SoftCOM 2005: 13 th International Conference on

1. SoftCOM 2005: 13th 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. Presentation Plan • Introduction – Main Contribution • Definitions – Wireless Sensor Network Model • Linear Programming Formulation • Numerical Results • Conclusions – Issues for Further Study September 15-17, 2005, Marina Frapa - Split, Croatia

3. 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 September 15-17, 2005, Marina Frapa - Split, Croatia

4. 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 September 15-17, 2005, Marina Frapa - Split, Croatia

5. 2. Definitions – Wireless Sensor Network Model • Set N of static sensors, Eiinitial energy - Qidata generation rate at sensor i • Mobile sinks, set L of possible locations, tl 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 tl • 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, September 15-17, 2005, Marina Frapa - Split, Croatia

6. 3. Linear Programming Formulation Energy consumption (transmission and reception) at sensor i for time duration tl 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 tl and the rates that maximize network lifetime under the flow conservation condition for each location and under the energy constraint for each sensor September 15-17, 2005, Marina Frapa - Split, Croatia

7. 3. Linear Programming Formulation • : amount of information transferred from i to j during time tl • 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 September 15-17, 2005, Marina Frapa - Split, Croatia

8. 4. Numerical Results • Compared models : • LP Model with Shortest Path Routing (SPR) • LP Model with Multiple Shortest Path Routing (MSPR) • LP Model for the Static Sink case (Static Sink) • 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) September 15-17, 2005, Marina Frapa - Split, Croatia

9. 4. Numerical Results Average network lifetime (over all instances – various network sizes) • 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 September 15-17, 2005, Marina Frapa - Split, Croatia

10. 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 September 15-17, 2005, Marina Frapa - Split, Croatia

11. 4. Numerical Results 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 September 15-17, 2005, Marina Frapa - Split, Croatia

12. 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. September 15-17, 2005, Marina Frapa - Split, Croatia

13. 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 September 15-17, 2005, Marina Frapa - Split, Croatia