Recently, multihop wireless sensor networks (WSNs) are widely developed and applied to energy efficient data collections from environments by establishing reliable transmission radio links and employing data aggregation algorithms, which can eliminate redundant transmissions and provide fusion information. In this paper, energy efficiency which consists of not only energy consumptions but also the amount of received data by the base station, as the performance metric to evaluate network utilities is presented for achieving energy efficient data collections. In order to optimize energy efficiency for improvements of network utilization, we firstly establish a graphical game theoretic model for energy efficiency in multihop WSNs, considering message length, practical energy consumptions and packet success probabilities. Afterwards, we propose a graphical protocol for performance optimization from Nash equilibrium of the graphical game theory. The approach also consists of the distributed protocol for generating optimum tree networks in practical WSNs. The experimental results show energy efficient multihop communications can be achieved by optimum tree networks of the approach. The quantitative evaluation and comparisons with related work are presented for the metric with respect to network energy consumptions and the amount of received data by the base station. The performances of our proposal are improved in all experiments. As an example, our proposal can achieve up to about 52% energy efficiency more than collection tree protocol (CTP). The corresponding tree structure is provided for the experiment.

As one of the most widely investigated studies in wireless sensor networks (WSNs), multihop networking is increasingly developed and applied for achieving energy efficient communications and enhancing transmission reliability. To accurately and realistically analyze the performance metric (energy efficiency), firstly we provide a measurement of the energy dissipation for each state and establish a practical energy consumption model for a WSN. According to the analytical model of connectivity, Gaussian approximation approaches to experimental connection probability are expressed for optimization problem on energy efficiency. Moreover, for integrating experimental results with theories, we propose the methodology in multihop wireless sensor networks to maximize efficiency by nonlinear programming, considering energy consumptions and the total quantity of sensing data to base station. Furthermore, we present evaluations adapting to various wireless sensor networks quantitatively with respect to energy efficiency and network configuration, in view of connectivity, the length of data, maximum number of hops and total number of nodes. As the consequence, the realistic analysis can be used in practical applications, especially on self-organization sensor networks. The analysis also shows correlations between the efficiency and maximum number of hops, that is the multihop systems with several hops can accommodate enough devices in ordinary applications. In this paper, our contribution distinguished from others is that our model and analysis are extended from experiments. Therefore, the results of analysis and proposal can be conveniently applied to actual networks.

In a multihop wireless network, wireless interference is a crucial factor in the maximum multiflow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks with a link schedule to support it. In this paper, we observe that network coding could help to decrease the impact of wireless interference, and thus propose a framework to study the MMF problem for multihop wireless networks with network coding. Firstly, a network model is established to describe the new conflict relations and schedulability modified by network coding. Next, we formulate the MMF problem to compute the maximum throughput of multiple unicast flows supported by the multihop wireless network with network coding, and show that its capacity region could be enlarged by performing network coding. Finally, we show that determining the capacity region of a multihop wireless network with network coding is an NP-hard problem, and thus propose a greedy heuristic algorithm, called coding-first collecting (CFC), to determine a capacity subregion of the network. We also show that finding an optimal hyperarc schedule to meet a given link demand function is NP-hard, and propose a polynomial algorithm, called coding-first scheduling (CFS), to find an approximate fractional hyperarc schedule in the multihop wireless network with network coding. A numerical analysis of a grid wireless network and a random wireless network is presented to demonstrate the efficiencies of the CFC algorithm and the CFS algorithm based on the framework.

Known an a criterion that solves the trade-off between fairness and efficiency, proportional fairness is well-studied in cellular networks in the Qualcomm High Data Rate System. In multi-hop wireless networks, proportional fairness is solved by maximizing the logarithmic aggregate utility function. However, this approach can deal with instantaneous rates only where long term fairness is to be targeted. In this case, cumulative rates are more suitable. This paper proposes a framework for multi-hop wireless networks to guarantee fairness of cumulative data rates. The framework can be extended to other kinds of fairness such as max-min fairness, and to more complex networks, multi-channel multi-radio wireless networks.

A wireless node is called isolated if it has no links to other nodes. The number of isolated nodes in a wireless network is an important connectivity index. However, most previous works on analytically determining the number of isolated nodes were not based on practical channel models. In this work, we study this problem using a generic probabilistic channel model that can capture the behaviors of the most widely used channel models, including the disk graph model, the Bernoulli link model, the Gaussian white noise model, the Rayleigh fading model, and the Nakagami fading model. We derive the expected number of isolated nodes and further prove that their distribution asymptotically follows a Poisson distribution. We also conjecture that the nonexistence of isolated nodes asymptotically implies the connectivity of the network, and that the probability of connectivity follows the Gumbel function.

IEEE 802.11 MAC protocol for medium access control in wireless Local Area Networks (LANs) is the de facto standard for wireless ad hoc networks. However, it does not perform well in terms of fairness, delay and throughput specially, in multihop networks. The problem is due to both the MAC and link layer contentions. Many research papers have been published in these fields. Among them, a modification of IEEE 802.11 MAC protocol was proposed to achieve per-node fairness, but modifications to the original MAC layer requires a change of hardware, therefore, it is difficult to implement. Moreover, it fails to solve the per-flow unfairness problem. In this paper, we propose a new scheduling method, Probabilistic Control on Round robin Queue (PCRQ) scheduling, aiming to achieve per-flow fairness in multihop ad hoc networks. PCRQ scheduling in the link layer is proposed without modifying IEEE 802.11 MAC protocol. Our proposed method achieves good performance results in both UDP and TCP traffic.

Recently, a promising packet forwarding architecture COPE was proposed to essentially improve the throughput of multihop wireless networks, where each network node can intelligently encode multiple packets together and forward them in a single transmission. However, COPE is still in its infancy and has the following limitations: (1) COPE adopts the FIFO packet scheduling and thus does not provide different priorities for different types of packets. (2) COPE simply classifies all packets destined to the same nexthop into small-size or large-size virtual queues and examines only the head packet of each virtual queue to find coding solutions. Such a queueing structure will lose some potential coding opportunities, because among packets destined to the same nexthop at most two packets (the head packets of small-size and large-size queues) will be examined in the coding process, regardless of the number of flows. (3) The coding algorithm adopted in COPE is fast but cannot always find good solutions. In order to address the above limitations, in this paper we first present a new queueing structure for COPE, which can provide more potential coding opportunities, and then propose a new packet scheduling algorithm for this queueing structure to assign different priorities to different types of packets. Finally, we propose an efficient coding algorithm to find appropriate packets for coding. Simulation results demonstrate that this new COPE architecture can further greatly improve the node transmission efficiency.

A QoS support technique for easily minimizing delay in multihop wireless networks is proposed. Using a priority queue operation that reduces delays overall, the proposed technique, Reduced Congestion Queuing (RCQ), solves problems peculiar to multihops. By adding RCQ to a multihop system, base station or access point density and cost can be more effectively curtailed than by simply applying multihops to a cellular network or wireless LAN because RCQ expands the multihop service area. Due to its simplicity, the proposed technique can be used in a wide range of applications, including VoIP.

A useful optimization problem to help solve various base station layout problems in multihop wireless networks is formulated. By solving the proposed generalized formula, the relation between the permissible largest number of hops and the minimum base station density necessary to cover an entire service area while guaranteeing a specified QoS is easily calculated. Our formula is extendable to other allocation problems by replacing parameters. The energy-cost transformation and scope of the multihop effect are also presented.

Recently, the mulitihop wireless network system attracts the interest of many people as a communication network system of the next generation. The multihop wireless network has unique features in which neither base stations nor wired backbone networks are required and a terminal can communicate with the other terminal beyond the transmission range by multihopping. In this network, a communication link between two terminals which can communicate directly is required a channel. Since cochannel interference may occur, we need to assign channels to communication links carefully. In this paper, we describe a channel assignment strategy which takes the degree of cochannel interference into consideration, and we evaluate an effectiveness of this strategy by computer simulations. We show that this strategy is more effective than a strategy which does not take the degree of cochannel interference into consideration. And we also consider a few channel assignment algorithms briefly.