An Analysis of the Optimum Node Density for Ad hoc Mobile Networks

1. An Analysis of the Optimum Node Density for Ad hoc Mobile Networks Elizabeth M. Royer, P. Michael Melliar-Smith and Louise E. Moser Presented by Aki Happonen

2. Outline • Introduction • Scope of The Paper • AODV (Ad hoc On-Demand Distance Vector Routing) • Simulations • Simulations • AODV • The Mobility Model • Topology Changes • Node Distribution • Throughput • Path Length • Probability to Establish Initial Route • Related Work • Conclusions • Future Work And Some Thoughts

3. Introduction • Ad hoc mobility network is a collection of nodes • Each communicates over wireless channel • Capable of movement • Each node have unique capability of transmission at different power levels • In mobile networks battery life and channel bandwidth are limited resources • Raises importance of transmission power to overall performance of network • Kleinrock, Silvester in 1978: Optimum number of neighbors for node is 5.89, so radius should be adjusted so that each node has six neighbors • Stationary network

4. Scope of the Paper • This paper examines effects of transmission power on mobile networks • Does any mobile has optimum transmission radius determined for stationary networks • Ad hoc On-Demand Distance Vector (AODV) routing protocol was used for route establishment • Result can be generalized to most on-demand ad hoc routing protocols

5. AODV • Route discovery • Source node broadcasts a Route Request (RREQ) containing IP address of destination and last known sequence number – timer to wait for reply • Nodes respond with Route Reply (RREP) to RREQ if • They are the destination • They have unexpired route to destination • If source does not receive RREP after timer is expired it rebroadcast RREQ for some maximum number of attempts – after that session is aborted • Route maintenance • Route Error (RERR) message is send in case of link breaks in active route • Advantages of AODV: • Nodes store only the routes that are needed • Need for broadcast is minimized • Reduce memory requirements and needless duplications • Quick response to link breakage in active routes • Loop-free routes maintained by use of destination sequence number • Scalable to large population of nodes

6. Simulations • GloMoSim Network Simulator by UCLA was used • Free space propagation model with threshold cutoff was used • Free space model has power attenuation of 1/d2, where d is the distance between nodes • Four different mobilities between 0m/s and 10m/s • Each simulation results are average of 10 different initial network configuration • Each simulation simulates 240 seconds and models a network of 100 nodes in 1000m x 1000m area • Number sources is set at 40 and each source sends 12 512-byte data packets/s • Network saturation

7. Simulations - AODV • AODV does not guarantee packet delivery – does find good routes for IP’s best-effort delivery • Data packets are not buffered for retransmission, these packets are likely to be lost • If a collision involving a data packet occurs at a node and packet cannot be captured, the packet is lost • Focus on the number of packets received by destination NOT the ratio of number of packets received to number of packets send

8. Simulations – The Mobility Model • Original model was Random Waypoint model • In the beginning: • Randomly placed nodes within the predefined simulation area • Each node selects destination and speed from a uniform distribution of user-specific speed • In simulation: • The node travels to its selected destination at selected speed • After reaching the destination it is stationary for some predefined time • At the end of pause time node selects a new destination and speed combination and resumes movement • Continues changes in topology of the network and number of neighbors varies as a function of time

9. Simulations – The Mobility Model • New model was developed – Random Direction • Instead of selection destination, node selects a direction (in degrees) in which to travel • In the beginning • Nodes select a degree between 0 and 359 – destination is found from the boundary in this direction of travel • Then node selects the speed • In simulation: • Node travels to destination at the given speed • After reaching the destination node rests for given pause time and then selects a new degree between 0 and 180 • Degree is limited because node is on the boundary and they are not allowed to pass through it • Degree is relative to the wall of the boundary area which the node is located • In Modified Random Direction model destination can be selected anywhere along that direction of travel

10. Simulations – Topology Changes Average neighbors/node: 1m/s 5m/s

11. In the beginning of the simulation nodes are evenly distributed After 400 s simulation time Random Waypoint model causes higher density Random Direction maintains initial node density Simulations – Node Distribution

12. Small radius and low connectivity, few data packets are delivered As the connectivity increases the number of delivered packets increases rapidly until curves level off There does not appear to be global optimal number of neighbors for all mobilities For 0m/s is it 7-8, almost the same than Kleinrock proved but when mobility increases optimal shifts to higher connectivity Simulations Results - Throughput

13. Lower transmission powers do have shorter path lengths – only routes that are able to complete When network is fully connected, path length increases and start to decrease when transmission power increases and fewer hops are needed to connect source and destination Simulations Results – Path Length

14. Sparsely connected network probability is fairly low When density increases the probability increases rapidly until stabilizes to one Simulations Results – Probability to Establish Initial Route

15. Related Work • Sanchez, Manzoni and Haas: • Calculated the minimum value for the transmission range that maintains full connectivity in the network- all network nodes use the same transmission range. • Ramanathan and Rosales-Hain: • Power control algorithm to respond topology changes • ElBatt, Krishnamurthy, Connors and Dao: • Networks with power control has better performance than networks without that kind of scheme

16. Conclusions • In this paper it has been explored transmission power trade off in mobile networks to determine the optimum node density for delivering maximum number of data packets • This paper shows that there does not exist a global optimum density • To achieve the maximum the node density should increase as the rate of node movement increases

17. Future Work And Some Thoughts • Extend model towards real world conditions • Terrain and atmospheric conditions effect to connectivity • Presenter thoughts: • What are requirements for power control algorithms? • Optimum number of neighbors is very close to L. Kleinrock and J. Silvester finding in their paper “Optimum Transmission Radii for Packet Radio Networks or Why Six is Magic Number” • Who about connect channel capacity and routing algorithms?