MaxWeight Algorithm Research Articles

Scheduling in Multi-Channel Wireless Networks: Rate Function Optimality in the Small-Buffer Regime

The problem of designing scheduling algorithms for a multichannel (e.g., orthogonal frequency division multiplexing-based) wireless downlink network is considered. The classic MaxWeight algorithm, although throughput-optimal, results in a very poor per-user delay performance in such systems. Hence, an alternate class of algorithms called iterated longest queues first (iLQF) is proposed for overcoming this issue. The iLQF-class algorithms are analyzed in a number of different system configurations. A particular algorithm in this class, called iLQF with pullup, is shown to be rate function optimal for the problem in an appropriate large deviations setting, and is shown to result in a strictly positive value of the rate function for a number of modifications to the basic system model. Thus, the proposed algorithm yields provable performance guarantees. The analytic results are confirmed through simulations.

Dynamic Index Coding for Wireless Broadcast Networks

We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of side information, and is a generalization of the well known (and unsolved) index coding problem of information theory. Rather than achieving the full capacity region, we develop a code-constrained capacity region, which restricts attention to a pre-specified set of coding actions. We develop a dynamic max-weight algorithm that allows for random packet arrivals and supports any traffic inside the code-constrained capacity region. Further, we provide a simple set of codes based on cycles in the underlying demand graph. We show these codes are optimal for a class of broadcast relay problems.

Low-Complexity Scheduling Algorithms for Multichannel Downlink Wireless Networks

This paper considers the problem of designing scheduling algorithms for multichannel (e.g., OFDM-based) wireless downlink networks, with a large number of users and proportionally large bandwidth. For this system, while the classical MaxWeight algorithm is known to be throughput-optimal, its buffer-overflow performance is very poor (formally, it is shown that it has zero rate function in our setting). To address this, a class of algorithms called iterated Heaviest matching with Longest Queues First (iHLQF) is proposed. The algorithms in this class are shown to be throughput-optimal for a general class of arrival/channel processes, and also rate-function-optimal (i.e., exponentially small buffer overflow probability) for certain arrival/channel processes. iHLQF, however, has higher complexity than MaxWeight ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> versus <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively). To overcome this issue, a new algorithm called Server-Side Greedy (SSG) is proposed. It is shown that SSG is throughput-optimal, results in a much better per-user buffer overflow performance than the MaxWeight algorithm (positive rate function for certain arrival/channel processes), and has a computational complexity ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) that is comparable to the MaxWeight algorithm. Thus, it provides a nice tradeoff between buffer-overflow performance and computational complexity. These results are validated by both analysis and simulations.

Throughput Optimal Multi-User Scheduling via Hierarchical Modulation

We investigate the network stability problem when two users are scheduled simultaneously. The key idea is to simultaneously transmit to more than one users experiencing different channel conditions by employing hierarchical modulation. For two-user scheduling problem, we develop a throughput-optimal algorithm which can stabilize the network whenever traffic load is stabilizable (i.e., it is within the achievable rate region.) In addition, we analytically prove that the proposed algorithm achieves larger achievable rate region compared to the conventional Max-Weight algorithm which employs uniform modulation and transmits to a single user. We demonstrate the efficacy of the algorithm on a realistic simulation environment using the parameters of High Data Rate protocol in a Code Division Multiple Access system. Simulation results show that with the proposed algorithm, the network can carry higher traffic load with lower delays.

Max Weight Learning Algorithms for Scheduling in Unknown Environments

We consider a discrete time queueing system where a controller makes a 2-stage decision every slot. The decision at the first stage reveals a hidden source of randomness with a control-dependent (but unknown) probability distribution. The decision at the second stage generates an attribute vector that depends on this revealed randomness. The goal is to stabilize all queues and optimize a utility function of time average attributes, subject to an additional set of time average constraints. This setting fits a wide class of stochastic optimization problems, including multi-user wireless scheduling with dynamic channel measurement decisions, and wireless multi-hop routing with multi-receiver diversity and opportunistic routing decisions. We develop a simple max-weight algorithm that learns efficient behavior by averaging functionals of previous outcomes.

Joint Opportunistic Scheduling and Selective Channel Feedback

It is well known that Max-Weight type scheduling algorithms are throughput optimal since they achieve the maximum throughput while maintaining the network stability. However, the majority of existing works employing Max-Weight algorithm require the complete channel state information (CSI) at the scheduler without taking into account the associated overhead. In this work, we design a Scheduling and Selective Feedback algorithm (SSF) taking into account the overhead due to acquisition of CSI. SSF algorithm collects CSI from only those users with sufficiently good channel quality so that it always schedules the user with the highest queue backlog and channel rate product at every slot. We characterize the achievable rate region of SSF algorithm by showing that SSF supports 1 + ϵ fraction of the rate region when CSI from all users are collected. We also show that the value of ϵ depends on the expected number of users which do not send back their CSI to the base station. For homogenous and heterogeneous channel conditions, we determine the minimum number of users that must be present in the network so that the rate region is expanded, i.e., ϵ > 0. We also demonstrate numerically in a realistic simulation setting that this rate region can be achieved by collecting CSI from only less than 50% of all users in a CDMA based cellular network utilizing high data rate (HDR) protocol.

Stability with file arrivals and departures in multichannel cellular wireless networks

This paper studies scheduling in multichannel wireless networks with flow-level dynamics. We consider a downlink network with a single base station, M channels (frequency bands), and multiple mobile users (flows). We also assume mobiles dynamically join the network to receive finite-size files and leave after downloading the complete files. A recent study van de Ven et al. (in Proc. IEEE Infocom., pp. 1701---1709, 2009) has shown that the MaxWeight algorithm fails to be throughput-optimal under these flow-level dynamics. The main contribution of this paper is the development of joint channel-assignment and workload-based scheduling algorithms for multichannel downlink networks with dynamic flow arrivals/departures. We prove that these algorithms are throughput-optimal. Our simulations further demonstrate that a hybrid channel-assignment and workload-based scheduling algorithm significantly improves the network performance (in terms of both file-transfer delay and blocking probability) compared to the existing algorithms.

Utility optimal scheduling in processing networks

We consider the problem of utility optimal scheduling in general processing networks with random arrivals and network conditions. These are generalizations of traditional data networks where commodities in one or more queues can be combined to produce new commodities that are delivered to other parts of the network, and can be used to model problems such as in-network data fusion, stream processing, MapReduce scheduling, and grid computing. Scheduling actions are complicated by the underflow problem that arises when some queues with required components go empty. In this paper, we develop a novel methodology for constructing and analyzing online algorithms for such processing networks. Specifically, we develop the Perturbed Max-Weight algorithm (PMW) to achieve optimal utility. The idea of PMW is to perturb the weights used by the usual Max-Weight algorithm to “push” queue levels toward non-zero values (avoiding underflows). We then show, using a novel combination of Lyapunov drift analysis and duality theory, that when the perturbations are carefully chosen, PMW is able to achieve a utility that is within O ( 1 / V ) of the optimal value for any V ≥ 1 , while ensuring an average network backlog of O ( V ) . The methodology developed here is very general and can also be applied to other problems that involve such underflow constraints.

Throughput-Optimal Opportunistic Scheduling in the Presence of Flow-Level Dynamics

We consider multiuser scheduling in wireless networks with channel variations and flow-level dynamics. Recently, it has been shown that the MaxWeight algorithm, which is throughput-optimal in networks with a fixed number of users, fails to achieve the maximum throughput in the presence of flow-level dynamics. In this paper, we propose a new algorithm, called Workload-based Scheduling with Learning, which is provably throughput-optimal, requires no prior knowledge of channels and user demands, and performs significantly better than previously suggested algorithms.

Fluid models of congestion collapse in overloaded switched networks

We consider a switched network (i.e. a queueing network in which there are constraints on which queues may be served simultaneously), in a state of overload. We analyse the behaviour of two scheduling algorithms for multihop switched networks: a generalized version of max-weight, and the ?-fair policy. We show that queue sizes grow linearly with time, under either algorithm, and we characterize the growth rates. We use this characterization to demonstrate examples of congestion collapse, i.e. cases in which throughput drops as the switched network becomes more overloaded. We further show that the loss of throughput can be made arbitrarily small by the max-weight algorithm with weight function f(q)=q ? as ??0.

Delay reduction via Lagrange multipliers in stochastic network optimization

In this paper, we consider the problem of reducing network delay in stochastic network utility optimization problems. We start by studying the recently proposed quadratic Lyapunov function based algorithms (QLA, also known as the MaxWeight algorithm). We show that for every stochastic problem, there is a corresponding deterministic problem, whose dual optimal solution “exponentially attracts” the network backlog process under QLA. In particular, the probability that the backlog vector under QLA deviates from the attractor is exponentially decreasing in their Euclidean distance. This is the first such result for the class of algorithms built upon quadratic Lyapunov functions. The result quantifies the “network gravity” role of Lagrange Multipliers in network scheduling. It not only helps to explain how QLA achieves the desired performance but also suggests that one can roughly “subtract out” a Lagrange multiplier from the system induced by QLA.

Scheduling Algorithms for Multicarrier Wireless Data Systems

We consider the problem of scheduling multicarrier wireless data in systems such as IEEE 802.16 (WiMAX). Each scheduling decision involves assigning carriers to users for each time slot, subject to the constraint that each carrier is assigned to at most one user, but multiple carriers can potentially be assigned to the same user. One important aspect of our problem is that a scheduler knows the channel rates across all users and all carriers whenever a scheduling decision is made. This “global” information may give a potential for enhancing performance via an optimized allocation of carriers to users. We analyze this problem in a situation where finite queues are fed by a data arrival process. The well-known MaxWeight algorithm for the single-carrier setting maximizes the product of queue size and service rate. We focus on how to adapt MaxWeight to the multicarrier setting. If the same objective is pursued, more service than needed may be assigned to drain a queue, thereby creating wastage. While a simple variant in the objective forbids this wastage, it turns an easy-to-compute old objective into an intractable new objective. We state the hardness of the new optimization problems and propose several extremely simple algorithms with provable performance bounds. We conclude with supporting simulation examples.

Scheduling in multichannel wireless networks with flow-level dynamics

This paper studies scheduling in multichannel wireless networks with flow-level dynamics. We consider a downlink network with a single base station, M channels (frequency bands), and multiple mobile users (flows). We also assume mobiles dynamically join the network to receive finite-size files and leave after downloading the complete files. A recent study [16] has shown that the MaxWeight algorithm fails to be throughput-optimal under this flow-level dynamics. The main contribution of this paper is the development of joint channel-assignment and workload-based scheduling algorithms for multichannel downlink networks with dynamic flow arrivals/departures. We prove that these algorithms are throughput-optimal. Our simulations further demonstrate that a hybrid channel-assignment and workload-based scheduling algorithm significantly improves the network performance (in terms of both file-transfer delay and blocking probability) compared to the existing algorithms.

Minimum energy scheduling in multi-hop wireless networks with retransmissions

MaxWeight algorithm, a.k.a., back-pressure algorithm [1]-[4], has received much attention as a viable solution for dynamic link scheduling in multi-hop wireless networks. The basic principle of the MaxWeight algorithm is to select a set of interference-free links with the maximum overall link weights in the network, where the link weight is determined by the queue difference between the transmitter and the receiver. While the throughput-optimality of the MaxWeight algorithm is well understood in the literature, the energy consumption induced by the MaxWeight algorithm is less studied, which is of great interest in energy-constrained wireless networks such as wireless sensor networks. In this paper, we propose a minimum energy scheduling (MES) algorithm for multi-hop wireless networks with stochastic traffic arrivals and time-varying channel conditions. We show that our algorithm is energy optimal in the sense that the proposed MES algorithm can achieve an energy consumption which is arbitrarily close to the global minimum solution. Moreover, the energy efficiency of the MES algorithm is achieved without losing the throughput-optimality. In other words, the proposed MES algorithm is still throughput optimal whereas the average consumed energy in the network is significantly reduced, as compared to the traditional MaxWeight algorithm. The theoretical results are substantiated via simulations.

Scheduling over a time-varying user-dependent channel with applications to high-speed wireless data

In a wireless network, a basestation transmits data to mobiles at time-varying, mobile-dependent rates due to the ever changing nature of the communication channels. In this article, we consider a wireless system in which the channel conditions and data arrival processes are governed by an adversary . We first consider a single server and a set of users. At each time step t , the server can only transmit data to one user. If user i is chosen, the transmission rate is r i ( t ). We say that the system is ( w , ε)- admissible if in any window of w time steps the adversary can schedule the users so that the total data arriving to each user is at most 1−ε times the total service it receives.Our objective is to design online scheduling algorithms to ensure stability in an admissible system. We first show, somewhat surprisingly, that the admissibility condition alone does not guarantee the existence of a stable online algorithm, even in a subcritical system (i.e., ε &gt; 0). For example, if the nonzero rates in an infinite rate set can be arbitrarily small, then a subcritical system can be unstable for any deterministic online algorithm.On a positive note, we present a tracking algorithm that attempts to mimic the behavior of the adversary. This algorithm ensures stability for all ( w , ε)-admissible systems that are not excluded by our instability results. As a special case, if the rate set is finite, then the tracking algorithm is stable even for a critical system (i.e., ε = 0). Moreover, the queue sizes are independent of ε. For subcritical systems, we also show that a simpler max weight algorithm is stable as long as the user rates are bounded away from zero.The offline version of our problem resembles the problem of scheduling unrelated machines and can be modeled by an integer program. We present a rounding algorithm for its linear relaxation and prove that the rounding technique cannot be substantially improved.