A study of general dynamic network programs with arc time-delays

SIAM Journal on Optimization

Volumn 7, Issue 4, 1997, Pages 889-912

  Pullan, Malcolm C ^a,b  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b ST JOHN S COLLEGE   (United Kingdom)

Author keywords

Continuous linear programming; Duality; Dynamic network flows; Linear optimal control

Indexed keywords

EID: 0031285671     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495288180     Document Type: Article

References (31)

1. R. K. AHUJA, T. L. MAGNANTI, AND J. B. ORLIN, Network Flows: Theory, Algorithms, and Applications, Prentice Hall, Englewood Cliffs, NJ, 1993.
2. E. J. ANDERSON, A Continuous Model For Job-Shop Scheduling, Ph.D. thesis, University of Cambridge, UK, 1978.
3. E. J. ANDERSON, Extreme-points for continuous network programs with arc delays, J. Inform. Optim. Sci., 10 (1989), pp. 45-52.
4. E. J. ANDERSON, P. NASH, AND A. F. PEROLD, Some properties of a class of continuous linear programs, SIAM J. Control Optim., 21 (1983), pp. 758-765.
5. E. J. ANDERSON, P. NASH, AND A. B. PHILPOTT, A class of continuous network flow problems, Math. Oper. Res., 7 (1982), pp. 501-514.
6. E. J. ANDERSON AND A. B. PHILPOTT, A continuous-time network simplex algorithm, Networks, 19 (1989), pp. 395-425.
7. E. J. ANDERSON AND A. B. PHILPOTT, On the solutions of a class of continuous linear programs, SIAM J. Control Optim., 32 (1994), pp. 1289-1296.
8. E. J. ANDERSON AND A. B. PHILPOTT, Optimisation of flows in networks over time, in Probability, Statistics and Optimisation, F. P. Kelly, ed., J. Wiley and Sons, Chichester, UK, 1994, pp. 369-382.
9. E. J. ANDERSON AND M. C. PULLAN, Purification for separated continuous linear programs, Z. Oper. Res., 43 (1996), pp. 9-33.
10. L. G. CHALMET, R. L. FRANCIS, AND P. B. SAUNDERS, Network models for building evacuation, Management Sci., 28 (1982), pp. 86-105.
11. N. DUNFORD AND J. T. SCHWARTZ, Linear Operators Part I: General Theory, Wiley-Interscience, New York, 1988.
12. W. H. FARR AND M. A. HANSON, Continuous time programming with nonlinear time-delayed constraints, J. Math. Anal. Appl., 46 (1974), pp. 41-61.
13. L. R. FORD AND D. R. FULKERSON, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
14. H. FRANK, Data communication networks, IEEE Trans. Comm. Tech., 15 (1967), pp. 156-163.
15. R. B. HOLMES, Geometric Functional Analysis and Its Applications, Springer-Verlag, New York, 1975.
16. A. N. KOLMOGOROV AND S. V. FOMIN, Introductory Real Analysis, Dover, New York, 1970.
17. S. E. LOVETSKII AND I. I. MELAMED, Dynamic flows in networks, Automat. Remote Control, 48 (1987), pp. 1417-1434.
18. F. H. MOSS AND A. SEGALL, An optimal control approach to dynamic routing in networks, IEEE Trans. Automat. Control, 27 (1982), pp. 329-339.
19. R. G. OGIER, Minimum-delay routing in continuous-time dynamic networks with piecewise-constant capacities, Networks, 18 (1988), pp. 303-318.
20. A. B. PHILPOTT, Algorithms For Continuous Network Flow Problems, Ph.D. thesis, University of Cambridge, UK, 1982.
21. A. B. PHILPOTT, Network programming in continuous time with node storage, in Infinite Programming: Proceedings of an International Symposium on Infinite Dimensional Linear Programming, E. J. Anderson and A. B. Philpott, eds., Springer-Verlag, Berlin, 1985, pp. 136-153.
22. A. B. PHILPOTT, Continuous-time flows in networks, Math. Oper. Res., 15 (1990), pp. 640-661.
23. A. B. PHILPOTT AND M. CRADDOCK, An adaptive discretization algorithm for a class of continuous network programs, Networks, 26 (1995), pp. 1-11.
24. M. C. PULLAN, An algorithm for a class of continuous linear programs, SIAM J. Control Optim., 31 (1993), pp. 1558-1577.
25. M. C. PULLAN, Forms of optimal solutions for separated continuous linear programs, SIAM J. Control Optim., 33 (1995), pp. 1952-1977.
26. M. C. PULLAN, Linear optimal control problems with piecewise analytic solutions, J. Math. Anal. Appl., 197 (1996), pp. 207-226.
27. M. C. PULLAN, A duality theory for separated continuous linear programs, SIAM J. Control Optim., 34 (1996), pp. 931-965.
28. M. C. PULLAN, An extended algorithm for separated continuous linear programs, Math. Programming, submitted.
29. M. C. PULLAN, Convergence of a general class of algorithms for separated continuous linear programs, SIAM J. Optim., submitted.
30. M. C. PULLAN, A study of special separated continuous linear programs and their use in developing an improved algorithm, J. Optim. Theory Appl., submitted.
31. A. SEGALL, The modeling of adaptive routing in data-communications networks, IEEE Trans. Comm., 25 (1977), pp. 85-95.