Abstract
The exponential pheromone signal of the AI hybrid of Markovian Ant Queuing System - MAQS, is divided into the spatial and deposit pheromone fractions which have the identical values. A new hybrid is formed. The convolution of two new exponential signals has the Erlang distribution. Introducing the inter-state in the process of markovization the Erlang Queuing Ant System - EQAS, is solved. Comparison of the average distance between artificial ants in MAQS and EAQS gave particular numerical specificity. The average distances are in ( equilibrium. Constant ( is a famous constant of the Golden ratio.
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References
Teodorović, D.: Swarm intelligence systems for transportation engineering: Principles and applications. Transportation Research Part C: Emerging Technologies 16(6), 651–667 (2008)
Badr, A., Fahmy, A.: A proof of convergence for Ant algorithms. Information Sciences 160(1-4), 267–279 (2004)
Dorigo, M., Socha, K.: An introduction to Ant Colony Optimisation. In: González, T.F. (ed.) Handbook of approximation algorithms and metaheurististics. Chapman & Hall/CRC Computer and Information Science Series. Taylor & Francis Group, USA (2007)
Teodorović, D., Lučić, P.: The fuzzy ant system for the vehicle routing problem when demand at nodes is uncertain. International Journal on Artificial Intelligence Tools 16(5), 751–770 (2007)
Jackson, D., Chaline, N.: Moduluation of pheromone trail strength with food quality in Pharaon’s ant, Monomorium pharaonis. Animal Behaviour 74(3), 463–470 (2007)
Robinson, E.J.H., Green, K.E., Jenner, E.A., Holcombe, M., Ratnieks, F.L.W.: Decay rates of attractive and repellent pheromones in an ant foraging trail network. Insectes Sociaux 55(1), 246–251 (2008)
Hölldobler, B., Morgan, E.D., Oldham, N.J., Liebig, J.: Recruitment pheromone in the harvester ant genus Pogonomyrmex. Journal of Insect Physiology 47(4-5), 369–374 (2001)
Sillam-Dussès, D., Kalinová, B., Jiroš, P., Březinová, A., Cvačka, J., Hanus, R., Šobotník, J., Bordereau, C., Valterová, I.: Identification by GC-EAD of the two-component trail-following pheromone of Prorhinotermes simplex. Journal of Insect Physiology 55(8), 751–757 (2009)
Sumpter, D.J.T., Beekman, M.: From nonlinearity to optimality: Pheromone trail foraging by ants. Animal Behaviour 66(2), 273–280 (2003)
Depickère, S., Fresneau, D., Deneubourg, J.L.: Effect of social and environmental factors on ant aggregation: A general response? Journal of Insect Physiology 54(9), 1349–1355 (2008)
Garnier, G., Gautrais, J., Theraulaz, G.: The biological principles of swarm intelligence. Swarm Intelligence 1, 3–31 (2007)
Jeanson, R., Ratnieks, F.L.W., Deneubourg, J.L.: Pheromone trail decay rates on different substrates in the Pharaoh’s ant, Monomorium pharaonis. Physiological Entomology 28(3), 192–198 (2008)
Niven, J.E.: Invertebrate Memory: Wide-Eyed Ants Retrieve Visual Snapshots. Current Biology 17(3), 85–87 (2007)
Tanackov, I., Simić, D., Mihaljev-Martinov, J., Stojić, G., Sremac, S.: The Spatial Pheromone Signal for Ant Colony Optimisation. In: Corchado, E., Yin, H. (eds.) IDEAL 2009. LNCS, vol. 5788, pp. 400–407. Springer, Heidelberg (2009)
Stakhov, A.: Fundamentals of a new kind of mathematics, based on the Golden Section. Chaos, Solitons & Fractals 27, 1124–1146 (2006)
El Nashie, M.S.: Is quantum space a random cantor set with a golden mean dimension at the core? Chaos, Solitons & Fractals 4, 177–179 (1994)
Coldea, R., Tennant, D.A., Wheeler, E.M., Wawrzynska, E., Prabhakaran, D., Telling, M., Habicht, K., Smeibidl, P., Kiefer, K.: Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8. Science 327, 177–180 (2010)
Yablonsky, G.S., Constales, D., Marin, G.B.: Coincidences in chemical kinetics: Surprising news about simple reactions. Chemical Engineering Science 65, 6065–6076 (2010)
Heyrovska, R.: Dependences of molar volumes in solids, partial molal and hydrated ionic volumes of alkali halides on covalent and ionic radii and the golden ratio. Chemical Physics Letters 436, 287–293 (2007)
Yamagishi, M.E.B., Shimabukuro, A.I.: Nucleotide Frequencies in Human Genome and Fibonacci Numbers. Bulletin of Mathematical Biology 70, 643–653 (2008)
Perez, J.C.: Codon populations in single-stranded whole human genome DNA Are fractal and fine-tuned by the Golden Ratio 1.618. Interdisciplinary Sciences: Computational Life Sciences 2, 228–240 (2010)
Mathai, A.M., Davis, A.D.: Constructing the sunflower head. Mathematical Biosciences 20, 117–133 (1974)
Ridley, J.N.: Packing efficiency in sunflower heads. Mathematical Biosciences 5, 129–139 (1982)
Lanling, Z.L., Wang, G.: Modeling golden section in plants. Progress in Natural Science 19, 255–260 (2009)
Pletzer, B., Kerschbaum, H., Klimesch, W.: When frequencies never synchronize: The golden mean and the resting EEG. Brain Research 1335, 91–102 (2010)
Schmid, K., Marx, D., Samal, A.: Computation of a face attractiveness index based on neoclassical canons, symmetry, and golden ratios. Pattern Recognition 41, 2710–2717 (2008)
Mizumoto, Y., Deguchi, T., Kelvin, W.C.F.: Assessment of facial golden proportions among young Japanese women. American Journal of Orthodontics and Dentofacial Orthopedics 136, 168–174 (2009)
Butusov, K.P.: The Golden Section in the solar system. Problemy Issledovania Vselennoy 7, 475–500 (1978)
Stakhov, A., Rozin, B.: The “golden” hyperbolic models of Universe. Chaos, Solitons & Fractals 34(2), 159–171 (2007)
Leonardo, D.G., Sigalotti, L.D.G., Mejias, A.: The golden ratio in special relativity. Chaos, Solitons & Fractals 30, 521–524 (2006)
Stakhov, A., Rozin, B.: On a new class of hyperbolic functions. Chaos, Solitons & Fractals 23, 379–389 (2005)
Tanackov, I., Simić, D., Sremac, S., Tepić, J., Kocić-Tanackov, S.: Markovian Ants in a Queuing System. In: Graña Romay, M., Corchado, E., Garcia Sebastian, M.T. (eds.) HAIS 2010. LNCS, vol. 6076, pp. 32–39. Springer, Heidelberg (2010)
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Tanackov, I., Stojić, G., Tepić, J., Kostelac, M., Sinani, F., Sremac, S. (2011). Golden Ratio (Sectiona Aurea) in Markovian Ants AI Hybrid. In: Bouchachia, A. (eds) Adaptive and Intelligent Systems. ICAIS 2011. Lecture Notes in Computer Science(), vol 6943. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23857-4_35
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DOI: https://doi.org/10.1007/978-3-642-23857-4_35
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