Anna Pantelidou

Minimum schedule lengths with rate control in wireless networks

In this paper, we study the problem of joint scheduling and rate control in wireless networks, when each transmitter has a finite amount of data traffic to deliver to its corresponding receiver. Our objective is to minimize the time required to deliver the total data traffic. The scheduling decisions take into account the constraints of the physical layer through the well-known physical interference model. First, we consider a time-slotted system. We provide an optimal solution through a graph-theoretic model, where the minimum-length scheduling problem is formulated as finding a shortest path on a single source directed acyclic graph. Next, due to the complexity of the discrete time problem, we simplify it in two dimensions: (i) we map it to a continuous time problem, and (ii) we restrict the set of feasible scheduling and rate control decisions that can be employed. We finally obtain an optimal scheduling and rate control policy of this simplified problem.

Joint Scheduling and Routing for Ad-hoc Networks Under Channel State Uncertainty

We determine a joint link activation and routing policy that maximizes the stable throughput region of time-varying wireless ad-hoc networks with multiple commodities. In practice, the state of the channel process from the time it is observed till the time a transmission actually takes place can be significantly different. With this in mind, we introduce a stationary policy that takes scheduling and routing decisions based on a possibly inaccurate estimate of the true channel state. We show optimality of this policy within a broad class of link activation processes under certain mild conditions. In particular, processes in this class may be induced almost by any policy, possibly non-stationary, even anticipative and aware of the entire sample paths of the arrival, estimated and true channel processes, provided that it has no knowledge on the current true channel state, besides that available through its estimate.

A Cross-Layer View of Optimal Scheduling

The problem of joint scheduling and rate control for multicast traffic in wireless networks is considered under the performance objectives of sum throughput maximization and proportional fairness. Our results are also valid for the special cases of unicast and broadcast traffic. First, the problem of maximizing the sum throughput of the network is studied and an optimal scheduling and rate control policy is obtained. Given the combinatorial complexity of providing an optimal policy, a simple, polynomial-time, suboptimal alternative scheme is introduced that restricts the space of scheduling and rate control decisions to operation one at a time or all together. The optimal policy to the problem of maximizing the sum throughput of the network with respect to this restricted action space is found. Next, the objective of proportional fairness is considered. Under this restricted space of actions, the resulting scheduling and rate control policy is explicitly characterized analytically and the effects of the current channel conditions are incorporated into the scheduling decisions. Furthermore, it is shown that the policy under this restricted action space is of threshold type. Finally, our analytical results are verified through a set of numerical experiments.

A cross-layer approach for stable throughput maximization under channel state uncertainty

Obtaining the stable throughput region of a wireless network, and a policy that achieves this throughput, has attracted the interest of the research community in the past years. A major simplifying assumption in this line of research has been to assume that the network control policy has full access to the current channel conditions at every time a decision is made. However, in practice one may only estimate the actual conditions of the wireless channel process, and hence the network control policy can at most have access to an estimate of the channel which can in fact be highly inaccurate. In this work we determine a stationary joint link activation and routing policy based on a weighted version of the “back-pressure” algorithm that maximizes the stable throughput region of time-varying wireless networks with multiple commodities by having access to only a possibly inaccurate estimate of the true channel state. We further show optimality of this policy within a broad class of stationary, non-stationary, and even anticipative policies under certain mild conditions. The only restriction is that policies in this class have no knowledge on the current true channel state, except what is available through its estimate.

Optimal rate control policies for proportional fairness in wireless networks

In this paper we consider a K transmitter and K receiver single-hop wireless network. We obtain a rate control policy that provides proportional fair rate allocation to the transmitters when the outcome of a transmission depends on the signal to interference plus noise ratio (SINR) at the corresponding receiver. The policy selects at any time slot one action from a set of actions that are described through two different schemes; the probability of selecting each action is optimized to achieve proportional fairness. The two schemes we consider are to either activate only a single transmitter at any given time slot or to allow all transmitters to transmit simultaneously. Although we demonstrate our approach by considering rates given by the Shannon formula, as well as rates obtained through a combination of phase shift keying (PSK) modulation with symbol rate control, our results are more general and are valid under any rate function that relates the maximum achievable rate to its required SINR.

Scheduling in Wireless Networks

We present a review of the problem of scheduled channel access in wireless networks with emphasis on ad hoc and sensor networks as opposed to WiFi, cellular, and infrastructure-based networks. After a brief introduction and problem definition, we examine in detail specific instances of the scheduling problem. These instances differ from each other in a number of ways, including the detailed network model and the objective function or performance criteria. They all share the “layerless” viewpoint that connects the access problem with the physical layer and, occasionally, with the routing layer. This review is intended to provide a reference point for the rich set of problems that arise in the allocation of resources in modern and future networks.

Minimum-length scheduling and rate control for time-varying wireless networks

We study the problem of minimum-length scheduling in time-varying, single-hop wireless networks where each source of traffic has a finite amount of data to deliver to its corresponding destination. Our objective is to obtain a joint scheduling and rate control policy that minimizes the overall time required to deliver all the data to its intended destinations. We incorporate the physical layer into the scheduling decisions through the Signal to Interference plus Noise Ratio (SINR) criterion. We show that the minimum-length scheduling problem can be formulated as a stochastic shortest path. We provide an optimal policy by employing principles of dynamic programming. Finally, we discuss the applicability of our results for solving the minimum-length scheduling problem in general multi-hop wireless networks.

A cross-layer view of wireless multicast optimization

We consider a system of multiple multicast transmitters with possibly overlapping receivers. We introduce a stationary policy that allocates the transmission rates and powers of every transmitter with the objective to maximize the overall user utility, which is measured in terms of the total average rate of each receiver. We show optimality of this policy by employing the theory of stochastic approximation for any utility function that is strictly concave and increasing in the average rate. The introduced policy is opportunistic in nature as it capitalizes on the variations of the wireless channel that are induced by fading. Specifically, we show through a set of simulations that the average throughput under unicast traffic observes a benefit under fading. Our results further indicate that this benefit is mitigated when multicast traffic is considered.

Energy-efficient scheduling and power control for multicast data

We consider the problem of multicasting from a single source to a set of destinations. We assume that the source can either reach the destinations directly or forward its traffic through a set of relays. Due to the non-linear attenuation of the signal with distance, employing the relays can help to improve the signal quality at the destinations. Meanwhile, relays also consume energy for retransmission of the received information and the rate of communication can be decreased due to the multi-hop transmission. Under the performance objective of maximizing the common amount of information (number of bits) that the source sends to all destinations per Joule of the total energy spent, we wish to identify whether direct transmission from the source to the destinations is preferable as opposed to multi-hop forwarding through the relays. In the latter case, we also identify a) which subset of the relays should be activated, b) for how long, and c) the respective destinations that each relay has to serve. Finally, we provide a set of numerical results to support our analysis.

Wireless Multicast Optimization: A Cross-Layer Approach

The problem of optimal scheduling of multicast traffic in time-varying wireless networks is studied in the framework of utility maximization. Since the wireless channel cannot be known exactly, only scheduling policies that take decisions based on a possibly inaccurate estimate of the wireless channel state are considered. A stationary, on-line, gradient-based scheduling and rate control policy is introduced which identifies at every decision instant the sources that should access the wireless medium along with their respective transmission rates. Furthermore, in the case that more than one optimal rate allocation is possible, the one that requires the minimum sum-power expenditure is selected by the policy. The optimality of the proposed policy among all policies that have access to the same estimate of the current wireless channel state is established through stochastic approximation arguments.