An analytical approach to the dynamic topology problem

Currently, it is possible to modify (say, hourly) the topology of a data communications network by adding or deleting network links and/or by increasing or decreasing bandwidth on existing links in response to changing traffic loads and/or projected network conditions. The intent of this paper is to study a Markov decision process (MDP) model of the dynamic topology problem (DTP), the problem of activating and/or deleting links, as a function of the current traffic in the network and of the most recent network topology design. We present a decomposition of this model and structural results for the decomposition. The decomposition and structural results enhance the tractability of procedures for determining optimal link control policies. A numerical example is used to illustrate these results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47986/1/11235_2005_Article_BF02110313.pd

Time-average and asymptotically optimal flow control policies in networks with multiple transmitters

We consider M transmitting stations sending packets to a single receiver over a slotted time-multiplexed link. For each phase consisting of T consecutive slots, the receiver dynamically allocates these slots among the M transmitters. Our objective is to characterize policies that minimize the long-term average of the total number of messages awaiting service at the M transmitters. We establish necessary and sufficient conditions on the arrival processes at the transmitters for the existence of finite cost time-average policies; it is not enough that the average arrival rate is strictly less than the slot capacity. We construct a pure strategy that attains a finite average cost under these conditions. This in turn leads to the existence of an optimal time-average pure policy for each phase length T , and to upper and lower bounds on the cost this policy achieves. Furthermore, we show that such an optimal time-average policy has the same properties as those of optimal discounted policies investigated by the authors in a previous paper. Finally, we prove that in the absence of costs accrued by messages within the phase, there exists a policy such that the time-average cost tends toward zero as the phase length T →∞.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44208/1/10479_2005_Article_BF02025184.pd