Robust packet scheduling in wireless cellular networks

This paper addresses the following robust scheduling problem: Given that only coarse-grained channel state information (i.e., bounds on channel errors, but not the fine-grained error pattern) is available, how to design a robust scheduler that ensures worst-case optimal performance? To solve this problem, we consider two coarse-grained channel error models and take a zero-sum game theoretic approach, in which the scheduler and the channel error act as non-cooperative adversaries in the scheduling process. Our results show that in the heavy channel error case, the optimal scheduler adopts a threshold form. It does not schedule a flow if the price (the flow is willing to pay) is too small, in order to maximize the system revenue. Among the scheduled flows, the scheduler schedules a flow with a probability inversely proportional to the flow price such that the risk of being caught by the channel error adversary is minimized. We also show that in the mild channel error model, the robust scheduling policy exhibits a balanced trade-off between a greedy decision and a conservative policy. The scheduler is likely to take a greedy decision if it evaluates the risk of encountering the channel error adversary now to be small. Therefore, robust scheduling does not always imply conservative decision. The scheduler is willing to take "risks" to expect higher gain in some scenarios. Our solution also shows that probabilistic scheduling may lead to higher worst-case performance compared to traditional deterministic policies. Finally, the current efforts show the feasibility to explore a probabilistic approach to cope with dynamic channel error conditions.