On the structure of the optimal server control for fluid networks

This paper derives the optimal trajectories in a general fluid network with server control. The stationary optimal policy in the complete state space is constructed. The optimal policy is constant on polyhedral convex cones. An algorithm is derived that computes these cones and the optimal policy. Generalized Klimov indices are introduced, they are used for characterizing myopic and time-uniformly optimal policies.

[1]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[2]  Shaler Stidham,et al.  Conservation Laws for Single-Server Fluid Networks , 2001, Queueing Syst. Theory Appl..

[3]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[4]  Knut Sydsæter,et al.  Optimal control theory with economic applications , 1987 .

[5]  Arie Hordijk,et al.  Fluid approximation of a controlled multiclass tandem network , 2000, Queueing Syst. Theory Appl..

[6]  N. Bäuerle.  Asymptotic optimality of tracking policies in stochastic networks , 2001 .

[7]  Shaler Stidham,et al.  Sample-path conservation laws, with applications to scheduling queues and fluid systems , 2000, Queueing Syst. Theory Appl..

[8]  M. Pullan.  Forms of Optimal Solutions for Separated Continuous Linear Programs , 1995 .

[9]  Nicole Bäuerle,et al.  Optimal control of single-server fluid networks , 2000, Queueing Syst. Theory Appl..

[10]  C. Maglaras.  Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality , 2000 .

[11]  Ad Ridder.  Large-deviations analysis of the fluid approximation for a controllable tandem queue , 2003 .

[12]  Gideon Weiss,et al.  An algorithm for minimum wait drainingof two‐station fluid re‐entrant line , 1999, Ann. Oper. Res..

[13]  Hong Chen,et al.  Dynamic Scheduling of a Multiclass Fluid Network , 1993, Oper. Res..

[14]  G. Klimov.  Time-Sharing Service Systems. I , 1975 .

[15]  J. Dai.  On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[16]  M. Pullan.  A Duality Theory for Separated Continuous Linear Programs , 1996 .

[17]  Sean P. Meyn,et al.  Fluid Network Models: Linear Programs for Control and Performance Bounds , 1996 .

[18]  Florin Avram,et al.  Fluid models of sequencing problems in open queueing networks; an optimal control approach , 1995 .