Regular ordering and applications in control policies

We show how Schur convexity and multi-modularity can be related and used to define a notion of regularity. This provides a new insight on the multimodular functions and extends some optimization results in queueing control problems.

[1]  Eitan Altman,et al.  Optimal Open-Loop Control of Vacations, Polling and Service Assignment , 2000, Queueing Syst. Theory Appl..

[2]  David D. Yao,et al.  Monotone Optimal Control of Permutable GSMPs , 1994, Math. Oper. Res..

[3]  Eitan Altman,et al.  Optimal Routing Problems and Multimodularity , 1999 .

[4]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[5]  Baryshnikov,et al.  Complexity of trajectories in rectangular billiards , 1994, chao-dyn/9406001.

[6]  Ronald L. Graham,et al.  Covering the Positive Integers by Disjoint Sets of the Form {[n alpha + beta]: n = 1, 2, ...} , 1973, J. Comb. Theory, Ser. A.

[7]  F. Baccelli.  Ergodic Theory of Stochastic Petri Networks , 1992 .

[8]  Eitan Altman,et al.  Balanced sequences and optimal routing , 2000, JACM.

[9]  Eitan Altman,et al.  Multimodularity, Convexity, and Optimization Properties , 2000, Math. Oper. Res..

[10]  M. Senechal.  Quasicrystals and geometry , 1995 .

[11]  Ingram Olkin,et al.  Inequalities: Theory of Majorization and Its Application , 1979 .

[12]  Bruno Gaujal.  Optimal Allocation Sequences of Two Processes Sharing a Resource , 1997, Discret. Event Dyn. Syst..

[13]  Bruce E. Hajek,et al.  Extremal Splittings of Point Processes , 1985, Math. Oper. Res..

[14]  G. A. Hedlund,et al.  Symbolic Dynamics II. Sturmian Trajectories , 1940 .

[15]  Eitan Altman,et al.  Optimal admission, routing and service assignment control: the case of single buffer queues , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[16]  Onno J. Boxma,et al.  Optimization of Static Traffic Allocation Policies , 1994, Theor. Comput. Sci..

[17]  B. Hajek.  Optimal control of two interacting service stations , 1982, 1982 21st IEEE Conference on Decision and Control.

[18]  Eitan Altman,et al.  Admission control in stochastic event graphs , 2000, IEEE Trans. Autom. Control..