Asymptotic optimality of tracking policies in stochastic networks

Control problems in stochastic queuing networks are hard to solve. However, it is well known that the fluid model provides a useful approximation to t he stochastic network. We will formulate a general class of control problem s in stochastic queuing networks and consider the corresponding fluid optim ization problem (F) which is a deterministic control problem and often easy to solve. Contrary to previous literature, our cost rate function is rathe r general. The value function of (F) provides an asymptotic lower bound on the value function of the stochastic network under fluid scaling. Moreover, we can construct from the optimal control of(F) a so-called tracking polic y for the stochastic queuing network which achieves the lower bound as the fluid scaling parameter tends to oo. In this case we say that the tracking policy is asymptotically optimal. This statement is true for multiclass que uing networks and admission and routing problems. The convergence is monoto ne under some convexity assumptions. The tracking policy approach also show s that a given fluid model solution can be attained as a fluid limit of the original discrete model.