������� �������� ������� ���� ������ �� � �������� ����� � ��� � � ��� Elham Torabi EECE 565 - Term Paper - April 2006 Department of Electrical & Computer Engineering The University of British Columbia
Outline 2 1. Overview and Introduction 2. Power Efficient Routing Algorithms • Minimum Total Transmission Power Routing (MTPR) • Minimum Battery Cost Routing (MBCR) • Min-Max Battery Cost Routing (MMBCR) • Conditional Min-Max Battery Capacity Routing (CMMBCR) • Max-Min zP min Routing • Flow Augmentation (FA) Routing 3. Performance Comparison Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
1. Overview and Introduction 3 • Ad-hoc wireless sensor networks consist of large numbers of sensor nodes, which are tiny, low-cost, low-power radio devices dedicated to performing functions such as collecting data, limited data processing, and sending data to infrastructure processing gateways.. • Most nodes operate on their limited battery energy. • The power consumption is closely coupled with the route selection in these networks. • It is important to minimize the power consumption of the entire network, this implies maximizing the network lifetime. • Power consumption categorization: 1. communication related power used for transmission and reception of mes- sages. 2. non-communication related power used for operations such as sensing and data processing. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Minimum Total Transmission Power (MTPR) 4 • For successful transmissions, the signal-to-noise ratio (SNR) received at node n j should be greater than a specified threshold ψ j , and satisfy the following P i G i,j SNR j = ψ j ( BER ) , (1) � k � = i P k G k,j + η j where P i is the transmission power of host n j , G i,j = 1 /d n i,j is the path gain between nodes n i , n j , d i,j is distance between two nodes, and n is the propagation exponent. η j is the thermal noise. The transmission power P ( n i , n j ) between nodes n i , n j can be used as metric, and the total transmission power for route l , P l , can be derived from D − 1 � , for all node n i ∈ route, P l = P ( n i , n i +1 ) (2) i =0 The desired route k can be obtained (using Bellman-Ford algorithm) from P k = min l ∈ A P l , (3) where A is the set containing all possible routes. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Minimum Total Transmission Power (MTPR) 5 • Modification resulting in fewer hops: Using distributed Bellman-Ford algo- rithm, at node n j , it computes C i,j = P transmit ( n i , n j ) + P transceiver ( n j ) + Cost ( n j ) , (4) where n i is a neighboring node of n j , P transceiver ( n j ) is the transceiver power at node n j , and Cost ( n j ) is the total power cost from the source node to node n j . This value is sent to node n i , where it computes its power cost by using the following equation Cost ( n i ) = j ∈ NH ( i ) C i,j , min (5) where NH ( i ) = { j ; n j is a neighbor node of n i } . The path with min- imum cost from the source node to node n i is selected. This procedure is repeated until the destination node is reached. • If the minimum total transmission power routes are via specific nodes, the battery of these nodes will be exhausted quickly and may cause network par- titioning. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Minimum Battery Cost (MBCR) 6 • The remaining battery capacity of each node is a more accurate metric to find the lifetime of each node f i ( c t i ) = 1 /c t i , (6) where f i ( c t i ) is defined as a battery cost function of node n i , where c t i is the battery capacity of node n i at time t . • The battery cost R j for route i consisting of D nodes is D j − 1 � f i ( c t R j = i ) . (7) i =0 • The route with maximum remaining battery capacity is selected as R i = min { R j | j ∈ A } , (8) where A is the set containing all possible routes. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Minimum Battery Cost (MBCR) 7 • This algorithm prevents nodes from being overused. • Since, only the summation of values of battery cost functions is considered, a route containing nodes with little residual battery capacity may still be selected. Figure 1: An illustration of the shortcoming in minimum-hop routing. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Min-Max Battery Cost (MMBCR) 8 • The objective function in MBCR can be modified as i ∈ route j f i ( c t R j = max i ) . (9) Similarly the desired route i can be obtained as R i = min { R j | j ∈ A } (10) • In this algorithm the battery of each node will be used more fairly than in previous schemes. • There is no guarantee that minimum total transmission power paths will be selected under all circumstances. • This approach can consume more power to transmit node traffic from a source to a destination, which will reduce the lifetime of all nodes. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Conditional Min-Max Battery Capacity (CMMBCR) 9 • The goal is to maximize the lifetime of each node and use the battery fairly. • The battery capacity R c j for route j at time t is defined as R c i ∈ route j c t j = min i . (11) A is a set containing all possible routes between any two nodes at time t and satisfying the following equation R c j ≥ γ. for any route j ∈ A , (12) where γ is a threshold between 0 and 100 . Let Q denote the set containing all possible paths between the specified source and destination nodes at time t , then – If A ∩ Q � = ∅ , that implies all nodes at some paths have remaining battery capacity higher than γ , choose a path in A ∩ Q by applying the MTPR scheme. – Otherwise, choose route i with the maximum battery capacity: R c i = � R c � max j | j ∈ Q . Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Conditional Min-Max Battery Capacity (CMMBCR) 10 • γ can be considered as a protection margin. • The performance of CMMBCR depends on the value of γ . The normalized Figure 2: Normalized network lifetime of CMMBCR versus its parameter γ . network lifetime R X denotes the ratio between the network (system) lifetime of the algorithm and the optimal solution obtained by solving the linear pro- gramming problem. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Max-Min zP min 11 • This is an online power-aware routing algorithm in a sense that it does not know ahead of time the sequence of messages that has to be routed over the network. • Maximizing the lifetime of the network is modeled as the time to the earliest time a message can not be sent. • The maximal number of messages sustained by a network from the source node to the sink node can be formulated as a linear programming problem, and goal is to maximize the number of messages in the network � Maximize n sj s.t. j � n ij · e ij ≤ P i , j � � n ij = n ji ( for i � = s, t ) , (13) j j Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Max-Min zP min 12 where the total number of messages from node v i to node v j is denoted by n ij , and e ij represents the power cost to send a message from node v i to node v j , and s and t denote the source and the sink in the network. P i denotes the power of node i . • It’s desired to route messages along the path with the maximal minimal frac- tion of remaining power after the message is transmitted, called the max-min path, but the performance of max-min path can be very bad as seen below Figure 3: The performance of max-min path can be very bad. • Going through the nodes with high residual power may be expensive as com- pared to the path with the minimal power consumption, where too much power consumption decreases the overall power level of the network, and thus decreases its lifetime. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
2. Power Efficient Routing Algorithms: Max-Min zP min 13 • Therefore, a trade-off between minimizing the total power consumption and maximizing the minimal residual power of the network should be considered. • Enhancing a max-min path by limiting its total power consumption will be the goal. • The two extreme solutions to power-aware routing for one message are: 1. compute a path with minimal power consumption P min 2. compute a path that maximizes the minimal residual power in the network. This algorithm optimizes both criteria. • The minimal power consumption for the message is relaxed to be zP min with parameter z ≥ 1 to restrict the power consumption for sending one message to zP min . Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks
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