12.Nov.2007 Capacity of Ad Hoc Wireless Networks Jinyang Li Charles Blake Douglas S. J. De Coutu Hu Imm Lee Robert Morris Paper presentation by Tonio Gsell © ETH Zürich | Taskforce Kommunikation

12.Nov.2007 Tonio Introduction  Ad hoc wireless networks promise convenient infrastructure- free communication  Does Capacity benefit or suffer from area growth?  More spatial re-use of the spectrum (+)  Nodes are increasingly imposed to forwarding load (-)  Overall question: Are ad hoc wireless networks scalable? 2

12.Nov.2007 Tonio Related work  Most related work’s analysis base on random traffic patterns  Gupta and Kumar assume the average path length to grow with the spatial diameter of the network:  End-to-end throughput available to each node:  Approaches zero! 3

12.Nov.2007 Tonio Background  Four way exchange  RTS (ready to send)  CTS (clear to send)  Data  ACK (acknowledgment)  NAV (network allocation vector)  Stores the time remaining till the network comes available again  RTS & CTS include busy time → stored to NAV  On timeout (no CTS) the backoff window will be doubled (exponential backoff) 4

12.Nov.2007 Tonio MAC Interactions Overview  Simulation of detailed interaction between Ad Hoc forwarding and MAC  Simple to complex scenarios  ns with CMU wireless extensions  Model Lucent Wavelan card 2Mbps  Stationary nodes  Transmission range of 250m  Interfering range of 550m  Nodes mostly separated by 200m 5

12.Nov.2007 Tonio MAC Interactions Single Cell Capacity  Framework:  Single cell 200m 200m  Sending as fast as allowed  Randomly selected destination  Expectations:   With interframe timings throughput 1.7Mbps 6

12.Nov.2007 Tonio MAC Interactions Capacity of a Chain of Nodes  Framework:  Single chain of nodes  Packets are originated at first node and forwarded to the last node in the chain  Expectations:  Maximum utilization should be 7

12.Nov.2007 Tonio MAC Interactions Capacity of a Chain of Nodes  Simulation results (1.5kB):  2 nodes achieve 1.7Mbps throughput as expected  Longer chain → approaches 0.25Mbps throughput -Only about of the maximum of 1.7Mbps  Real Hardware results:  Average difference is only 6% 8

12.Nov.2007 Tonio MAC Interactions Capacity of a Chain of Nodes  Explanation:  No optimum schedule discovery  Bandwidth allocation unevenly  Wasted backoff time 9

12.Nov.2007 Tonio MAC Interactions Capacity of Regular Lattice Network  Framework:  Horizontal traffic flow (left → right)  square lattice  Expectations:  Every third chain can operate without interchain interference → Maximum throughput should be 10

12.Nov.2007 Tonio MAC Interactions Capacity of Regular Lattice Network  Simulation results (1.5kB):  Per flow throughput settles at about 0.1Mbps  Explanation:  Nodes in the beginning experience less contention  Wasted backoff periods (0.75%) 11

12.Nov.2007 Tonio MAC Interactions Cross Traffic in a Latice  Framework:  Vertical and horizontal traffic flow (up → down, left → right)  Square lattice  Expectations:  Horizontal in one time cycle, vertical in the next → of the channel capacity 12

12.Nov.2007 Tonio MAC Interactions Cross Traffic in a Latice  Simulation results (1.5kB):  Per flow throughput settles at about 0.04Mbps, this is slightly less than of the per flow throughput of a lattice network  Explanation:  More wasted backoff periods (2.23%) 13

12.Nov.2007 Tonio MAC Interactions Excurse: One-hop network throughput  Alternate analysis  Measure the total one-hop network throughput: Count all radio transmissions for data packets that successfully arrive at their final destinations, including packets forwarded by intermediate nodes. 14

12.Nov.2007 Tonio MAC Interactions Random Traffic in a Random Layout  Framework:  Uniformly random node placement on square universe  Every node sends each packet to randomly chosen destination  No routing but precomputed shortest path  75 nodes per square kilometer  Expectations:  Similar one-hop throughput to the horizontal/vertical lattice 15

12.Nov.2007 Tonio MAC Interactions Random Traffic in a Random Layout  Simulation results (1.5kB):  Somewhat less capacity than the horizontal/vertical lattice  Explanation:  Some empty areas → wastes of spatial diversity  More packets routed through the centre 16

12.Nov.2007 Tonio Scaling Ad Hoc Networks Larger view: total capacity vs. single node load  Estimate the useful bandwidth each node can expect for its own traffic.  Load increases with the number of nodes  Load increases with the distance over which each node wishes to communicate  Total bandwidth increases with the physical area covered by the network 17

12.Nov.2007 Tonio Scaling Ad Hoc Networks Path Length : fixed radio transmission range : uniform node density : rate of originated packages per node : expected physical path length : constant  As the expected path length increases, the per node bandwidth to originate packets decreases. 18

12.Nov.2007 Tonio Scaling Ad Hoc Networks Random traffic pattern  The listed probability density function (pdf) gives the probability of a node randomly communicating with another one at distance x:  The expected path length for a random traffic pattern follows as:  So the per node capacity for a constant density is. 19

12.Nov.2007 Tonio Scaling Ad Hoc Networks Traffic Patterns that Scale  Power law distance distribution:  So the average path length is:  With it scales similar to random traffic with  With it scales roughly constant 20

12.Nov.2007 Tonio Conclusion  From the ideal node chain capacity, MAC achieves  does a reasonable job scheduling packet transmissions in ad hoc networks  is much more efficient for orderly local traffic patterns  can approach the theoretical maximum capacity of per node in a large random network  Locality of traffic is the key argument for the scalability 21