Information theory at multiple time-scales: the case of scheduling

In this paper, we make the case for a deeper understanding of time-variations in sources and channels at multiple time-scales. The case is made using packet scheduling over noisy channels, where packets from a bursty source are scheduled over a wireless channel to achieve a desired objective (power reduction, fairness etc.). Focusing our attention on minimal power scheduling with delay constraints, we show the following two claims. First, we show that scheduling is equivalent to a low-pass filter and present the optimal robust scheduler, which performs time water-filling over finite time horizons. Second, scheduling over Gaussian channels can be interpreted as lossy source compression, where the timing information of the packets is compressed with delay as distortion. Both results bring out connections with well known information theory concepts, motivating further study of multiple time-scales in wireless system design.