A Cross-Layer Study of the Scheduling Problem

Title of dissertation: A CROSS-LAYER STUDY OF THE SCHEDULING PROBLEM Anna Pantelidou, Doctor of Philosophy, 2009 Dissertation directed by: Professor Anthony Ephremides Department of Electrical and Computer Engineering This thesis is inspired by the need to study and understand th e interdependence between the transmission powers and rates in an interference n etwork, and how these two relate to the outcome of scheduled transmissions. A commonl y used criterion that relates these two parameters is the Signal to Interference plus Nois e Ratio (SINR). Under this criterion a transmission is successful if the SINR exceeds a threshold. The fact that this threshold is an increasing function of the transmission rat e gives rise to a fundamental trade-off regarding the amount of time-sharing that must be permitted for optimal performance in accessing the wireless channel. In particular, it i s not immediate whether more concurrent activations at lower rates would yield a better p erformance than less concurrent activations at higher rates. Naturally, the balance depend s o the performance objective under consideration. Analyzing this fundamental trade-of f under a variety of performance objectives has been the main steering impetus of this thesis . We start by considering single-hop, static networks compri sing of a set of alwaysbacklogged sources, each multicasting traffic to its corres ponding destinations. We study the problem of joint scheduling and rate control under two pe rformance objectives, namely sum throughput maximization and proportional fairness. Un der total throughput maximization, we observe that the optimal policy always activat es the multicast source that sustains the highest rate. Under proportional fairness, we explicitly characterize the optimal policy under the assumption that the rate control and s cheduling decisions are restricted to activating a single source at any given time or al l of them simultaneously. In the sequel, we extend our results in four ways, namely we (i ) turn our focus on time-varying wireless networks, (ii) assume policies that ve access to only a, perhaps inaccurate, estimate of the current channel state, (iii) co nsider a broader class of utility functions, and finally (iv) permit all possible rate control and scheduling actions. We introduce an online, gradient-based algorithm under a fadi ng environment that selects the transmission rates at every decision instant by having acce ss to only an estimate of the current channel state so that the total user utility is maxim ized. In the event that more than one rate allocation is optimal, the introduced algorithm se lects the one that minimizes the transmission power sum. We show that this algorithm is optim al among all algorithms that do not have access to a better estimate of the current cha nel state. Next, we turn our attention to the minimum-length schedulin g problem, i.e., instead of a system with saturated sources, we assume that each n twork source has a finite amount of data traffic to deliver to its corresponding de stination in minimum time. We consider both networks with time-invariant as well as tim e-varying channels under unicast traffic. In the time-invariant (or static) network c ase we map the problem of finding a schedule of minimum length to finding a shortest path on a Directed Acyclic Graph (DAG). In the time-varying network case, we map the cor responding problem to a stochastic shortest path and we provide an optimal solutio n through stochastic control methods. Finally, instead of considering a system where sources are a lways backlogged or have a finite amount of data traffic, we focus on bursty traffic. Our objective is to characterize the stable throughput region of a multi-hop networ k with a set of commodities of anycast traffic. We introduce a joint scheduling and routi ng policy, having access to only an estimate of the channel state and further characteri ze the stable throughput region of the network. We also show that the introduced policy is opt imal with respect to maximizing the stable throughput region of the network within a broad class of stationary, non-stationary, and anticipative policies. A Cross-Layer Study of the Scheduling Problem