Modelling and Implementation of QoS in Wireless Sensor Networks: A Multiconstrained Traffic Engineering Model
© Antoine B. Bagula. 2010
Received: 16 February 2010
Accepted: 12 June 2010
Published: 4 July 2010
This paper revisits the problem of Quality of Service (QoS) provisioning to assess the relevance of using multipath routing to improve the reliability and packet delivery in wireless sensor networks while maintaining lower power consumption levels. Building upon a previous benchmark, we propose a traffic engineering model that relies on delay, reliability, and energy-constrained paths to achieve faster, reliable, and energy-efficient transmission of the information routed by a wireless sensor network. As a step forward into the implementation of the proposed QoS model, we describe the initial steps of its packet forwarding protocol and highlight the tradeoff between the complexity of the model and the ease of implementation. Using simulation, we demonstrate the relative efficiency of our proposed model compared to single path routing, disjoint path routing, and the previously proposed benchmarks. The results reveal that by achieving a good tradeoff between delay minimization, reliability maximization, and path set selection, our model outperforms the other models in terms of energy consumption and quality of paths used to route the information.
When deployed in a sensor field to perform sensing operations, a sensor node may fall into one of the following states .
Sensing. A sensing node monitors the source using an integrated sensor, digitizes the information, processes it, and stores the data in its on-board buffer. This information will be eventually sent to the base station.
Relaying. A relaying node receives data from other nodes and forwards it towards their destination.
Sleeping. For a sleeping node, most of the device is either shut down or works in low-power mode. A sleeping node does not participate in either sensing or relaying. However, it "wakes up" from time to time and listens to the communication channel in order to answer requests from other nodes. Upon receiving a request, a state transition to "sensing" or "relaying" may occur.
Dead. A dead node is no longer available to the sensor network. It has either used up its energy or has suffered vital damage. Once a node is dead, it cannot re-enter any other state.
A typical WSN deployment scenario consists of placing sensor devices into a given environment to sense what is happening in that environment and report the results wirelessly to a processing place where appropriate decisions are taken about the environment being controlled. This can be applied, for example, in Precision agriculture by using sensors to measure the humidity and temperature levels at different points of the ground and take appropriate irrigation decisions. In a region-wide emergency situation, a sensor network could also be deployed in a gas contaminated urban area by air-dropping chemical sensors from Unmanned Aerial Vehicles (UAVs) to achieve real-time situation assessment, report the extent and movement of gas back to nearby UAVs and take appropriate decisions concerning an evacuation plan. Embedding sensors in roadbeds, alongside highways, or bridge structures and placing cameras at street intersections to measure traffic flow and detect traffic violations have become common practice in many modern cities. These devices are networked to build a smart road network infrastructure used to make roads safer, reduce congestion, help people find the nearest available parking space in an unfamiliar city, achieve routing assistance, or provide early warnings on weather-related road conditions. The efficiency of such deployments may be measured by ( ) the lifetime of the WSN often expressed by the time spanning from the outset of the WSN and the time when the first sensor is battery depleted, ( ) the throughput expressed by the proportion of the information sensed in the environment which has successfully reached the gateway, and ( ) the delay and time taken by the information collected by the WSN to travel from the sensing area to the gateway where the information is processed.
Energy conservation is a key parameter upon which the lifetime of WSNs depends since the sensor nodes often operate unattended in unrecoverable locations where the labor and costs associated with the batteries use and replacement may outweigh the ROI (Return on Investment) that the sensor network could deliver.
WSNs are by nature broadcasting networks which require tight control to avoid duplication of the same information on the network which might waste bandwidth and reduce the throughput of the network. Furthermore, the uncontrolled deployment of a WSN may lead to the unwanted behavior where high packet drop may arise from competition on the mac layer between sensor nodes trying to send information on a shared medium (channel) using the CSMA protocol.
Many of the emerging WSN deployments involve delay sensitive applications with real-time delay constraints. Meeting such delay constraints may require both hardware efficiency at the level of the clock of the WSN and software efficiency by deploying efficient routing techniques that can improve delay and on-time packet delivery.
Traffic engineering (TE) is a network management technique which, once the preserve of fixed networks, will be reinvented to address the issues associated with the performance parameters described above. Traffic engineering moves the traffic (information collected in the WSN) to where the network resources are available to achieve QoS agreements between the offered traffic and the available resources.
1.1. Related Work
Single path (SP) routing approaches using different schemes have been proposed as TE approaches for energy efficient communication in wireless networks. Some are based on data-centric routing schemes such as directed diffusion  using the flooding of interest by sinks to allow gradients to be set up within the wireless network. Other approaches rely on routing metrics (costs) such as the distance to the destination or the node residual energy level  to reduce energy consumption in WSNs.These follow the work of Stojmenovic and Lin  where routing algorithms for wireless networks are discussed with the goal of increasing the network lifetime by defining a new power-cost metric based on the combination of both node's lifetime and distance-based power metric, thus proposing power aware routing algorithm that attempts to minimize the total power needed to route a message between a source and a destination. In , a protocol is proposed which, given a communication network, computes a sub-network such that, for every pair of nodes connected in the original network, there is a minimum-energy path and in the subnetwork where a minimum-energy path is the one that allows messages to be transmitted with a minimum use of energy. Liu and Li  considered the problem of topology control in a network of heterogeneous wireless devices with different maximum transmission ranges, where asymmetric wireless links are not uncommon. P. X. Liu and Y. Liu  developed a novel energy-efficient routing called the THEEM (Two Hop-Energy-Efficient Mesh) protocol for wireless sensor network. However, though appearing simple, flexible, and scalable, SP routing might result in the faster depletion of the nodes energy supply and subsequent shorter lifetime, higher transmission delays and are unreliable.
Multipath routing is a TE strategy which provides the potential to increase the likelihood of reliable data delivery of information from source to destination by sending multiple copies of the same data along different paths . It can also increase the throughput of a network by sending different pieces of the information in parallel over different paths and restoring the entire information at the destination. This might result in better playback delay (the maximum delay taken by all the pieces of information to arrive to the destination) and minimized on-time packet delivery. Multipath routing algorithms minimizing the energy consumption to extend the lifetime of a network while satisfying the QoS traffic requirements such as delay and reliability are important parameters upon which the wide deployment of WSNs depend. The routing protocols proposed in [10, 11] use multiple path routing with network reliability as design priority. They are implemented by having data transmission relying mostly on an optimal primary path and an alternative path reserved as an emergency path used only when the nodes on the primary route fail. The energy-aware routing proposed in  uses localized request messages flooding to find all possible routes between the sources and sinks, as well as the energy costs associated to these paths. By using a sensor node routing table where every neighbor is associated with a given transmission probability computed based on the cost of the path passing through it, the scheme maintains multiple paths but uses only one of them at a time, in order to avoid stressing a particular path and extend the network lifetime. Pointed out by Ganesan et al. , the traditional disjoint paths (node disjoint paths) have the same attractive resilience properties, but they can be energy inefficient. Alternate node-disjoint path can be longer and therefore expends significantly more energy than that expended on the primary path. Since this energy can adversely impact the lifetime and the performance of a sensor network, they have considered a slightly different kind of multipath, namely, a braided multi-path, which relaxes the requirement for node disjointedness. Alternate paths in a braid are partially disjoint from the primary path, not completely node-disjoint. The multipath routing approach proposed in  expands on directed diffusion  to improve the resilience to node failures by exploring the possibility of finding alternate paths connecting the source and sinknodes when node failures occur. Sue and Chiou  explored the possibility of extending the braided multi-path routing method proposed by Servetto and Barrenechea  to the case of more general random geometric graphs. The Barrenechea et al. scheme is based on constrained random walks and achieves almost stateless multi-path routing on a grid network. The works presented in [14, 15] revisit multipath routing to extend the Dynamic Source Routing (DSR) and Ad hoc On-demand Distance Vector (AODV) routing protocols to improve the energy efficiency of ad hoc networks using frequency of route discovery reduction. Using a retransmission probability function to reduce redundant copies of the same event data, Directed transmission  is proposed as one of the probabilistic routing techniques built around the flooding mechanism. This mechanism uses the hop distance to the destination and the number of steps that the data packets have traveled as routing parameters. It is also based on a retransmission control mechanism to avoid intensive usage of the shortest path. Assuming sources transmitting data packets at a constant rate,  proposes a multipath routing scheme formulated as a linear programming problem with the objective of maximizing the time until the first sensor node runs out of energy. The work presented in  uses a multipath routing algorithm where the routing process is formulated as a constrained optimization problem using deterministic network calculus. Reference  highlights the issue of sensor coverage as a major challenge in wireless sensor network through the investigation of two algorithms that address the energy efficient communication in wireless sensor network using multipath routing while preserving coverage. They also propose a metric referred to as Standard Deviation of Source Partition times to measure coverage and show that their proposals outperform previously proposed algorithms proposed in  in terms of network coverage and first-source partition time without compromising on other performance metrics.
1.2. Contributions and Outline
Taking into account the unpredictability of network topology, Huang and Fang  proposed a braided multi-path routing scheme that delivers packets to the sink on time and at desired reliability with the objective of trying to minimize energy consumption. This scheme referred to as Multi-Constrained Multi-Path routing (MCMP) addresses the issue of multi-constrained QoS in wireless sensor networks by mapping a path-based model into a probabilistic routing scheme. Using the work done in  as benchmark, we proposed in  the Energy Constrained Multipath (ECMP) Routing scheme which fine-tunes the MCMP model to achieve better energy performance.
This paper revisits the problem of Quality of Service (QoS) provisioning to ( ) assess the relevance of using multipath routing to improve the reliability and packet delivery in wireless sensor networks while maintaining lower power consumption levels and ( ) proposing an implementation model supporting QoS in WSNs. The main contributions of this work are twofold.
WSN QoS Modelling
Firstly, building upon the works done in [21, 22], we formulate the problem of QoS routing in WSNs as an energy-aware traffic engineering model relying on delay, reliability and energy constraints to route the information collected from sources to the sink of a WSN. We also propose its algorithmic solution under the ECMP umbrella. Our work reveals through an illustrative example the relevance of integrating energy-awareness in the routing process and adds to the MCMP model a new constraint which translates into an efficient path set selection. Using extensive simulation, we demonstrate the robustness of our model and expand the initial work done in  on several performance parameters. These include the assessment of the tradeoff between delay and reliability constraints and the impact of the sensing intensity on the network performance.
WSN QoS Implementation
Multipath routing has been widely studied for wireless ad hoc networks. However, it is widely known that multipath routing solutions proposed for ad hoc network do not apply to sensor networks since while the former can be implemented with global identity (ID), wireless sensor networks lack global ID. Furthermore, the complexity of QoS models proposed for wireless sensor networks may become a limiting factor for the implementation of these solutions in real-world sensor network platforms. Building upon the breadth-first routing nature of the ECMP solution, we propose a simple and easy to implement packet forwarding protocol solution and discuss its implementation in modern WSN platforms. The proposed traffic engineering model is, to the best of our knowledge, a first step towards QoS routing implementation in real world testbed platforms.
2. The Proposed Traffic Engineering Model
In a wireless sensor network, a path is a series system of links while a path set is represented by a parallel system of paths which can split the traffic offered to a source and carry the information concurrently to the destination in order to achieve load balancing and rapid delivery of the information. In a wireless sensor network, both single paths and path sets are associated with performance parameters such as delay, energy consumption, and reliability which define the quality of service (QoS) received by the information carried by a path or a path set.
2.1. Path Delay, Energy, and Reliability
where is the delay of data over the link
where with the energy per bit consumed by as transmitter and the energy per bit consumed as receiver, and accounts for the energy dissipated in the transmitting operation. Typical values for and are, respectively, = and = for the path loss exponent experienced by a radio transmission = or = for the path loss exponent experienced by a radio transmission . is the location of the sensor node and is the euclidean distance between the two sensor nodes and
where is the reliability of the link
2.2. Path Set Delay, Energy, and Reliability
Path Set Delay
where is given by (1). Note that as expressed above, the delay expresses the play-back delay, defining the delay before all the packets of the data source carried over parallel paths reach the destination.
Path Set Energy.
where is expressed by (2).
Path Set Reliability
where is the path reliability defined by (5).
2.3. Multi-Path Routing Advantage
Multipath Reliability Advantage
As defined by (8), the reliability expression reveals the advantage related to multipath routing by showing the following.
As , the product is reduced with the increase of the path set multiplicity (the number of paths carrying the information). It thus increases the path set reliability.
On the other hand, the expression of the path reliability reveals that the reliability of the links can increase the path reliability when high or reduce the path reliability when low.
Therefore, the reliability of a path set carrying information on a source-destination pair increases with the reliability of the links composing the associated paths and the path set multiplicity.
Multipath Delay Advantage
Multipath Power Consumption
While resulting in reliability and delay gains, multipath routing may increase power consumption by allowing many receptions and transmissions on many several paths. As expressed by (7), the energy consumed in a multipath setting is the sum of the energy consumed by the paths. It thus increases with the path multiplicity and the energy consumed on the paths. When deployed, multipath routing should therefore be carefully controlled to avoid high path multiplicity resulting in higher consumption. While sleeping and wake-up mechanisms are widely recognized as powerful mechanisms allowing high energy savings in wireless sensor networks, their deployment in multi-path settings is irrelevant in order to avoid the routing instability which might result from some packets of the same flow arriving later than the others because the path used by these packets was in sleeping mode while the other packets were routed by paths which were awake.
2.4. The Energy Constrained Routing Paradigm
where is implemented as a priority queue of neighbors of the links of the neighbor sorted in ascending order of their distances to . We observe the following.
- (i)These neigbhors belong to the set(14)
As expressed by (13), the forwarding queue discards higher energy consuming links by having successive links differ by a predefined energy threshold .
2.5. The Traffic Engineering Problem
Let us consider a wireless sensor network represented by a directed graph where is the set of sensor nodes and is the set of wireless links between nodes. Huang and Fang  proposed a distributed link-based QoS routing model where a data source located at a given location sensed by the node is routed with some QoS requirements expressed in term of delay and reliability .
The ECMP Problem
with tunable forgetting parameters and for smoothing the variations of and in time. Note the following.
While (16) expresses the energy-awareness constraint, (17) is the delay constraint and (18), (19) and (20) express the reliability constraints. Equation (21) is an expression of the zero-one optimization.
As formulated in this section, the QoS routing model borrows from  the delay and reliability constraints but adds the energy-awareness requirement to the set of constraints.
subject to the constraints (17), (18), (19), (20), and (21).
3. The Algorithmic and Protocol Solution
Routing consists of moving information across an internetwork from a source to a destination using a multi-hop process where at least one intermediate node is used as transit along the way to the destination. The topic of routing has been covered in computer science literature for more than two decades, but for WSN, routing is just emerging as a main concern because of the need for the deployment of relatively large-scale wireless sensor networks. There are two basic activities involved in the routing process: optimal routing paths determination using routing algorithms and packets transportation using the optimal routing paths found through the paths determination process. Routing protocols are used to implement these two processes by having the paths determination using routing algorithms and packets transportation implemented using a packet forwarding algorithm. In both fixed and wireless networks, the paths determination lead to the creation of routing tables and the packet forwarding to the creation of forwarding tables, both used to determine the next hop that packets coming from a given source to a destination will follow. While  proposed only an algorithmic solution to the paths selection process, our work takes the QoS problem some steps ahead by both looking at the algorithmic path finding solution and proposing an implementation model revealing how to build the sensor nodes forwarding tables.
3.1. The Algorithmic Solution
The ECMP and MCMP problems are deterministic linear zero-one problems which can be solved using several methods proposed by the literature such as in [25, 26]. In both problems, the number of constraints is and the number of the decision variables is which is the size of Thus, the problem size is relatively small and might be proportional to the node density. Building upon the zero-one framework proposed in , an implementation of the two local routing problems MCMP and ECMP may be solved using the Bala's Algorithm but with different path set selection strategies: ( ) a random selection for the MCMP algorithm where the next hop to the sink is selected arbitrarily among the neigbhors of a node and ( ) energy-efficient selection where a set of well-chosen closest neighbors in terms of euclidean distance is used by a node as next hops to the sink. This path selection algorithm has been presented in Section 2.4, and the efficiency of the two algorithms is evaluated in Section 4.
3.2. The Implementation Model
The ECMP key features.
Use of a simple ad hoc routing protocol which creates a breadth-first spanning tree rooted at the sink through recursive broadcasting of routing update beacon messages and recording of parents.
The beacon messages are ( ) broadcasted at periodic intervals called epochs, ( ) propagated progressively to neighbors, and ( ) received by a few nodes which are in the vicinity of the source of the beacon message.
The transmission of the beacon is build around a source marking, progressive propagation to neighbors and rebroadcasting progress which sets up a breadth-first spanning tree rooted at the sink.
The energy-aware routing is integrated into the process by selecting a subset of neigbhors which is sorted by distance and includes only a minimum number of close neighbors. This subset excludes neighbors that largely increase the path set power consumption.
The ECM forwarding protocol follows the main steps described in Algorithm 1.
Algorithm 1: The ECM forwarding protocol.
( ) For each epoch, the sink of a WSN broadcasts a route update beacon with itself as the transmitting
node and a hop count set to 0;
( ) All the nodes hearing the beacon from either the sink or another node mark the source of the
beacon as probable parent and build their forwarding tables as described below
( ) Build the Forwarding queue ;
( ) forwarding ;
( ) ; ;
( ) While do
( ) Update and .
( ) if inequality (17) hold for and then
( ) * add link to forwarding and confirm as parent of
( ) * Dequeue( );
( ) end if
( ) endo while
( ) Check forwarding for reliability constraints (18) and (19).
( ) Node forwards the beacon message with its address as source of the beacon, increment the hop
count, adjust , and broadcast the update beacon.
( ) Recursively, nodes will mark as their probable parent the node from which they hear the beacon
from and broadcast the beacon.
Note that current generation sensor nodes may be broadly classified into two types: some being endowed with a high hardware processing capabilities and a rich set of software instructions allowing them to compute complex functions such as those involved in the constraints used in this paper while other have poor hardware processing capabilities with only a set of software instructions allowing to compute only an elementary set of functions. While our implementation model fits well for the former, the set of steps proposed above may be used in a more elementary processing context assuming some approximations to the functions used in the constraints.
4. Performance Evaluation
In this section, we evaluate the efficiency of the ECMP scheme by comparing its performance to the performance of baseline single path routing, MCMP and LDPR algorithms and the impact of different routing parameters such as the sensing intensity (number of sensor nodes generating data) and the probability of meeting the reliability constraints ( ) on the efficiency of the ECMP model. LDPR is a multipath routing algorithm that uses node disjoint paths. For some experiments, we assume a test network of sensor nodes randomly deployed in a sensing field of square area and the transmission range is . Among these sensor nodes, approximately to are chosen to generate data. We conducted other experiments using a -node test network with similar configuration parameters.
In our experiments, the link reliability and delay are random variables with the reliability uniformly distributed in the range and the delay in ms range. As considered, the delay includes the queuing time, transmission time, retransmission time and the propagation time. The delay requirements are taken in the range of ms with an interval of 10 ms which produces delay requirement levels and the threshold of reliability is set to . The probability of meeting the delay and reliability constraints and is set to The size of a data packet is bytes and is assumed to have an energy field that is updated during the packet transmission to calculate the total energy consumption in the network. We have applied different random seeds to generate different network configuration during the runs. Each simulation lasted sec where in the same run the four algorithms are simulated for comparison.
4.1. Experimental Results
The performance parameters considered in our experiments include the average energy consumption, the packet delivery ratio, the average data delivery delay, the average energy consumption, and the quality of paths used by the algorithms.
Average Energy Consumption. As a certain number of nodes are selected to transmit results to the gateway, the network might consume energy differently depending on the network topology and the number of information transmitting nodes. The average energy consumed is an indication of the energy consumption in transmission and reception of all packets in the network. This metric reveals the efficiency of an approach with respect to the life time of a wireless sensor network.
Packet Delivery Ratio. The packet delivery ratio is one of the most important metrics in real-time applications which indicates the number of packets that could meet the specified QoS level. It is the ratio of successful packet receptions referred to as received packets, to attempted packet transmissions referred to as sent packets.
Average Data Delivery Delay. The average data delivery delay is the end-to-end delay experienced by successfully received packets. In our case, we consider the play-back delay which is expressed by the maximum time taken by different packets of the same flow travelling on different parallel paths in a multipath setting.
Quality of Paths. The quality of paths used by MCMP and ECMP schemes indicates the path length (number of hops of paths used), path usage (frequency of reuse of the same paths), and path multiplicity (average number of paths used to send data to the base station). The value of these parameters provides an indication on the reliability and stability of the algorithms used.
4.2. Experiment 1: Comparing the Four Routing Algorithms
4.3. Experiment 2: The Quality of Paths
4.4. Experiment 3: The Impact of Reliability on ECMP
4.5. Experiment 4: The Impact of Sensing Intensity on ECMP
5. Conclusion and Future Work
This paper proposed and evaluated the performance of an energy-aware traffic engineering algorithm for wireless sensor networks referred to as Energy Constrained Multipath (ECMP). In contrast to a previously proposed benchmark in  referred to as MCMP, the ECMP algorithm selects its forwarding links based on a location-aware model that uses preferably the closest neighbors to reduce transmission power with the expectation of routing packets on the least energy consuming paths. Using simulation, we evaluated the efficiency of both algorithms compared to single path routing and a link disjoint path routing in terms of several performance parameters. The results revealed the efficiency of the ECMP algorithm and its relevance as an efficient algorithm to be used in wireless sensor networking settings. As modelled in this paper, the ECMP algorithm minimizes energy consumption through closest neighbour selection to reduce the transmission power. We also proposed the first steps for the implementation of the model in terms of a simple packet forwarding protocol which is built upon the breadth-first nature of the ECMP model. It is expected that further energy improvements may be achieved by the ECMP by including into the ECMP picture the remaining energy of receiver in order to energy balance the wireless sensor network. The design and implementation of such an energy balancing algorithm/protocol has been reserved for future research work. As traditionally deployed, sensor nodes are energy- and range-limited devices sharing a single communication channel to achieve energy saving and scalability. Multichannel wireless sensor networks another option that has been recently investigated by researchers such as in . Multi-path routing in wireless sensor networks may lead to different issues and provide different results depending on whether multi-channel or single-channel deployment has been considered. The evaluation of the QoS provided by our model by considering the issue of contention in single channel routing and comparing single- and multi-channel deployments is another avenue for future work.
The author would like to acknowledge the help of colleagues of the intelligent systems and advanced telecommunication (ISAT) laboratory of the department of computer science of the University of Cape Town for proofreading and reviewing an initial version of this paper. He is grateful to Muthoni, Ashish, and Pheeha for helping to make this paper more readable.
- Akyildiz IF, Su W, Sankarasubramaniam Y, Cayirci E: Wireless sensor networks: a survey. Computer Networks 2002, 38(4):393-422. 10.1016/S1389-1286(01)00302-4View ArticleGoogle Scholar
- Li W, Cassandras CG: A minimum-power wireless sensor network self-deployment scheme. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC '05), March 2005 1897-1902.Google Scholar
- Intanagonwiwat C, Govindan R, Estrin D: Directed diffusion: a scalable and robust communication paradigm for sensor networks. Proceedings of the ACM/IEEE Annual International Conference on Mobile Computing and Networking (MOBICOM '00), August 2000, Boston, Mass, USA 56-67.Google Scholar
- Xu Y, Heidemann J, Estrin D: Geography-informed energy conservation for ad hoc routing. Proceedings of the ACM/IEEE Annual International Conference on Mobile Computing and Networking (MOBICOM '01), July 2001, Rome, Italy 70-84.Google Scholar
- Stojmenovic I, Lin X: Power-aware localized routing in wireless networks. IEEE Transactions on Parallel and Distributed Systems 2001, 12(11):1122-1133. 10.1109/71.969123View ArticleGoogle Scholar
- Li L, Halpern JY: Minimum-energy mobile wireless networks revisited. Proceedings of the International Conference on Communications (ICC '01), June 2000 1: 278-283.View ArticleGoogle Scholar
- Liu J, Li B: Distributed topology control in wireless sensor networks with asymmetric links. Proceedings of the IEEE Global Telecommunications Conference (Globecom '03), 2003 3: 1257-1262.View ArticleGoogle Scholar
- Liu PX, Liu Y: A two-hop energy-efficient mesh protocol for wireless sensor network. International Journal of Information Acquisition 2004, 1(3):237-247. 10.1142/S0219878904000276View ArticleGoogle Scholar
- Dulman S, Wu J, Havinga P: An energy efficient multipath routing algorithm for wireless sensor networks. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC '03), 2003Google Scholar
- Shah R, Rabaey J: Energy aware routing for low energy ad hoc sensor networks. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC '02), March 2002, Orlando, Fla, USA 350-355.Google Scholar
- Ganesan D, Govindan R, Shenker S, Estrin D: Highly-resilient, energy-efficient multipath routing in wireless sensor networks. ACM SIGMOBILE Mobile Computing and Communications Review 2001, 5(4):11-25. 10.1145/509506.509514View ArticleGoogle Scholar
- Sue C-C, Chiou R-J: A hybrid multipath routing in mobile ad hoc networks. Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing (PRDC '06), December 2006 399-400.Google Scholar
- Servetto SD, Barrenechea G: Constrained random walks on random graphs: routing algorithms for large scale wireless sensor networks. Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, September 2002 12-21.View ArticleGoogle Scholar
- Nasipuri A, Das S: On-demand multipath routing for mobilead hoc networks. Proceedings of the International Conference on Computer Communications and Networks (IC3N '99), October 1999, Boston, Mass, USAGoogle Scholar
- Marina M, Das S: On-demand multipath distance vector routingin ad hoc networks. Proceedings of the 9th International Conference forNetwork Protocols (ICNP '01), November 2001, Riverside, Calif, USAGoogle Scholar
- Barrett CL, Eidenbenz SJ, Kroc L, Marathe M, Smith JP: Parametric probabilistic sensor network routing. Proceedings of the 2nd ACM International Workshop on Wireless Sensor Networks and Applications (WSNA '03), September 2003, San Diego, Calif, USA 122-131.Google Scholar
- Chang J-H, Tassiulas L: Energy conserving routing in wireless ad-hoc networks. Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM '00), March 2000, Tel-Aviv, Israel 1: 22-31.Google Scholar
- Mao S, Panwar SS, Hou YT: On optimal traffic partitioning for multipath transport. Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM '05), March 2005, Miami, Fla, USA 4: 2325-2336.View ArticleGoogle Scholar
- Ponduru V, Ghosal D, Mukherjee B: A distributed coverage-preserving multipath routing protocol in wireless sensor networks. Proceedings of the IEEE Global Telecommunications Conference (Globecom '04), 2004Google Scholar
- Singh S, Woo M, Raghavendra CS: Power-aware routing inmobile ad hoc networks. Proceedings of the 4th Annual ACM/IEEE International Conference on Mobile Computing and Networking, October 1998Google Scholar
- Huang X, Fang Y: Multiconstrained QoS multipath routing in wireless sensor networks. ACM Wireless Networks 2008, 14(4):465-478. 10.1007/s11276-006-0731-9View ArticleGoogle Scholar
- Bagula AB, Mazandu KG: Energy constrained multipath routing in wireless sensor networks. Proceedings of the 5th International Conference on Ubiquitous Intelligence and Computing (UIC '08), June 2008, Oslo, Norway, Lecture Notes in Computer Science 5061: 453-467.View ArticleGoogle Scholar
- Trivedi KS: Probability and Statistics with Reliability, Queuing and Computer Science Applications. John Wiley & Sons, New York, NY, USA; 2002.MATHGoogle Scholar
- Leung KK, Klein TE, Mooney CF, Haner M: Methods to improve TCP throughput in wireless networks with high delay variability. Proceedings of the 60th IEEE Vehicular Technology Conference (VTC '04), September 2004 4: 3015-3019.Google Scholar
- Taha HA: Integer Programming: Theory, Applications, and Computations. Academic Press, New York, NY, USA; 1975.MATHGoogle Scholar
- Kocay W, Kreher DL: Graphs, Algorithms, and Optimization. Chapman & Hall/CRC, Boca Raton, Fla, USA; 2005.MATHGoogle Scholar
- Incel OD: Multi-channel wireless sensor networks: protocols, design and evaluation, Ph.D. thesis. Pervasive Systems Research Group, Faculty of Electrical Engineering, Mathematics and Informatics, University of Twente, Twente, The Netherlands; 2009.Google Scholar
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