0 0 1000 2000 3000 4000 5000 time (iterations) attendance attendance attendance 100 80 60 40 20 0 0 1000 2000 3000 4000 5000 time (iterations) 100 80 60 40 20 0 0 100 1000 2000 time (iterations) 3000 4000 80 60 40 20 0 0 1000 2000 3000 4000 5000 time (iterations) Figure 3.6: The overall attendance and the probabilities for each of the M agents for budget (budget= 10) and modified budget (budget= 10, wait=3, 6) algorithms.
Page 1: The El Farol Bar Problem for next g
Page 4 and 5: List of Figures 1.1. Bar attendance
Page 6 and 7: Acknowledgements I would like to de
Page 8 and 9: 2 CHAPTER 1. CHAOS, COMPLEXITY AND
Page 16 and 17: 10 CHAPTER 2. PREVIOUS APPROACHES T
Page 30 and 31: 24 CHAPTER 3. ANALYSIS AND EXTENSIO
Page 44 and 45: 38 CHAPTER 4. CASE STUDY: MULTIPLE
Page 50 and 51: 44 CHAPTER 5. CONCLUSIONS Another n
Page 52 and 53: 46 CHAPTER 5. CONCLUSIONS
Page 54 and 55: 48 APPENDIX A. C CODE FOR THE EL FA
Page 66: 60 BIBLIOGRAPHY [14] Challet D. and

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