Citation Context

... for the case where the system is near heavy traffic as well. This point will be elaborated on later. All discrete review policies described to date in the literature of heavy traffic network control =-=[15, 33, 34, 39]-=- require the system manager to solve a new linear programming problem at each review point. However, by fully exploiting the special structure of CRP networks, we arrive at a far simpler type of polic...

Citation Context

... servers. In Chapter 7, we will design and study characteristics of various resource allocation policies for the Beneficiary-Donor model (see Figure 1.11), which frequently comes up in the literature =-=[4, 17, 58, 61, 71, 105, 125, 176, 181, 182, 185, 186, 205]-=-. Whereas the standard metric for evaluating resource allocation policies for the Beneficiary-Donor model is the (weighted) mean response time, we choose to consider an additional metric, which we ref...

Citation Context

...ion is that the control problem is simpler to solve. Eorts at choosing the cost criterion forsuid models of queues so that the optimal controls are useful for the stochastic problem are described in [=-=30, 31]-=-. Alternative scalings, reserve levels and the choice of the parameter n. In the scaling used so far, time was not rescaled but the queue content was scaled by 1=n . This scaling determined the level ...

Citation Context

...er (or law of large number) approximations to the original open stochastic processing networks. Asymptotic regimes in which these models are relevant include those of large initial queue lengths (see =-=[31, 35]-=- and references therein) and large numbers of buffers or servers (see [30] and references therein). Frequently, these models are used for analyzing “subcritical” systems where the load placed on the s...

Citation Context

...has been described above in the context of bounds. There is also work that views the fluid model as the limit of a stochastic system. For example, fluid limit models are explicitly considered in Meyn =-=[52]-=- and [53]. The optimal policy for the fluid model provides a policy for a stochastic network model that is “almost optimal in heavy traffic” (see [53] for details). Also, Maglaras [48] uses fluid limi...

Citation Context

...e initial conditions. The latter view of optimization has received significant attention recently due to its tractability, and the stability properties that may be obtained for the controlled network =-=[6, 13, 11, 19]-=-. Optimality under each of these criteria is formally defined as follows: A policy is called average-cost optimal for the stochastic model if the average cost, # := lim sup t## E[c(Q(t; x))] is minimi...

Citation Context

...er, even the related Proportional Fair scheduler is known to be destabilizing for certain stochastic models [1]. In contrast, stability of the fluid model under a myopic policy is virtually universal =-=[10, 7, 33]-=-. To explain this gap, consider the following two models. The controlled random walk (CRW) model evolves on Z ℓ + according to the recursion, Q(t + 1) = Q(t) + B(t + 1)U(t) + A(t + 1), t ≥ 0, Q(0) = x...