This paper concerns control of stochastic networks using state-dependent safety-stocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the Dai-Wang re-entrant line. In each case, a single policy is proposed that is independent of network load. The policy is fluid-scale optimal, and approximately average-cost optimal: The steady-state cost η satisfies the bound

η_** < *η* < *η*_** + k_0 log( η*_** ) ,

where η*_** is the optimal steady-state cost. These results are based on the construction of an approximate solution to the average-cost dynamic programming equations via the one-dimensional relaxation and an associated fluid model.

This work has been extended to general network models in *Stability and Asymptotic Optimality of Generalized MaxWeight Policies* and in the networks monograph, *Control Techniques for Complex Networks*

**Reference**

@article{mey05a,

Author = {Meyn, S. P.},

Journal = QS,

Pages = {255--297},

Title = {Dynamic safety-stocks for asymptotic optimality in stochastic networks},

Volume = {50},

Year = {2005}}

@article{mey09a,

Author = {Meyn, S.},

Journal = SICON,

Number = {6},

Pages = {3259-3294},

Title = {Stability and Asymptotic Optimality of Generalized {MaxWeight} Policies},

Volume = {47},

Year = {2009}}

@book{CTCN,

Address = {Cambridge},

Author = {Meyn, S. P.},

Publisher = {Cambridge University Press},

Title = {Control Techniques for Complex Networks},

Year = {2007}}