CNDS ‘03 URL: Improving the Lifetime of Sensor Networks via Intelligent Selection of Data Aggregation Trees Konstantinos Kalpakis, Koustuv Dasgupta, Parag Namjoshi Department of Computer Science and Electrical Engineering University of Maryland Baltimore County {kalpakis, dasgupta,

CNDS ‘03 2 URL: Sensor Networks – Goals and Challenges Recent advances in micro-sensor technology and low-power analog/digital electronics have led to the advent of wireless networks of sensor devices Sensor network – a tool for distributed sensing of physical phenomena  Establish paths between point(s) of interest and observer(s) One or more base stations  Comprises of relatively inexpensive sensor nodes  Readily deployable in physical environments to collect useful information  Typically ad-hoc and multi-hop networks Applications: military surveillance, object tracking, habitat monitoring, search and rescue operations

CNDS ‘03 3 URL: Sensor Networks – Goals and Challenges Sensor networks are severely resource-constrained  Energy  Computing capabilities  Communication resources Energy - the most critical resource  Each sensor is typically fitted with a finite non- replenishable energy source (battery)  Replacing batteries in possibly harsh terrains might be infeasible The lifetime and hence the utility of the sensor network is determined by energy usage

CNDS ‘03 4 URL: Data Aggregation in Sensor Networks Data aggregation  In-network fusion of data from different sensors to eliminate redundant transmissions to the base station.  This significantly reduces the amount of data traffic as well as the distances over which the data needs to be transmitted In the process of in-network aggregation, the value generated at each sensor in each round must influence the value that reaches the base-station in that round ! Source 1Source 2 A B Sink Data Aggregation

CNDS ‘03 5 URL: Energy-Efficient Sensor Networks Energy-aware routing protocols [Singh et al 1998] LEACH [Heinzelman et al 1999]  Clustering-based protocol for transmitting data to the base station Chang and Tassiulas [2001]  routing algorithms that maximize the time until the sensor energies drain out Bharadwaj et al [2001]  upper bounds on the lifetime of an energy-constrained sensor network PEGASIS [Lindsey et al 2001]  Chains formed among sensors to gather and aggregate data  Sensors take turns to transmit to the base station PEGASIS-based hierarchical scheme [Lindsey et al 2001]  R educes the delay incurred in each round of data gathering TinyOS [Madden et al 2002]  Implements the basic database predicates like COUNT, MIN, MAX, and AVERAGE. These predicates are well suited to the in-network regime.

CNDS ‘03 6 URL: Overview System Model. Maximum Lifetime Data Aggregation Problem.  Kalpakis, Dasgupta, and Namjoshi [2002] A- Restricted MLDA.  An efficient algorithm for data gathering problem. Experimental Results. Conclusions.

CNDS ‘03 7 URL: System Model The locations of the sensors and base station are fixed and known a-priori Each sensor has a finite, non-replenishable energy source Any sensor can transmit to any other sensor or to the base station in one hop  Sensors can adjust the antenna range to minimize the energy usage to reach the intended recipient Continuous data delivery  Each sensor observes a continuous phenomenon and produces some information as it monitors its vicinity A k-bit data packet is generated every time unit  Each time unit is referred to as a round  Data gathering at each round, one data packet must be collected from each sensor to be transmitted to the base station the lifetime of the system is defined to be the number of rounds until the first sensor is drained of its energy

CNDS ‘03 8 URL: Energy Model for Sensors Energy Model  First Order Radio Model  Each time sensor transmits or receives data, it expends some energy  Energy spent for transmitting k bits from sensor i to sensor j over d ij meters is:  Energy spent for receiving k bits at sensor i is: where, ε elec = 50 nJ/bit for driving transmitter/receiver circuitry ε amp = 100 pJ/bit/m 2 for the transmitter amplifier d ij = distance between sensors i and j

CNDS ‘03 9 URL: Maximum Lifetime Data Aggregation (MLDA) Problem The MLDA problem is to find a data gathering schedule with maximum lifetime for a sensor network which allows in- network data aggregation  An aggregation tree is a directed tree rooted at the base station and spanning all the sensors. An aggregation tree specifies, how the data packets from all the sensors are collected, aggregated and transmitted to base station. There is one such aggregation tree for each round.  A schedule with lifetime T is a collection of up to T aggregation trees An aggregation tree may be used more than once in a schedule. If an aggregation tree is used for f rounds, then it has lifetime f. The lifetime of a schedule is the sum of the lifetimes of aggregation trees in the schedule.  A feasible schedule is a schedule which respects the energy constraints of the sensors

CNDS ‘03 10 URL: Aggregation Trees XX

CNDS ‘03 11 URL: Maximum Lifetime Data Aggregation (MLDA) Problem… Kalpakis, Dasgupta, and Namjoshi [ICN 2002] give a near optimal solution to the MLDA problem.  The problem is formulated as a flow problem with linear objective function and linear constraints.  An integer program is presented to solve the MLDA problem.  The linear relaxation of the integer program can be computed in polynomial time. MLDA problem can be shown to be NP-complete by reduction from Hamiltonian Path problem.  A integer solution is computed by flooring the flow variables given by the linear program and re-computing the linear program with the floored flows as constraints.  Experiments show that this solution is within 5 rounds of fractional optimal solution.  MLDA approximation algorithm has a very high time complexity.

CNDS ‘03 12 URL: A- Restricted MLDA A -Restricted MLDA is an alternate formulation of Maximum Lifetime Data Gathering problem. Suppose that we are restricted to use a set of aggregation trees A. (candidate set). A -Restricted MLDA problem is to find the maximum lifetime schedule using the aggregation trees from candidate set only.  in other words, we must decide the lifetime of each aggregation tree in A, such that sum of all lifetimes is maximized.

CNDS ‘03 13 URL: A few more definitions… For an aggregation tree A i, we define its energy vector E(i) as a vector of size n indicating the energy consumed by each sensor, in A i.  Intuitively, energy vector denotes energy expended by each sensor during one round of data gathering using tree A i.  Given a candidate set comprising of m trees, let S be a schedule that uses the aggregation trees only from candidate set.  is a vector of size n indicating the initial energy of each sensor. To solve A -Restricted MLDA problem, we need to determine the lifetime i of each tree in the candidate set in schedule S such that lifetime of the system is maximized.

CNDS ‘03 14 URL: A Linear Programming Formulation for A- Restricted MLDA The above integer program with linear constraints can be used to solve A -Restricted MLDA problem.  This integer program computes maximum lifetime schedule S comprising of trees in candidate set  The energy constraint ensures that no sensor expends more than its initial energy.  n constraints (one for each sensor) and m variables (one for each tree in candidate set)

CNDS ‘03 15 URL: A Linear Programming Formulation for A- Restricted MLDA… The linear relaxation of the integer program where i are allowed to take fractional values, can be computed in polynomial time.  We obtain the approximate solution by fixing the lifetime of each aggregation tree to the floor of its lifetime obtained from linear program.  This ensures that energy constraints are never violated by any sensor. If the candidate set contained all possible aggregation trees, solution for A -Restricted MLDA problem is the solution for MLDA problem.  Unfortunately, for a network with n sensors, number of such aggregation trees is  (2 n ). The linear relaxation of the integer program provides us with an approximation scheme for MLDA problem.

CNDS ‘03 16 URL: A Linear Programming Formulation for A- Restricted MLDA… Better lifetimes can potentially be obtained by the LP if a larger candidate set is used.  To be precise, if S 1  S 2, then lifetime for S 1  the lifetime for S 2. Thus, we are interested in finding easily computable candidate sets with few ( O(n c ) for some small constant c ) aggregation trees, that provide us with “good” lifetime. We describe two approaches to construct the candidate sets and discuss the performance of these schemes.

CNDS ‘03 17 URL: The A- LRS Algorithm The LRS Protocol (PEGASIS-based hierarchical scheme)  [Lindsey, Raghavendra and Sivalingam, 2001]  LRS protocol clusters sensors greedily based on their distances from each other and the base-station.  Chains are formed among the nodes in the clusters at the lowest level of the hierarchy.  Gathered data moves along the chain, gets aggregated and reaches a designated leader of the chain i.e. cluster head.  The cluster heads from level one are again clustered into one or more clusters (chains), and data is collected and aggregated in each chain in a similar manner.  In the final level of the hierarchy, one sensor is chosen to transmit the aggregated data packet for that round to the base station.  The leader in each round in each chain is selected in round robin manner.  The number of hierarchies is always 3.  Note that the manner in which chain leaders are selected in each level of hierarchy, naturally defines an aggregation tree

CNDS ‘03 18 URL: The A- LRS Algorithm… LRS imposes an implicit ordering among the sensors in each cluster at every level of the hierarchy.  clusters are arranged in a chain.  data always moves along the chain towards the leader.  This ordering is determined during initialization, but remains fixed thereafter. LRS then simply alternates between the members of each chain in a round-robin fashion to determine the leader(s) for a particular round. During the first n rounds of data gathering, LRS induces a set of n distinct aggregation trees.  After the first n rounds, these n trees are used by the LRS protocol in a round-robin manner.  We refer to these trees as the LRS aggregation trees. The LRS trees form a suitable candidate set for the A - Restricted MLDA.

CNDS ‘03 19 URL: The A-Randomized- LRS Algorithm A larger candidate set of aggregation trees can potentially lead to a data gathering schedule with better lifetime. We augment the LRS set of aggregation trees by permuting the sensors in each cluster (chain) at the lowest level of the LRS hierarchy. Recall that, LRS imposes an implicit ordering among the sensors within each cluster (chain) at the lowest level of the hierarchy. This ordering limits the number of distinct aggregation trees used. By using a different ordering of the sensors in one or more clusters, one can easily construct a different set of aggregation trees.

CNDS ‘03 20 URL: A-Randomized- LRS Trees

CNDS ‘03 21 URL: The A-Randomized- LRS Algorithm… We start with a greedy clustering of the sensors into chains,so that every sensor transmits to a close neighbor as in LRS. Using P random permutations of the sensors, where each permutation randomly permutes the sensors within each cluster at the lowest level of the hierarchy, we obtain additional P orderings. We can obtain additional ( P x n ) LRS aggregation trees by running LRS for each of these orderings. By choosing P to be a small constant, we can still solve the A- Restricted MLDA problem efficiently, and potentially obtain superior system lifetimes with respect to the A- LRS algorithm.

CNDS ‘03 22 URL: Maximum Lifetime Data Routing (MLDR) Problem Data aggregation is not applicable in all sensing environments. In some environments, no aggregation may be feasible.  video images from distant regions of a battlefield with no overlap  this implies that the number and size of transmissions will increase, thereby draining the sensor energies much faster. Problem is to find an efficient schedule to collect and transmit the data to the base station, such that the system lifetime T is maximized. This problem can be viewed as a maximum flow problem with energy constraints at the sensors, subject to integral flows. Note that MLDR schedule is a collection of paths to the base station from each sensor.

CNDS ‘03 23 URL: Maximum Lifetime Data Routing (MLDR) Problem… The linear relaxation of the above integer program can be computed in polynomial time. A near-optimal solution to the MLDR problem can be obtained by running the above linear program again and fixing the values of the f i,j variables to the floor of their values obtained in the previous step.  The solution obtained in this second step is guaranteed to have integer values for all the variables, since it is a max-flow problem with integer capacities.

CNDS ‘03 24 URL: Performance Evaluation We will compares the performance of various schemes for  unlimited aggregation, MLDA, A- LRS, A-Randomized- LRS and LRS schemes  limited aggregation, A- LRS, A-Randomized- LRS and LRS schemes

CNDS ‘03 25 URL: Experimental Setup We consider a network with sensors randomly distributed in 50m x 50m field Number of sensors is varied between 40, 50, 60, 80 and 100 Each sensor has initial energy 1 Joule The base-station is located at (25m, 150m) Each sensor generated data packets of size 1000 bits Energy model used is the First Order Radio Model For each experiment, we measure the lifetime of the sensor network for A- LRS and A-R -LRS algorithms For A-R -LRS algorithm, we experiment with 10, 25, 50, 75, 100, 250, 500, 750, and 1000 permutations. We compare our results with the LRS protocol [Lindsey et al 2001], MLDA and the fractional optimal.

CNDS ‘03 26 URL: Results with Unlimited Aggregation

CNDS ‘03 27 URL: Comparisons for a 50 sensor network

CNDS ‘03 28 URL: Comparisons for a 100 sensor network

CNDS ‘03 29 URL: Limited Aggregation Model Limited aggregation  Unlimited aggregation may not always be applicable.  We now consider a simple “limited” aggregation model and study its effects on system lifetime.  Note that the MLDA algorithm cannot be used in this limited aggregation model. We define weight of a data packet W, to be the number of sensors whose measurements are reflected in the information in that data packet.  Recall that, in our unlimited aggregation model, we allow each sensor to aggregate any number of incoming packets into one single outgoing packet of same size.  Thus, in the unlimited aggregation case, the weight of a data packet is not bounded by any constant.

CNDS ‘03 30 URL: Limited Aggregation Model… In our Limited Aggregation Model each data packet has a capacity to carry a fixed weight, K. In any single round, if a sensor receives incoming packets of total weight W, it will need to send as many packets as required to hold weight W+1.  Thus,  (W+1)/K  data packets will be sent. the total weight of all the outgoing packets equal to W+1. each outgoing packet weighs no more than K.  The aggregation ratio is K:1.  A- Restricted MLDA and therefore the A- LRS and A-R- LRS algorithms can be used to solve the data aggregation problem even in the limited aggregation case.  Note that we do not claim applicability of this particular Limited Aggregation model in all cases and the schemes presented here are independent of this particular model.

CNDS ‘03 31 URL: Experimental Setup We consider a network with sensors randomly distributed in 100m x 100m field. Number of sensors is varied between 100 to 500. Each sensor has initial energy 1 Joule. The base-station is located at (50m, 300m). Each sensor generated data packets of size 1000 bits. Energy model used is the First Order Radio Model. For each experiment, we measure the lifetime of the sensor network for A- LRS and A-R -LRS algorithms. For the A-R -LRS algorithm,  Aggregation ratios range from  :1 to 2:1.  Number of permutations P, is fixed to 100. We compare our results with the LRS protocol.

CNDS ‘03 32 URL: Results with Limited Aggregation

CNDS ‘03 33 URL: Results with Limited Aggregation…..

CNDS ‘03 34 URL: Conclusions and Future Directions A approximation algorithm for the Maximum Lifetime Data Aggregation problem in sensor networks. Our scheme significantly improves the system lifetime when compared to one of the best known existing protocols and is close to optimal. Solves Maximum Lifetime Data Aggregation problem in the limited aggregation case. Future directions …  We plan to investigate modification which would allow addition (removal) of sensors from the network, without having to re-compute the schedule.

CNDS ‘03 35 URL: Thank You !!!