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?C1709, 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.     

Optimization architecture for joint multi-path routing and scheduling in wireless mesh networks

In Wireless Mesh Networks (WMN), the optimal routing of data depends on the link capacities which are determined by link scheduling. The optimal performance of the network, therefore, can only be achieved by joint routing and scheduling optimization. Although the joint single-path routing and scheduling optimization problem has been extensively studied, its multi-path counterpart within wireless mesh networks has not yet been fully investigated. In this paper, we present an optimization architecture for joint multi-path QoS routing and the underlying wireless link scheduling in wireless mesh networks. By employing the contention matrix to represent the wireless link interference, we formulate a utility maximization problem for the joint multi-path routing and MAC scheduling and resolve it using the primal–dual method. Since the multi-path routing usually results in the non-strict concavity of the primal objective function, we first introduce the Proximal Optimization Algorithm to get around such difficulty. We then propose an algorithm to solve the routing subproblem and the scheduling subproblem via the dual decomposition. Simulations demonstrate the efficiency and correctness of our algorithm.     

Interacting queues with server selection and coordinated scheduling—application to cellular data networks

We consider a system of parallel servers handling users of various classes, whose service rates depend not only on user classes, but also on the set of active servers. We investigate the stability under two types of allocation strategies: (i) server assignment where the users are assigned to servers based on rates, load, and other considerations, and (ii) coordinated scheduling where the activity states of servers are coordinated. We show how the model may be applied to evaluate the downlink capacity of wireless data networks. Specifically, we examine the potential gains in wireless capacity from the two types of resource allocation strategies.     

Layouts for mobility management in wireless ATM networks

In this paper, we present a new model that combines quality of service and mobility aspects in wireless ATM networks. Namely, besides the hop count and load parameters of the basic ATM layouts, we introduce a new notion of distance that estimates the time needed to reconstruct the virtual channel of a wireless user when he moves through the network. Quality of service guarantee dictates that the rerouting phase must be imperceptible, that is, the maximum distance between two virtual channels must be maintained as low as possible. Therefore, a natural combinatorial problem arises in which suitable trade-offs must be determined between the different performance measures. We first show that establishing the existence of a layout with maximum hop count h, load l and distance d is NP-complete, even in the very restricted case h=2, l=1 and d=1. We then provide optimal layout constructions for basic interconnection networks, such as chains and rings.     

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of $\varTheta(\frac{1}{1-\rho})$ with the system load ρ, in contrast to the $\varTheta(\frac{1}{(1-\rho)^{2}})$ delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.     

Analysis of a queueing system with a general service scheduling function,with applications to telecommunication network traffic control

In this paper we analyze a queueing system with a general service scheduling function. There are two types of customer with different service requirements. The service order for customers of each type is determined by the service scheduling function α_k(i, j) where α_k(i, j) is the probability for type-k customer to be selected when there are i type-1 and j type-2 customers. This model is motivated by traffic control to support traffic streams with different traffic characteristics in telecommunication networks (in particular, ATM networks). By using the embedded Markov chain and supplementary variable methods, we obtain the queue-length distribution as well as the loss probability and the mean waiting time for each type of customer. We also apply our model to traffic control to support diverse traffics in telecommunication networks. Finally, the performance measures of the existing diverse scheduling policies are compared. We expect to help the system designers select appropriate scheduling policy for their systems.     

Towards a queueing-based framework for in-network function computation

We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network computation as compared to simple data forwarding. To this end, we define a class of functions, the Fully-Multiplexible functions, which includes several functions such as parity, MAX, and kth-order statistics. For such functions we characterize the maximum achievable refresh rate of the network in terms of an underlying graph primitive, the min-mincut. In acyclic wireline networks we show that the maximum refresh rate is achievable by a simple algorithm that is dynamic, distributed, and only dependent on local information. In the case of wireless networks we provide a MaxWeight-like algorithm with dynamic flow-splitting, which is shown to be throughput-optimal.     

Random waypoint model in n-dimensional space

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of mobile wireless networks. In this paper we extend the previous work by deriving an analytical formula for the stationary distribution of a node moving according to a RWP model in n-dimensional space.     

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 α-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 ^α as α→0.     

A branch-and-cut algorithm for the minimum-adjacency vertex coloring problem

In this work we study a particular way of dealing with interference in combinatorial optimization models representing wireless communication networks. In a typical wireless network, co-channel interference occurs whenever two overlapping antennas use the same frequency channel, and a less critical interference is generated whenever two overlapping antennas use adjacent channels. This motivates the formulation of the minimum-adjacency vertex coloring problem which, given an interference graph $G$ representing the potential interference between the antennas and a set of prespecified colors/channels, asks for a vertex coloring of $G$ minimizing the number of edges receiving adjacent colors. We propose an integer programming model for this problem and present three families of facet-inducing valid inequalities. Based on these results, we implement a branch-and-cut algorithm for this problem, and we provide promising computational results.     

Improved algorithm for broadcast scheduling of minimal latency in wireless ad hoc networks

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648（rmax/rmin）^2 times that of the optimal schedule, where rmax and rmin are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most （1 ＋ 2rmax/rmin）^2＋32, Moreover, under the proposed scheduling each node just needs to forward a message at most once.     

On the combinatorial structure of chromatic scheduling polytopes

Chromatic scheduling polytopes arise as solution sets of the bandwidth allocation problem in certain radio access networks, supplying wireless access to voice/data communication networks for customers with individual communication demands. To maintain the links, only frequencies from a certain spectrum can be used, which typically causes capacity problems. Hence it is necessary to reuse frequencies but no interference must be caused by this reuse. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard, and there do not even exist polynomial time algorithms with a fixed quality guarantee.As algorithms based on cutting planes have shown to be successful for many other combinatorial optimization problems, the goal is to apply such methods to the bandwidth allocation problem. For that, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring the combinatorial structure of chromatic scheduling polytopes for increasing frequency spans. We observe that the polytopes pass through various stages—emptyness, non-emptyness but low-dimensionality, full-dimensionality but combinatorial instability, and combinatorial stability—as the frequency span increases. We discuss the thresholds for this increasing “quantity” giving rise to a new combinatorial “quality” of the polytopes, and we prove bounds on these thresholds. In particular, we prove combinatorial equivalence of chromatic scheduling polytopes for large frequency spans and we establish relations to the linear ordering polytope.     

Optimization of the capacity of wireless mesh networks

This is a summary of the authors PhD thesis supervised by Hervé Rivano and defended on 29 October 2009 at the Université de Nice-Sophia Antipolis. The thesis is written in French and is available from . This work deals with the optimization of the capacity of wireless mesh networks, defined as the throughput offered to each flow. We develop optimization models integrating the cross-layer characteristics of radio communications. The joint routing and scheduling is studied and solved using column generation. A linear formulation focusing on the transport capacity available on the network cuts is derived. We prove the equivalence of the models, and adapt the resolution method into a cross line and column generation process. Thorough tests, a contention area located around the gateways which constraints the capacity is highlighted. These results are applied to a quantitative study of the effects of acknowledgments on the capacity. Finally, a stability study of a protocol routing a traffic injected arbitrarily is investigated.     

A rolling window optimization method for large-scale WCDMA base stations planning problem

The large-scale base station planning problem for wideband code division multiple access (WCDMA) wireless networks is studied in this paper. A new rolling window optimization method is presented, where the global optimization problem is decomposed into small optimization sub-problems, which are defined on a series of successive rolling windows. Effective rolling strategies are designed in the rolling optimization method based on the prediction of the interference among the base stations in the WCDMA wireless network. We show that the proposed method has the property that the global objective is non-increasing in the successive optimization procedure. Simulations are carried out to analyze the performance of the proposed optimization method, which show the importance of the rolling strategy.     

On distributed scheduling with heterogeneously delayed network-state information

We study the problem of distributed scheduling in wireless networks, where each node makes individual scheduling decisions based on heterogeneously delayed network state information (NSI). This leads to inconsistency in the views of the network across nodes, which, coupled with interference, makes it challenging to schedule for high throughputs. We characterize the network throughput region for this setup, and develop optimal scheduling policies to achieve the same. Our scheduling policies have a threshold-based structure and, moreover, require the nodes to use only the “smallest critical subset” of the available delayed NSI to make decisions. In addition, using Markov chain mixing techniques, we quantify the impact of delayed NSI on the throughput region. This not only highlights the value of extra NSI for scheduling, but also characterizes the loss in throughput incurred by lower complexity scheduling policies which use homogeneously delayed NSI.     

The N-policy of a discrete time Geo/G/1 queue with disasters and its application to wireless sensor networks

We analyze an N-policy of a discrete time Geo/G/1 queue with disasters. We obtain the probability generating functions of the queue length, the sojourn time, and regeneration cycles such as the idle period and the busy period. We apply the queue to a power saving scheme in wireless sensor networks under unreliable network connections where data packets are lost by external attacks or shocks. We present various numerical experiments for application to power consumption control in wireless sensor networks. We investigate the characteristics of the optimal N-policy that minimizes power consumption and derive practical insights on the operation of the N-policy in wireless sensor networks.     

Fast performance assessment of IEEE 802.11-based wireless networks

In this paper, we introduce a brand new analytical perspective for analyzing and evaluating the IEEE 802.11-based networks. We identify a tightly-coupled relationship between the number of contending nodes and their contention window sizes in the networks. Based on the relationship, we propose a downsizing model for reducing the computational complexity and for improving the simulation performance in the evaluation of the IEEE 802.11-based networks. We first formally prove that the proposed model preserves the operational characteristics of the original networks in their downsized networks through well-known analytical frameworks, such as the models proposed by Bianchi (2000) [7], Calí et al. (2000) [2], and Hu et al. (2006) [8]. We then demonstrate that the proposed model speeds up the simulation by maximally two orders of magnitude. Even though the simulation shows some difference between the results from an original network and those in its corresponding downsized networks in a wide range of network sizes and traffic patterns, the difference is acceptable since it has minimal values of 1% in most cases and maximum values of 10% in a very few cases. We also present the effectiveness of both the downsizing model and the downsizing-model-based simulation in comparison with other performance models and simulation techniques. As the size and complexity of wireless networks are increasing nowadays, we vision that the new proposed model will be of great advantage in conducting fast and accurate packet-level wireless simulations, as well as being a helpful tool for performing the numerically tractable theoretical studies for extensive performance evaluations, such as determining the network-wide throughput or end-to-end delays.     

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processor-sharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.     

Optimal Network Design for Wireless Local Area Network

Network design for wireless local area networks is an important issue in the deployment of these networks. Research activities are presently being undertaken in two major areas: determining the location of base stations (BSs) and assigning the frequency channels for these stations. Our BS location problem selects a set of BSs to provide the best demand area coverage and maximize the signal level and physical area attendance priority. Adequate channel assignment reduces signal interference and improves network throughput. This paper reports a real world experiment where we applied the concepts of two classical outdoor problems namely the optimal BS location problem and the fixed channel assignment problem to build a WLAN into an indoor environment. We propose a mathematical model that we solve by a commercial software and report the computational results.