Networks: Optimisation and evolution

Networks: Optimisation and Evolution

Volumn 9780521871006, Issue , 2007, Pages 1-271

  Whittle, Peter ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84926203212     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511618673     Document Type: Book

References (174)

1. Ahuja, R. K., Magnanti, T. L. and Orlin, J. B. (1993) Network Flows: Theory, Algorithms and Applications. Englewood Cliffs, NJ: Prentice-Hall
2. Albert, R., Jeong, H. and Barabási, A. L. (1999) Diameter of the world-wide web. Nature, 401, 130–31
3. Albert, R. and Barabási, A. L. (2002) Statistical mechanics of complex networks. Rev. Mod. Phys., 74, 47–97
4. Aldous, D. J. (1987) Ultimate instability of exponential back-off protocol for acknowledgementbased transmission control of random access communication channels. IEEE Trans. Inf. Th., IT-33, 219–23
5. Amari, S. (1998) Natural gradient works efficiently in learning. Neural Computat., 10, 251–76
6. Amari, S. and Nagaoka, H. (2000) Methods of Information Geometry. New York: Oxford University Press and American Mathematical Society
7. Arthurs, A. M. (1970, republished 1980) Complementary Variational Principles. Oxford: Clarendon Press
8. Bagge, M. (2000) A model of bone adaptation as an optimization process. J. Biomechs., 33, 1349–57
9. Ball, M. O., Magnanti, T. L., Monma, C. L. and Nemhauser, G. L. (eds) (1995a) Network Models. Volume 7, Handbooks in Operational Research and Management Science. Amsterdam: North- Holland
10. Ball, M. O., Magnanti, T. L., Monma, C. L. and Nemhauser, G. L. (eds) (1995b) Network Routing. Volume 8, Handbooks in Operational Research and Management Science. Amsterdam: North- Holland
11. Bando, M., Hasebe, K., Nakayama, A., Shibata, A. and Sugiyama, Y. (1995) Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E, 51, 1035–42
12. Barabási, A. L. and Albert, R. (1999) Emergence of scaling in random networks. Science, 286, 509–12
13. Beckmann, M., McGuire, C. B. and Winsten, C. B. (1956) Studies in the Economics of Transportation. New Haven, CT: Yale University Press
14. Bendsøe, M. P. (1986) Generalized plate models and optimal design. In Erickson, J. L. et al. (eds), Homogenization and Effective Moduli of Materials and Media. Berlin: Springer-Verlag; pp 1–26
15. Bendsøe, M. P. and Kikuchi, N. (1988) Generating optimal topologies in structural design using a homogenization method. Comput. Meth. Appl. Mech. Eng., 71, 197–224
16. Bendsøe, M. P. and Sigmund, O. (2003) Topology Optimization. Heidelberg: Springer-Verlag
17. Bertsekas, D. P. (1987) Dynamic Programming; Deterministic and Stochastic Models. Englewood Cliffs, NJ: Prentice-Hall
18. Bertsekas, D. P. (1998) Network Optimization: Continuous and Discrete Models. Nashua, NH: Athena Scientific
19. Bertsekas, D. P., Nedic, A. and Asuman, E. O. (2003) Convex Analysis and Optimization. Nashua, NH: Athena Scientific
20. Bollobás, B. (2001) Random Graphs, 2nd edn. Cambridge: Cambridge University Press
21. Bollobás, B., Riordan, O., Spencer, J. and Tusnády, G. (2001) The degree sequence of a scale-free random graph process. Random Structures and Algorithms, 18, 279–90
22. Bonald, T. and Massoulié, L. (2001) Impact of fairness on Internet performance. Proc. ACM Sigmetrics2001
23. Borel, E. (1925) Principes et formules classiques du Calcul des Probabilités. Traité du Calcul des Probabilités et de ses Applications. Paris: Gauthier-Villars
24. Braess, D. (1968) Über ein paradoxon der verkehrsplanung. Unternehmensforschung, 12, 258–68
25. Bramson, M. (1994a) Instability of FIFO queueing networks. Ann. Appl. Prob., 4, 414–31
26. Bramson, M. (1994b) Instability of FIFO queueing networks with quick service times. Ann. Appl. Prob., 4, 693–718
27. Bramson, M. (1996) Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Systems, 22, 5–45
28. Bramson, M. (1998) State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems, 30, 89–148
29. Bramson, M. and Dai, J. G. (2001) Heavy traffic limits for some queueing networks. Ann. Appl. Prob., 11, 49–90
30. Brockmeyer, E., Halstrom, H. L. and Jensen, A. (1948) The Life and Works of A. K. Erlang. Copenhagen: Academy of Technical Sciences
31. Burman, D. Y., Lehoczky, J. P. and Lim, Y. (1984) Insensitivity of blocking probabilities in a circuit-switching network. J. Appl. Prob., 21, 850–59
32. Carter, D. R. and Beaupré, G. S. (2001) Skeletal Function and Form. Cambridge: Cambridge University Press
33. Carter, D. R., Orr, T. E. and Fyhrie, D. P. (1989) Relationships between loading history and femoral cancellous bone architecture. J. Biomech., 22, 231–44
34. Cheng, G. D. and Olhoff, N. (1982) Regularized formulation for optimal design of axisymmetric plates. Int. J. Solids Struct., 18, 153–69
35. Cheng, G. D. and Pedersen, P. (1997) On sufficiency conditions for optimal design based on extremal principles of mechanics. J. Mech. Phys. Solids, 45, 135–50
36. Dai, J. G. (1995) On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob., 5, 49–77
37. de Veciana, G., Lee, T. -J. and Konstantopoulos, T. (2001) Stability and performance analysis of networks supporting elastic services. IEEE/ACM Trans. Network., 9, 2–14
38. Dorogovtsev, S.N. and Mendes, J. F. F. (2000) Evolution of networks with aging of sites. Phys. Rev. E, 62, 1842–1845
39. Dorogovtsev, S. N. and Mendes, J. F. F. (2003) Evolution of Networks. Oxford: Oxford University Press
40. Dorogovtsev, S. N., Mendes, J. F. F. and Samukhin, A. N. (2000) Structure of growing networks with preferential linking. Phys. Rev. Lett., 85, 4633–4636
41. Doyle, P. G. and Snell, J. L. A. (1984) Random Walks and Electrical Networks. Carus Mathematical Monographs. Mathematical Association of America
42. Erdös, P. and Rényi, A. (1959) On random graphs I. Publ. Math. Debrecen, 5, 290–97
43. Erdös, P. and Rényi, A. (1960) On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl., 5, 17–61
44. Fletcher, R. (1987) Practical Methods of Optimization. New York: John Wiley & Sons
45. Flory, P. J. (1953) Principles of Polymer Chemistry. Ithaca, NY: Cornell University Press
46. Freeman, W. J. (1975) Mass Action in the Nervous System. New York: Academic Press
47. Freeman, W. J. (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol. Cybernet., 56, 139–50
48. Freeman, W. J. (1992) Tutorial on neurobiology: from single neurons to brain chaos. Int. J. Bifurcat. Chaos, 2, 451–82
49. Freeman, W. J. (1994) Role of chaotic dynamics in neural plasticity. In van Pelt, J., Corner, M. A., Uylings, H. B. M. and Lopez da Silva, F. H. (eds), Progress in Brain Research, Vol. 102. Amsterdan: Elsevier; pp 319–33
50. Freeman, W. J., Yao, Y. and Burke, B. (1988) Central pattern generating and recognizing in the olfactory bulb: a correlation learning rule. Neural Networks, 1, 277–88
51. Frégnac, Y. (1999) A tale of two spikes. Nature Neurosci., 2, 299–301
52. Gallager, R. G. (1977) A minimum delay routing algorithm using distributed computation. IEEE Trans. Commun., 25, 73–85
53. Gerla, M. and Kleinrock, L. (1977) On the topological nature of distributed computer networks. IEEE Trans. Commun., 25, 48–60
54. Gibbens, R. J. (1988) Dynamic routing in circuit-switched networks: the dynamic alternative routing strategy. Ph.D. thesis, University of Cambridge
55. Gibbens, R. J., Kelly, F. P. and Key, P. B. (1988) Dynamic alternative routing – modelling and behaviour. In Bonatti, M. (ed.), Proc. 12th Int. Teletraffic Congress, Turin. Amsterdam: Elsevier
56. Gibbens, R. J. and Kelly, F. P. (1990) Dynamic routing in fully connected networks. IMA J. Math. Cont. Informat., 7, 77–111
57. Gibbens, R. J. and Kelly, F. P. (1999) Resource pricing and the evolution of congestion control. Automatica, 35, 196–198
58. Girard, A. and Ouimet, Y. (1983) End-to-end blocking for circuit-switched networks: polynomial algorithms for some special cases. IEEE Trans. Commun., 31, 1269-73
59. Gittins, J. C. (1979) Bandit processes and dynamic allocation indices. J. Roy. Statist. Soc. B, 41, 148–77
60. Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Chichester: John Wiley & Sons
61. Gittins, J. C. and Jones, D. M. (1974) A dynamic allocation index for the sequential design of experiments. In Gani, J. (ed.), Progress in Statistics. Amsterdam: North-Holland; pp 241–66
62. Good, I. J. (1960) Generalisations to several variables of Lagrange’s expansion, with applications to stochastic processes. Proc. Camb. Phil. Soc., 56, 366–80
63. Good, I. J. (1963) Cascade theory and the molecular weight averages of the sol fraction. Proc. Roy. Soc. A, 272, 54–9
64. Gordon, M. (1962) Good’s theory of cascade processes applied to the statistics of polymer distributions. Proc. Roy. Soc. A, 268, 240–59
65. Grossberg, S. (1988) Nonlinear neural networks: principles, mechanisms and architectures. Neural Networks, 1, 17–62
66. Harrison, J. M. (1985) Brownian Motion and Stochastic Flow Systems. New York: John Wiley & Sons
67. Harrison, J. M. and Nguyen, V. (1993) Brownian models of multiclass queueing networks. Queueing Systems, 13, 5–40
68. Harrison, J. M. and Wein, L. M. (1990) Scheduling networks of queues: heavy traffic analysis of a simple open network. Oper. Res., 38, 1052–64
69. Harrison, J. M. (2000) Brownian models of open processing networks: canonical representation of workload. Ann. Appl. Prob., 10, 75–103
70. Harrison, J. M. (2003) A broader view of Brownian networks. Ann. Appl. Prob., 13, 1119–50
71. Hassoun, M. H. (1995) Fundamentals of Artificial Neural Networks. Cambridge MA, London: MIT Press
72. Hebb, D. O. (1949) The Organisation of Behaviour. New York: John Wiley & Sons
73. Hemp, W. S. (1973) Optimal Structures. Oxford: Clarendon Press
74. Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci., 79, 2254–8
75. Huiskes, R. (2000) If bone is the answer, what is the question? J. Anat., 197, 145–56
76. Intriligator, M. D. (republished 2002) Mathematical Optimization and Economic Theory. SIAM
77. Jackson, J. R. (1963) Jobshop-like queueing systems. Mgmt. Sci., 10, 131–42
78. Jackson, R. R. P. (1954) Queueing systems with phase-type service. Operat. Res. Quart., 5, 109–20
79. Jacobson, V. (1988) Congestion avoidance and control. In Proc. ACM SIG-COMM’88, pp 314–29
80. Kasteleyn, P. W. and Fortuin, C. M. (1969) Phase transitions in lattice systems with random local properties. J. Phys. Soc. Japan, 26(Suppl.), 11–14
81. Kay, L. M., Shimoide, K. and Freeman, W. J. (1995) Comparison with EEG time series from rat olfactory system with model composed of nonlinear coupled oscillators. Int. J. Bifurcat. Chaos, 5, 849–58
82. Kelly, F. P. (1979) Reversibility and Stochastic Networks. Chichester: John Wiley & Sons
83. Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob., 18, 473–505
84. Kelly, F. P. (1986) Blocking and routing in circuit-switched networks. In Boxma, O. J., Cohen, J. W. and Syski, R. (eds), Teletraffic Analysis and Computer Performance Evaluation. Amsterdam: Elsevier; pp 37–45
85. Kelly, F. P. (1988a) Routing in circuit-switched networks: optimization, shadow prices and decentralization. Adv. Appl. Prob., 20, 112–44
86. Kelly, F. P. (1988b) The optimisation of queueing and loss networks. In Boxma, O. J. and Syski, R. (eds), Queueing Theory and its Applications. Amsterdam: Elsevier; pp 375–92
87. Kelly, F. P. (1990) Routing and capacity allocation in networks with trunk reservation. Maths. Op. Res., 15, 771–93
88. Kelly, F. P. (1991a) Loss networks. Ann. Appl. Prob., 1, 317–78
89. Kelly, F. P. (1991b) Network routing. Phil. Trans. Roy. Soc. London A, 337, 343–67
90. Kelly, F. P. (1995) Modelling communications networks, present and future. Proc. Roy. Soc. A, 444, 1–20
91. Kelly, F. P. (2000) Models for a self-managed Internet. Phil. Trans. Roy. Soc. A, 358, 2335–48
92. Kelly, F. P. (2001) Mathematical modelling of the Internet. In Engquist, B. and Schmid, W. (eds), Mathematics Unlimited – 2001 and Beyond. Berlin: Springer-Verlag; pp 685–702
93. Kelly, F. P. (2003) Fairness and stability of end-to-end congestion control. Europ. J. Control, 9, 159–76
94. Kelly, F. P. and Gibbens, R. J. (1990) Dynamic routing in fully connected networks. IMA J. Math. Control. Inf., 7, 77–111
95. Kelly, F. P., Gibbens, R. J. and Key, P. B. (1995) Dynamic alternative routing. In Steenstrup, M. E. (ed.), Routing in Communication Networks. Englewood Cliffs, NJ: Prentice-Hall; pp 13–47
96. Kelly, F. P. and Laws, C. N. (1993) Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling. Queueing Systems, 13, 47–86
97. Kelly, F. P. and MacPhee, I. M. (1987) The number of packets transmitted by collision detect random access schemes. Ann. Prob., 15, 1557–68
98. Kelly, F. P., Maulloo, A.K. and Tan, D. K. H. (1998) Rate control in communication networks: shadow prices, proportional fairness and stability. J. Op. Res. Soc., 49, 237–52
99. Kelly, F. P. and Williams, R. J. (2004) Fluid model for a network operating under a fair bandwidthsharing policy. Ann. Appl. Prob., 14, 1055–83
100. Kerner, B. S. and Konhäuser, P. (1994) Structure and parameters of clusters in traffic flow. Phys. Rev. E, 50, 54–83
101. Key, P., Massoulié, L., Bain, A. and Kelly, F. P. (2004) Fair Internet traffic integration: network flow models and analysis. Ann. des Télécomm., 59, 1338–52
102. Kleinrock, K. (1964) Communication Nets: Stochastic Message Flow and Delay. New York: McGraw-Hill
103. Kleinrock, L. (1976) Queueing Systems, Volume 2: Computer Applications. New York: John Wiley & Sons
104. Klimov, G. P. (1974) Time-sharing service systems I. Theory. Prob. Appl., 19, 532–51
105. Klimov, G. P. (1978) Time-sharing service systems II. Theory. Prob. Appl., 23, 314–21
106. Kumar, S., Saini, S. and Prakash, P. (1996) Alien attractors and memory annihilation of structured sets in Hopfield networks. IEEE Trans. Neural Networks, 7, 1305–9
107. Levy, R. (1991) Fixed point theory and structural optimization. Eng. Opt., 17, 251–261
108. Li, L., Alderson, D., Willinger, W. and Doyle, J. (2004) A first-principles approach to understanding the Internet’s router-level topology. Proc. 2004 SIGCOMM Conference on Applications, Technologies, Architectures and Protocols for Computer Communications. New York: ACM Press; pp 3–14. Available at http//portal.acm.org
109. Lighthill, M. J. and Whitham, G. B. (1955) On kinematic waves. I. Flood movement in long rivers. II: A theory of traffic flow on long, crowded roads. Proc. Roy. Soc. A, 229, 281–345
110. Lin, X., Shroff, N. B. and Srikant, R. (2006) On the connection-level stability of congestioncontrolled cummunication networks. Working paper, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign. Available at http://comm.csl.uinc.edu/∼srikant
111. Lippmann, R. P. (1987) An introduction to computing with neural nets. IEEE Mag. Acoust., Signals Speech Process., 4, 4–22
112. Luenberger, D. G. (1989) Linear and Nonlinear Programming. Addison-Wesley
113. Massoulié, L. and Roberts, J. W. (2000) Bandwidth sharing and admission control for elastic traffic. Telecomm. Systems, 15, 185–201
114. Masur, E. F. (1970) Optimum stiffness and strength of elastic structures. J. Eng. Mechs., 96, 621–40
115. Michell, A. G. M. (1904) The limits of economy of material in frame structures. Phil. Mag., 8, 589–97
116. Mo, J. and Walrand, J. (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Network., 8, 556–67
117. Nagel, K., Wagner, P. and Woesler, R. (2003) Still flowing: approaches to traffic flow and traffic jam modelling. Operat. Res., 51, 681–710
118. Nagurney, A. (1993) Network Economics. Dordrecht: Kluwer
119. Newman, M. E. J., Strogatz, S. H. and Watts, D. J. (2001) Random graphs with arbitrary degree distribution and their applications. Phys. Rev. E, 64, 026118–1–026118–17
120. Oja, E. (1982) A simplified neuron model as a principal component analyzer. J. Math. Biol., 15, 267–73
121. Olivier, von G. (1972) Cost-minimum priorities in queueing systems of type M/G/1. Elektron. Rechenanl., 14, 262–71
122. Paganini, F., Wang, Z., Doyle, J. C. and Low, S. H. (2005) Congestion control for high performance, stability and fairness in general networks. IEEE/ACM Trans. Networking, 13, 43–56
123. Percus, J. K. (1971) Combinatorial Methods. Berlin: Springer
124. Prager, W. and Taylor, G. I. N. (1968) Problems of optimal structural design. J. Appl. Mech.35, 102–6
125. Querin, Q. M. (1997) Evolutionary structural optimization, formulation and implementation. Ph.D. thesis, Department of Aeronautical Engineering, University of Sydney, Australia
126. Rattray, M. and Saad, D. (1999) Analysis of natural gradient descent for multilayer neural networks. Phys. Rev. E, 59, 4523–32
127. Rougham, M., Greenberg, A., Kalmanek, C., Rumsewicz, M., Yates, J. and Zhang, Y. (2003) Experience in measuring backbone traffic variability: models, metrics, measurements and meaning. International Teletraffic Congress (ITC), 18, 2003
128. Rozvany, G. I. N. and Zhou, M. (1991) The COC algorithm, part I: Cross-section optimization or sizing. Comput. Meth. Appl. Mech. Eng.,89, 281–308
129. Rozvany, G. I. N., Zhou, M. and Sigmund, O. (1994) Topology optimization in structural design. In Adeli, H. (ed.), Advances in Design Optimization. London: Chapman and Hall; pp 340–99
130. Rumelhart, D. E., Hinton, G. E. and Williams, R. J. (1986) Learning internal representations by error propagation. In Rumelhart, D. E., McClelland, J. L. and PDP Research Group (eds), Parallel Distributed Programming: Explorations in the Microstructure of Cognition, Vol. 1, Foundations. Cambridge, MA: MIT Press; pp 318–62
131. Rybko, A. N. and Stolyar, A. L. (1992) Ergodicity of stochastic processes that describe the functioning of open queueing networks. Prob. Inform. Trans., 28, 3–26
132. Scott, J. W., McBride, R. L. and Schneider, S. P. (1980) The organization of projections from the olfactory bulb to the pyriform cortex and olfactory tubercle in the rat. J. Comp. Neurol., 194, 519–34
133. Sewell, M. J. (1987) Maximum and Minimum Principles. Cambridge, UK. Cambridge University Press
134. Steenstrup, M. (ed.) (1995) Routing in Communications Networks. Englewood Cliffs, NJ: Prentice-Hall
135. Stockmayer, W. H. (1943) Theory of molecular size distribution and gel formation in branched chain polymers. J. Chem. Phys., 11, 45–55
136. Stockmayer, W. H. (1944) Theory of molecular size distribution and gel formation in branched polymers. II. General cross-linking. J. Chem. Phys., 12, 125–31
137. Stolyar, A. L. (2005) Maximizing queueing network utility subject to stability. Queueing Systems, 50, 401–57
138. Svanberg, K. (1994) Global convergence of the stress ratio method for truss sizing. Struct. Optim., 8, 60–68
139. Taylor, J. E. (1969) Maximum strength elastic structural design. Proc. ASCE, 95, 653–63
140. Taylor, J. E and Rossow, M. P. (1977) Optimal truss design based on an algorithm using optimality criteria. Int. J. Solid Structs., 13, 913–23
141. Thompson, J. M. T. and Hunt, G.W. (1973) A General Theory of Elastic Stability. New York: John Wiley & Sons
142. Toader, A. M. (1997) Convergence of an algorithm in optimal design. Struct. Optim., 13, 195–198
143. Turing, A. M. (1952) The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. London B, 237, 37–72
144. Vinnicombe, G. (2002a) On the stability of networks operating TCP-like congestion control. Proc. 15th World Congress on Automatic Control, 2002. Available at http://www.control.eng.com.ac.uk/gv/internet/ifac.pdf
145. Vinnicombe, G. (2002b) Robust congestion control for the internet. Working paper, Department of Engineering, University of Cambridge. Available at http://www.control.eng.com.ac.uk/gv/internet/sigcomm.pdf
146. von der Malsburg, C. (1973) Self-organization of orientation-sensitive cells in the striate cortex. Kybernetik, 14, 85–100
147. Vvedenskaya, N. D., Dobrushin, R. I. and Karpelevich, F. I. (1996) A queueing system with selection of the shortest of two queues. Prob. Inform. Trans., 32, 15–27
148. Wang, X. -J. and Rinzel, J. (2003) Oscillatory and bursting properties of neurons. In Arbib, M. A. (ed.), The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press; pp 835–40
149. Wasiutynski, Z. (1960) On the congruency of the forming according to the minimal potential energy with that according to equal strength. Bull. de l’Académie Polonaise des Sciences, Série des Sciences Techniques, 8, 259–68
150. Watson, G. S. (1958) On Goldberg’s theory of the precipitin reaction. J. Immunol., 80, 182–5
151. Whittle, P. (1965a) Statistical processes of aggregation and polymerisation. Proc. Camb. Phil. Soc., 61, 475–95
152. Whittle, P. (1965b) The equilibrium statistics of a clustering process in the uncondensed phase. Proc. Roy. Soc. A, 285, 501–19
153. Whittle, P. (1980a) Multi-armed bandits and the Gittins index. J. Roy. Statist. Soc. B, 42, 143–9
154. Whittle, P. (1980b) Polymerisation processes with intra-polymer bonding. I. One type of unit. II. Stratified processes. III. Several types of unit. Adv. Appl. Prob., 12, 94–115, 116–34, 135–53
155. Whittle, P. (1981a) Arm-acquiring bandits. Ann. Prob., 9, 284–92
156. Whittle, P. (1981b) A direct derivation of the equilibrium distribution for a polymerisation process. Teoriya Veroyatnostei, 26, 350–61
157. Whittle, P. (1982) Optimisation over Time, Vol. 1. Chichester: John Wiley & Sons
158. Whittle, P. (1985) Random graphs and polymerisation processes. Ann. Discrete Math., 28, 337–48
159. Whittle, P. (1986) Systems in Stochastic Equilibrium. Chichester: John Wiley & Sons
160. Whittle, P. (1988) Approximation in large-scale circuit-switched networks. Prob. Eng. Inf. Sci., 2, 279–91
161. Whittle, P. (1990a) The statistics of random directed graphs. J. Stat. Phys., 56, 499–516
162. Whittle, P. (1990b) Fields and flows on random graphs. In Grimmett, G. R. and Welsh, D. J. A. (eds), Disorder in Physical Systems. Oxford: Oxford University Press; pp 337–48
163. Whittle, P. (1992) Random fields on random graphs. Adv. Appl. Prob., 24, 455–73
164. Whittle, P. (1994) Polymer models and generalised Potts–Kasteleyn models. J. Stat. Phys., 75, 1063–92
165. Whittle, P. (1998) Neural Nets and Chaotic Carriers. Chichester: John Wiley & Sons
166. Whittle, P. (2004) The distribution of species numbers in a controlled environment. Austr. NZ J. Statistics, 46, 23–7
167. Whittle, P. (2005) Tax problems in the undiscounted case. J. Appl. Prob., 42, 754–65
168. Williams, R. J. (1998) Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse. Queueing Systems, 30, 27–88
169. Wilson, H. R. and Cowan, J. D. (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J., 12, 1–24
170. Wolff, J. (1986) The Law of Bone Remodelling. Berlin: Springer-Verlag. (A translation of the original 1892 text Das Gesetz der Transformationen der Knochen, Hirschwald, Berlin.)
171. Wu, F. Y. (1982) The Potts model. Rev. Mod. Phys., 54, 235–68. Phil. Mag., 8, 589–97
172. Xie, Y. M. and Steven, G. P. (1997) Evolutionary Structural Optimization. Berlin: Springer-Verlag
173. Yao, Y. and Freeman, W. J. (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks, 3, 483–501
174. Zhou, M. and Rozvany, G. I. N. (2001) On the stability of ESO type methods in topology optimization. Struct. Multidisc. Opt., 21, 80–83