1. SoftCOM 2005: 13 th International Conference on Software, Telecommunications and Computer Networks September 15-17, 2005, Marina Frapa - Split, Croatia Symposium on : Future Wireless Systems II Paper : Maximum Lifetime Routing to Mobile Sink in Wireless Sensor Networks Ioannis Papadimitriou Co-Author : Prof. Leonidas Georgiadis ARISTOTLE UNIVERSITY OF THESSALONIKI, GREECE FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING Division of Telecommunications

2. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia2 Presentation Plan 1.Introduction – Main Contribution 2.Definitions – Wireless Sensor Network Model 3.Linear Programming Formulation 4.Numerical Results 5.Conclusions – Issues for Further Study

3. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia3 1. Introduction – Main Contribution Maximum Lifetime Routing in Wireless Sensor Networks Assumptions : Battery–operated sensors Efficient management of available energy Mobile sink Different locations during network operation Multiple hops Flexibility of power control Two joint problems : Scheduling : Determine the sink sojourn times at different locations Routing : Find the appropriate energy–efficient paths to the sink Our Linear Programming formulation provides the optimal solution to both of these problems and maximizes network lifetime

4. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia4 1. Introduction – Main Contribution Main idea : Exploit sink mobility to avoid bottleneck sensors → more efficient utilization of remaining energies → fair balancing of energy depletion among sensors → network lifetime (time to first battery depletion) is maximized Advantages of our setup :  Non-homogeneous sensors (different initial energies and data generation rates)  Realistic random deployment of sensors (no specific pattern)  Sensor locations and possible sink locations are not necessarily the same  Power control (the energy consumption rate per unit information transmission depends on the choice of the next hop node)  Our LP model gives the best achievable network lifetime

5. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia5 2. Definitions – Wireless Sensor Network Model Set N of static sensors, E i initial energy - Q i data generation rate at sensor i Mobile sink s, set L of possible locations, t l sink sojourn time at location l set of neighboring nodes of sensor i for location l data unit transmission energy from i to j, reception energy at j information transfer rate from i to j during time t l Example : Sensor A can reach sensors B,C For location 1, sink s is also in transmission range of A For locations 2, 3, 4, it is not Therefore,

6. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia6 3. Linear Programming Formulation Energy consumption (transmission and reception) at sensor i for time duration t l Total energy consumed at sensor i for all possible sink locations Network lifetime (time to first battery drain-out) = sum of sink sojourn times Objective : Find the sink sojourn times t l and the rates that maximize network lifetime under the flow conservation condition for each location and under the energy constraint for each sensor

7. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia7 3. Linear Programming Formulation  : amount of information transferred from i to j during time t l  The problem can be written as a Linear Programming model (Energy constraints) (Flow conservation conditions) The LP model solves optimally the scheduling and the routing problem and maximizes network lifetime

8. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia8 4. Numerical Results Compared models : 1)LP Model with Shortest Path Routing ( SPR ) 2)LP Model with Multiple Shortest Path Routing ( MSPR ) 3)LP Model for the Static Sink case ( Static Sink ) 4)Optimal LP Formulation ( LP-opt ) Networks created : 100 random sparsely connected networks for a given |N| (20,40,…,100) sensors randomly placed in a square area of size 100×100 Data unit transmission energy from i to j, Sink location coordinates (0,0), (0,100), (100,0), (100,100), (50,50)

9. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia9 4. Numerical Results  Our LP-opt model performs significantly better than the other models  Lifetime improvement ratio increases with the network size  SPR and MSPR models perform almost the same  Static Sink model performs better than SPR and MSPR Average network lifetime (over all instances – various network sizes)

10. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia10 4. Numerical Results Average sink sojourn times (over all instances – various network sizes)  The sink node stays most of the time at the center of the network and considerably less at the four corners  Sink locations are not uniform with respect to the sensors’ deployment  There are more sensors around the center of network, which can be used to relay the packets of all other sensors

11. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia11 4. Numerical Results |N||N| E i ´ = 0E i ´ < 0.25  E i E i ´ < 0.5  E i SPRStaticLP-optSPRStaticLP-optSPRStaticLP-opt 2015%25%47%22%32%52%32%41%61% 409%27%54%15%31%59%25%39%65% 607%32%63%11%36%66%20%43%70% 805%31%68%10%35%71%18%41%75% 1004%31%70%8%34%73%16%40%76% Average percentages of sensors whose Residual Energy satisfies the following relations  An indication about the distribution of sensors’ residual energies  LP-opt model results in fair balancing of energy depletion among sensors  Higher percentages of sensor’s with little (or even zero) residual energy, usually imply a higher overall network lifetime

12. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia12 5. Conclusions – Issues for Further Study Adaptive environment :  If the sensors do not know the schedule of the sink and their data transfer rates in advance, new on-line algorithms are necessary.  The sink determines on-line the time to spend in every location.  The remaining lifetimes of the sensors can be used by the routing algorithm to determine new paths to the sink to avoid the bottleneck nodes. Distributed Implementation :  Sink sojourn times and information transfer rates are not determined by a central node (possibly the sink).  Distributed maximum lifetime routing algorithms must be used.

13. SoftCOM 2005September 15-17, 2005, Marina Frapa - Split, Croatia13 End of Presentation Thank you for your attention Paper : Maximum Lifetime Routing to Mobile Sink in Wireless Sensor Networks Ioannis Papadimitriou Co-Author : Prof. Leonidas Georgiadis ARISTOTLE UNIVERSITY OF THESSALONIKI, GREECE FACULTY OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING Division of Telecommunications