Optimal Control of Service Rates of Queues in the Presence of a Continuous Disturbance Process: Applications to Spread Spectrum Wireless Networks

摘要

We consider a continuous-time queueing system consisting of M infinite-capacity parallel queues and M servers, one for each queue. The rates of the servers are functions of (i) a control applied by each server, and (ii) a continuous random disturbance process. In addition, the service rate functions are nonlinearly interdependent. At certain time instants (decision epochs), the servers may adjust their rates by changing the values of their controls. We study the manner in which the continuous disturbance process and the nonlinear interdependencies between rate functions affect the dynamics and stability properties of the system. We establish necessary and sufficient conditions for stability; the sufficient condition depends on the frequency of the decision epochs and the magnitude of the fluctuations of the disturbance in the intervals between epochs. We also provide an optimal dynamic control algorithm. The model has direct applications to power control in mobile direct-sequence spread spectrum wireless packet data networks.