Maximizing Path Durations in Mobile Ad- Hoc Networks Yijie Han and Richard J. La Department of ECE & ISR University of Maryland, College Park CISS, Princeton University March 22nd, 2006

Outline Background Basic Model Setup Distributional convergence Proposed algorithm  Maximizing expected path durations NS-2 simulation results  Parameter update Conclusion & Future Directions

Background Ad hoc network routing protocols  Table-driven routing protocols (proactive) Attempt to maintain consistent, up-to-date routing information from each node to every other node in the network.  Each node maintains one or more tables to store routing information. Example: DSDV (Destination-Sequenced Distance-Vector), WRP (Wireless Routing Protocol), etc  On-demand routing protocol (reactive) Attempt to minimize the number of required broadcasts by providing a path only when requested Require path/route discovery phase/mechanism Examples: AODV( Ad-hoc On-demand Distance Vector), DSR (Dynamic Source Routing)

Motivation On-demand routing protocols in ad-hoc networks  Path recovery procedure initiated when an existing path is broken Disruption in network service to applications  Performance and overhead shaped by the distribution of link and path durations Suggests that (expected) path duration should be taken into account when selecting a path  Reduce overhead  Provide more reliable network service to applications  Requires understanding of statistical properties of path duration

Existing protocols Ad-hoc On-demand Distance Vector (AODV)  Selects the first discovered route Dynamic Source Routing (DSR)  Selects the min-hop route Associativity Based Routing (ABR)  Each node maintains “associativity” for each neighbor from beacons Higher beacon counts = more stable links  Destination selects the path with the highest average associativity

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Basic Model (for studying statistical properties of path duration ) V = {1, …, I} - set of mobile nodes moving across a domain D of R 2 or R 3  - location/trajectory of node i Connectivity between nodes  {0, 1}- valued reachability process between two nodes  ij (t) = 1 – if the link (i,j) is up  ij (t) = 0 – if the link (i,j) is down  ij (t) =  ji (t) – symmetric links

Basic Model Reachability processes defined in multiple ways   Signal strength or SINR based model Signal strength - SINR based model -

Basic Model Link durations  {U ij (k), k = 1, 2,,…} and {D ij (k), k = 1, 2, …}  U ij (k) (resp. D ij (k)) – duration of k- th up (resp. down) time Time-varying graph (V, E(t))  t Basic Model

Path discovery phase  Path available between s and d if a set of links provides connectivity May not be unique Routing algorithm selects one  Denote the set of links along the selected path by L sd (t) s d n1 n2 n3 n4

For each link  - time to live or excess life after time t Time to live or duration of a path  Path available till one of the links goes down  Path duration = amount of time that elapses till one of the links in breaks down Excess Life and Path Duration

Question: What does the distribution of look like?  In particular, when the hop counter is large In a large scale MANET, the number of hops is expected to be large

Outline Background Basic Model Setup – Parametric Scenario and Difficulties Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Scaling: For each fixed n = 1, 2, …,  -- set of mobile nodes  -- domain across which nodes move Stationarity: Reachability processes jointly stationary  constitutes a stationary sequence with generic marginals  - CDF of A pair of source and destination nodes selected at time t = 0 for each n Parametric Scenario

Define  Excess or residual life of a link Distribution of forward recurrence time Follows from elementary renewal theory Parametric Scenario (cont’d)

Path duration - Explore the distributional properties of the rvs as Parametric Scenario (cont’d)

Sources of Difficulty 1. - random set that depends on Assume is a deterministic sequence with for convenience Example:  Fix the domain, and randomly select the locations of the source and destination  Randomly place n 2 – 2 other nodes in the domain  Transmission range decreases as 1/ n  Number of hops along the shortest path increases with n

Sources of Difficulty (cont’d) 2. Dependence of reachability processes  Introduces dependence in link excess lives  Asymptotic independence – dependence in link excess lives goes away asymptotically as hop distance increases Mixing conditions

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Assumptions Assumption 1: (scaling) There exists such that where  Scaling introduced for defining limit distribution parameter Assumption 2: For every and any given there exists an integer such that -Interpretation: probability that a link duration is strictly positive is one

Definitions  Array of -valued rvs   for notational convenience

Definitions Let be a sequence of real numbers  Usually increases with n

Definitions  Sufficient condition:

Define  A sufficient condition is that there exists an arbitrarily small constant  > 0 such that for all and Assumptions

Interpretation of Assumption 4

 Implications: For sufficiently large hop count, the expected path duration can be approximated by Distributional convergence

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Proposed algorithm Link durations seen by a node likely to depend on its own type and the types of neighbors  Different nodes with different speeds and capabilities  Each node maintains average link durations  Can maintain a separate average for each type of neighbors  Average link duration used as estimate of expected link durations (during path discovery)

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results - AODV  Parameter update Conclusion & Future Directions

NS-2 simulation - Setup Modified AODV routing protocol 200 nodes in 2 km x 2 km rectangular region Transmission range = 250 m Two classes of nodes  Nodes with different speed (e.g., soldiers vs. jeeps or tanks)  Class 1 node speed ~ [1, 5] m/s  Class 2 node speed ~ [10, 30] m/s Varying mixture  Class1:Class2 = 140:60, 160:40, and 180:20

NS-2 simulation

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Estimation of expected path duration Recall: For sufficiently large hop count, the expected path duration can be approximated by Question: For finite hop counts, how good is this approximation?  For back-up paths  Local recovery after a link failure

Threshold update – local recovery Select a back-up path only if the estimated probability of being available exceeds a certain threshold  Probability of being available estimated to be  Not accurate due to discrepancy in exp. parameter and collected IPD value (sum of inverses of expected link durations) Target probability Update the threshold as follows where is the threshold after n back-up path tries and is the indicator function of a back-up path being available Amount of time since last update

Threshold update Define to be the indicator function of the event that a selected backup path is available when the threshold value is and - unknown distribution of and its mean, respectively  Assume (i) is strictly increasing in, and (ii) there exists such that

Outline Background Basic Model Setup Distributional convergence Proposed algorithm NS-2 simulation results  Parameter update Conclusion & Future Directions

Conclusions & Future Directions Studied the statistical properties of path durations in MANETS  Showed distributional convergence with increasing hop count  Relationship between link durations and path duration Proposed an algorithm for maximizing expected durations of selected paths  Stochastic approximation based algorithm for handling the discrepancy between IPD values and exponential parameters Plan to implement with other on-demand routing protocols  Validation of assumptions  Convergence speed

Proposed algorithm in AODV Each node maintains a route entry from each known dest node  Up to k paths (instead of a single path in AODV)  (i) dest seq. number, (ii) next hop, (iii) hop count, and (iv) Inverse Path Duration (IPD) IPD = sum of the inverses of average link durations reported in a path reply message  Paths ranked based on (i) seq. number, (ii) IPD value, (iii) hop count Request message  (i) src ID, seq. number, (ii) broadcast ID, (iii) dest ID and seq. number, and (iv) hop count to the src Reply message  (i) dest ID, (ii) dest seq. number, (iii) IPD value, and (iv) hop count Either an intermediate node or dest generates a reply message  Intermediate node – copy information from its entry  Dest node – initialize IPD and hop count to zero