Mode Locking and Chaos in a Deterministic Queueing Model with Feedback

References

• Agnew C. E. Dynamic modelling and control of congestion-prone systems. Oper. Res. (1976) 24:400–419Link, Google Scholar
• Bak P., Bohr T., Jensen M. H. Transition to chaos by interaction of resonances in dissipative systems (II): Josephson Junction, charge waves and standard maps. Physical Rev. A (1984) 30:1070–1081Google Scholar
• Bak P., Bohr T., Jensen M. H. Mode-locking and the transition to chaos in dissipative systems. Physica Scripta (1985) 9:50–58Crossref, Google Scholar
• Borovkov K. A. Propagation of chaos for queueing networks. Theory Probab. Appl. (1997) 42(3):385–394Crossref, Google Scholar
• Brock W. A. Distinguishing random and deterministic systems. J. Econom. Theory (1986) 40:168–195Crossref, Google Scholar
• Colding-Jørgensen M. A model of the firing pattern of a paced nerve cell. J. Theoret. Biol. (1983) 101:541–568Crossref, Google Scholar
• Devaney R. L.An Introduction to Chaotic Dynamics (1988) (Benjamin, New York) Google Scholar
• Dewan S., Mendelson H. User delay costs and internal pricing for a service facility. Management Sci. (1990) 36(12):1502–1517Link, Google Scholar
• Edelson N., Hildebrand D. Congestion tolls for Poisson queuing processes. Econometrica (1975) 43(1):81–92Crossref, Google Scholar
• Erramilli A., Singh R. P., Pruthi P. An application of deterministic chaotic maps to model packet traffic. Queueing Systems (1995) 20:171–206Crossref, Google Scholar
• Gaeta G. Dynamical bifurcation with noise. Internat. J. Theoret. Phys. (1995) 34(4):595–603Crossref, Google Scholar
• Glass L., Mackey M. C.From Clocks to Chaos: The Rhythms of Life (1988) (Princeton University Press, Princeton, NJ) Google Scholar
• Graham C. Chaoticity on path space for a queueing network with selection of the shortest queue among several. J. Appl. Probab. (2000) 37:198–211Crossref, Google Scholar
• Gross D., Harris C. M.Fundamentals of Queueing Theory (1998) 3rd ed.(Wiley, New York) Google Scholar
• Guckenheimer J., Holmes P.Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983) (Springer-Verlag, New York) Crossref, Google Scholar
• Hilborn R. C. Chaos and nonlinear dynamics. (1994) (Oxford University Press Inc., New York) Google Scholar
• Knudsen C., Sturis J., Thomsen J. S. Generic bifurcation structure of Arnol'd Tongues in the forced oscillator. Physical Rev. A (1991) 36:3503–3510Crossref, Google Scholar
• Larsen E. R., Haxholdt C. Mode-locking in a forced business cycle. Tech. Forecasting and Soc. Change (1997) 56:119–130Crossref, Google Scholar
• Larsen E. R., Morecroft J., Mosekilde E., Thomsen J. S. Devil's staircase and chaos from macroeconomic mode-interaction. J. Econom. Dynam. and Control (1993) 17:759–769Crossref, Google Scholar
• Lomi A., Larsen E. R., Ginsberg A. Adaptive learning in organizations: A system dynamics-based exploration. J. Management (1997) 23(4):561–582Crossref, Google Scholar
• Mandelbrot B. B.Fractals: Forms, Change and Dimension (1977) (Freeman, San Francisco, CA) Google Scholar
• Mosekilde E.Topics in Nonlinear Dynamics, Applications to Physics, Biology and Economic Systems (1996) (World Scientific, Singapore) Google Scholar
• Naor P. On the regulation of queue size by levying tolls. Econometrica (1969) 36(1):15–24Crossref, Google Scholar
• Ogata S., Iwayama T., Terachi S. Effect of system noise on chaotic behavior in Roessler type nonlinear system. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. (1997) 7(12):2871–2879Crossref, Google Scholar
• Oi W. Y. A Disneyland dilemma: Two-part tariffs for a Mickey Mouse monopoly. Quart. J. Econom. (1971) 85:77–96Crossref, Google Scholar
• Rump C. M., Stidham S. Stability and chaos in input pricing for a service facility with adaptive customer response to congestion. Management Sci. (1998) 44(2):246–261Link, Google Scholar
• Schuster H. W.Deterministic Chaos (1988) (VCH Verlagsgeselschaft, Weinheim, Germany) Google Scholar
• Sterman J. Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment. Management Sci. (1989) 35(3):321–339Link, Google Scholar
• Sterman J.Business Dynamics (2000) (Irwing, McGraw-Hill, Boston, MA) Google Scholar
• Stidham S. Pricing capacity decisions for a service facility: Stability and multiple local optima. Management Sci. (1992) 38(8):1121–1139Link, Google Scholar
• Sturis J., van Cauter E., Blackman J. D., Polonsky K. S. Entrainment of ultradian pulses of insulin secretion by oscillatory glucose infusion. J. Medical Investigation (1991) 87:493–445Google Scholar
• Thomsen J. M. T., Stewart H. B.Nonlinear Dynamics and Chaos (1986) (Wiley, Chichester, U.K.) Google Scholar
• Togeby M., Mosekilde E., Sturis J. Frequency-locking in a model of two coupled thermostatically controlled radiators. Paper 88 WA/DSC-14. Proc. Annual Winter Meeting Amer. Soc. Mech. Engrgs. (1988) Google Scholar
• van Ackere A. Capacity management: Pricing strategy, performance and the role of information. Internat. J. Production Econom. (1995) 40:89–100Crossref, Google Scholar
• Wolf A., Holden A. V. Quantifying chaos with Lyapunov exponents. Chaos (1986) (Manchester University Press, Manchester, U.K.) Crossref, Google Scholar
• Wolf A., Swift J. B., Swinney H. L. Determining Lyapunov exponents from time series. Physica D (1985) 16:285–317Crossref, Google Scholar