### Delay-bounded Energy-constrained Adaptive Routing in Wireless

```Shi Bai, Weiyi Zhang, Guoliang Xue, Jian Tang, and Chonggang Wang
University of Minnesota, AT&T Lab, Arizona State University, Syracuse
University, NEC Lab
2012 IEEE INFOCOM
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1. Introduction
2. Algorithm
◦ 2.1 Definition
◦ 2.2 Problem statement
◦ 2.3 DEAR Algorithm
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3. Experiment
4. Conclusion
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Wireless Sensor Networks
◦ Key Issue: Energy Consumption
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Routing (DEAR) Problem
 Splitting the traffic over multiple paths
◦ Differential delay
 Increased memory and buffer overflow
◦ Deliverable energy constraints
 Energy consumption of transmitting packet
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Def 1. Packet Allocation
◦ P is a set of s-BS paths.
◦ The aggregated packet of link e is the sum of the
packet allocations on link e of the paths in P:
 q(e) = ƩL(p)
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Def 2. Differential delay
◦ dh => the highest path delay
◦ dl => the lowest path delay
◦ => Dp= dh – dl
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Def 3. Energy Consumption
◦ Transmitting energy consumption
 E = w*q
 q => packet size transmitted on link
 w => Energy consumption of transmitting 1 bit
 W=[C*(2^b-1)+F]*(1/b)
 C => the quality of transmission and noise power
 F => the power consumption of electronic circuitry
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Def 4. Latency/Delay
◦ Queuing delay
 The time waiting at output link for transmission
◦ Transmission delay
 The amount of time required to push all of the packet bits into the
transmission media
◦ Propagation delay
 The time takes for the head of the signal to travel from the sender to
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Transmission delay
◦ Ignored transmission and queuing delay
◦ Without considering the transmission delay
 Allocate of packets have no impact on delivery of
packets
 Path:p1=(A,B,BS), p2=(A,C,BS), p3=(A,BS)
 Path delay: d(p1)=2, d(p2)=3, d(p3)=2
 Ex a) packet split => p1=10, p3 = 2
 Ex b) packet split => p1= 6, p3 = 6
 Path delay are the same
 Differential delay
 d(p1)-d(p3) = 2 – 2 = 0
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◦ Considering the transmission delay
 Allocations of packets on multiple paths will have
impact on path delays
 Path delay
 d(p1) = Ʃd(e) + ƩƬ(v)
 Ex a) d(p1) = 2 + (10 pk/(2 pk/s) + 10/2) = 12, d(p3) = 2
+ (2/4) = 2.5
 Ex b) d(p1) = 2 +(6/2 + 6/2) = 8, d(p3) = 2 + (6/4) = 3.5
 Path delay are different
 Ex a) Differential delay is 9.5=(12 - 2.5)
 Ex b) Differential delay is 4.5
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DEAR(Delay-bounded Energy constrained
◦ Seek set of paths P that can provide the following
 Delay bounded
 Energy constrained
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Graph G=(V, E, b, d, w, β)
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◦
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V represents the set of sensor nodes and BS.
E represents the set of links.
b represents bandwidth
d represents the delay of the path p
w represents transmission energy consumption
β represents the residual energy of sensor v
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Delay Bounded
◦ Any path p in P must satisfy the differential delay
constraint: dmin ≤ d(p) ≤ dmax
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Energy Constrained
◦ The energy consumption of transmitting packet for
each sensor i cannot exceed its residual energy
level β(i)
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◦ The size of aggregated packet of all paths in P is no
less than Q : q(P) ≥ Q
◦ Route the data such that any single link failure does
no affect more than x% of the total packets
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Feasible and infeasible solution by Adaptive
reliability and delay constraint
◦ Ex c) 2,2,8
 In case 8 packet drop => 67%
◦ Ex d) 6,4,2
 In case delay is 8 over between 4 and 5
◦ Ex e) 2,10
 In case 10 packet drop => over 70%
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IDEAR
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Linear Program solution
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ODEAR problem
◦ Optimization problem
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SPDEAR problem
◦ (1+α) approximation algorithm
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◦ Each u[t] means that node
u can transmit packet at
time t.
◦ This bandwidth ensures
that the packets sent by u
at time i can not exceed
b(e).
◦ This ensures that only the
packet, which arrive at BS
no earlier than dmin and no
later than dmax.
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Requirement Condition
◦ Packet Demand: 12 Packet
◦ Reliability requirement x% = 70%
◦ Delay requirement: dmin = 2 and dmax = 5
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Maximum flow by IDEAR
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◦
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P1=(A[0],B[2],BS[4],BS[5])
P2=(A[0],C[3],BS[5])
P3=(A[0],BS[3],BS[4],BS[5])
P4=(A[0],A[1],BS[4],BS[5])
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Fully Polynomial Time Approximation Scheme
for SPDEAR
◦ Scaling and rounding technique
◦ dΘ= ⌊d(e)*Θ⌋ + 1
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Approximation algorithm for ODEAR
◦ dmin ≥ 0
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Efficient Heuristic for DEAR
◦ Round the propagation delay of each link
◦ dmin and dmax
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Network topologies in an 100 * 100 sq
The power of Sensor node was randomly
distributed in [16, 20]
Bandwidth, propagation delay and
transmission energy consumption of each
in [6,10], [1,5], [1,3]
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Performance of different number of nodes
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Performance of different reliability
requirements
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Performance of different packet sizes
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Transmission delay in multipath routing
◦ The previous work ignored
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