Capacity of Ad Hoc Networks Wireless Networks Spring

Capacity of Ad Hoc Networks Wireless Networks Spring 2005

The Attenuation Model q Path loss: o Ratio of received power to transmitted power o Function of medium properties and propagation distance q If PR is received power, PT is the transmitted power, and d is distance q Where ranges from 2 to 4 Wireless Networks Spring 2005

Interference Models q In addition to path loss, bit-error rate of a received transmission depends on: o Noise power o Transmission powers and distances of other transmitters in the receiver’s vicinity q Two models [GK 00]: o Physical model o Protocol model Wireless Networks Spring 2005

The Physical Model q Let {Xi} denote set of nodes that are simultaneously transmitting q Let Pi be the transmission power of node Xi q Transmission of Xi is successfully received by Y if: q Where is the min signal-interference ratio (SIR) Wireless Networks Spring 2005

The Protocol Model q Transmission of Xi is successfully received by Y if for all k q where is a protocol-specified guard-zone to prevent interference Wireless Networks Spring 2005

Measures for Network Capacity q Throughput capacity [GK 00]: o Number of successful packets delivered per second o Dependent on the traffic pattern o What is the maximum achievable, over all protocols, for a random node distribution and a random destination for each source? q Transport capacity [GK 00]: o Network transports one bit-meter when one bit has been transported a distance of one meter o Number of bit-meters transported per second o What is the maximum achievable, over all node locations, and all traffic patterns, and all protocols? Wireless Networks Spring 2005

Transport Capacity: Assumptions q n nodes are arbitrarily located in a unit disk q We adopt the protocol model o Each node transmits with same power o Condition for successful transmission from Xi to Y: for any k q Transmissions are in synchronized slots Wireless Networks Spring 2005

Transport Capacity: Lower Bound q What configuration and traffic pattern will yield the highest transport capacity? q Distribute n/2 senders uniformly in the unit disk q Place n/2 receivers just close enough to senders so as to satisfy threshold Wireless Networks Spring 2005

Transport Capacity: Lower Bound sender receiver Wireless Networks Spring 2005

Transport Capacity: Lower Bound q Sender-receiver distance is q Assuming channel bandwidth W, transport capacity is q Thus, transport capacity per node is Wireless Networks Spring 2005

Transport Capacity: Upper Bound q For any slot, we will upper bound the total bitmeters transported q For a receiver j, let r_j denote the distance from its sender q If channel capacity is W, then bit-meters transported per second is Wireless Networks Spring 2005

Transport Capacity: Upper Bound q Consider two successful transmissions in a slot: Wireless Networks Spring 2005

Transport Capacity: Upper Bound q Balls of radii disjoint around , for all , are q So bit-meters transported per slot is Wireless Networks Spring 2005

Throughput Capacity of Random Networks q The throughput capacity of an network is -node random q There exist constants c and c’ such that Wireless Networks Spring 2005

Implications of Analysis q Transport capacity: o Per node transport capacity decreases as o Maximized when nodes transmit to neighbors q Throughput capacity: o For random networks, decreases as o Near-optimal when nodes transmit to neighbors q Designers should focus on small networks and/or local communication Wireless Networks Spring 2005

Remarks on Capacity Analysis q Similar claims hold in the physical model as well q Results are unchanged even if the channel can be broken into sub-channels q More general analysis: o Power law traffic patterns [LBD+03] o Hybrid networks [KT 03, LLT 03, Tou 04] o Asymmetric scenarios and cluster networks [Tou 04] Wireless Networks Spring 2005

Asymmetric Traffic Scenarios q Number of destinations smaller than number of sources o nd destinations for n sources; 0 < d <= 1 o Each source picks a random destination q If 0 < d < 1/2, capacity scales as nd q If 1/2 < d <= 1, capacity scales as n 1/2 q [Tou 04] Wireless Networks Spring 2005

Power Law Traffic Pattern q Probability that a node communicates with a node x units away is o For large negative , destinations clustered around sender o For large positive , destinations clustered at periphery q As goes from < -2 to > -1, capacity scaling goes from to [LBD+03] Wireless Networks Spring 2005

Relay Nodes q Offer improved capacity: o Better spatial reuse o Relay nodes do not count in o Expensive: addition of nodes as pure relays yields less than -fold increase q Hybrid networks: n wireless nodes and nd access points connected by a wired network o 0 < d < 1/2: No asymptotic benefit o 1/2 < d <= 1: Capacity scaling by a factor of nd Wireless Networks Spring 2005

Mobility and Capacity q A set of nodes communicating in random sourcedestination pairs q Expected number of hops is q Necessary scaling down of capacity q Suppose no tight delay constraint q Strategy: packet exchanged when source and destination are near each other o Fraction of time two nodes are near one another is q Refined strategy: Pick random relay node (a la Valiant) as intermediate destination [GT 01] q Constant scaling assuming that stationary distribution of node location is uniform Wireless Networks Spring 2005