Effective resource allocation in a queue: How much control is necessary?

In this paper, we consider a single-server queue with Poisson inputs and two distinct service rates. The service rate employed at any given instant is decided by a resource allocation policy, based on the queue occupancy. We deal with the question of how often control information needs to be sent to the rate scheduler so as to stay below a certain probability of congestion. We first consider some simple Markovian service rate allocation policies and derive the corresponding control rate vs. congestion probability tradeoffs in closed form. However, since a closed form solution is not possible for more general Markov policies, we resort to large deviation tools to characterize the congestion probabilities of various control policies. We also identify a simple dasiatwo-thresholdpsila policy which achieves the best possible tradeoff between rate of control and the decay exponent of the congestion probability. Finally, we also investigate the impact of control errors on the congestion probability of a resource allocation policy.