Abstract
We consider here the optimal control of the number of servers in the M/M/S queue and M/G/1 queue. There are switching costs for every change of the control variable and the finite horizon problem is considered.
We obtain optimality conditions which take the form of differential inequalities similar to those introduced by A. Bensoussan-J.L. Lions for the control of diffusion processes.
The method used here can be applied to more general processes than queuing processes.
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References
A. Bensoussan and J.L. Lions, “Nouvelles méthodes en contrôle impulsionnel”, Applied Mathematics and Optimization 1(4) (1975) 289–312.
A. Bensoussan and J.L. Lions, Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris, Série A Tome 276 (1974) 1189–1192, 1279–1284, 1333–1338.
A. Bensoussan and J.L. Lions, Temps d’arrêt optimal et contrôle impulsionnel, to appear.
E. Boel, “Optimal control of jump processes”, Tech. Rept., University of California, Berkeley, Calif., (1974).
E. Dynkin, Markov processes (Springer, Berlin, 1965).
J.L. Lions, Cours au Collège de France, 1973–1974; 1974–1975.
N.U. Prabhu and S. Stidham, “Optimal control of queueing systems”, in: Mathematical methods in queueing theory, Lecture Notes in Economics 98 (Springer, Berlin, 1974).
M. Sobel, “Optimal operation of queues”, in: Mathematical methods in queueing theory, Lecture Notes in Economics 98 (Springer, Berlin, 1974).
M. Robin, “Contrôle optimal de files d’attente”, IRIA-Laboria Rept. 117 (1975).
M. Robin, “Contrôle impulsionnel avec retard”, to appear.
T. Laetsch, “A uniqueness theorem for elliptic quasi variational inequalities”, Journal of Functional Analysis 18(3) (1975) 286–287.
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© 1976 The Mathematical Programming Society
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Robin, M. (1976). Some optimal control problems for queueing systems. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, II. Mathematical Programming Studies, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120749
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DOI: https://doi.org/10.1007/BFb0120749
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