1. Towards a Theory of Routing in MANETs: Models and Algorithms
J.J. Garcia-Luna-Aceves,
Hamid Sadjadpour,
Zhenjiang Li (cisco), Sudharsan Rangarajan (cisco),
Rolando Menchaca-Mendez,
Stephen Dabideen, Dhananjay Sampath,
Yali Wang, Xin Wang, Xianren Wu
University of California, Santa Cruz

2. Outline Motivation A new framework for routing in MANETs
Summary of related results routing in MANETs

3. Motivation
Logic and design: There is no theory of routing in MANETs that researchers can use to reason about the design and correctness of routing, multicasting and broadcasting in MANETs.
Fundamental limits: There is no link between the way in which routing protocols are designed and the capacity goals for a network
Performance: There are no analytical models for the characterization of performance of routing protocols in MANETs
Many researchers “show” that a routing protocol is “good” by simulations, go through multiple iterations trying to fix bugs, and propose approaches without a priori quantitative evidence of its benefit.

4. What Is A Theory of Routing for MANETs?
Problem definition:
Simple paths, shortest paths, policy-based paths, coded paths, opportunistic paths (a la DTN)
Mathematical structure(s) applicable to the problem solution(s)
Distributed algorithms that implement the solutions:
Signaling overhead must be minimized
Algorithm must be correct according to problem definition
Proofs of correctness based on mathematical structures defined for the problem.

5. What We Know from Capacity Results:
Signaling overhead of routing protocols should be close to Θ(1) ⇒ Confine signaling to “regions of interest!
Anycast & manycast ⇒ Use in-network storage to bring/send content from/to nearest nodes

6. What Is Routing? Correct routing ⇒
forward to node “closer” to destination
“Closer” relationship ⇒ Total or Partial Ordering of nodes with respect to each intended destination.
Algebraic structures for path problems in graphs have been proposed since the 1960s.
Carre* proposed a semi-ring structure in 1971
A set S and two binary operations, ⊕ (the generalized addition) and ⊗ (the generalized product)
A partial order ≼ over the semi-ring such that a≼b ↔ a ⊕ b = a
Many routing algebras have been proposed inspired by Carre’s work to reason about policy-based and shortest-path routing in the Internet (e.g., Sobrino’s algebra, Brad & JJ’s algebra ).
* B. A. Carre, “An Algebra for Network Routing Problems,” IMA Journal of Applied Mathematics Volume 7, Number 3 Pp

7. Our Work: Build Routing Algebra from Minimum Structure
MANET
A labeled graph G is a 3-tuple (V,E,ℓV)
V is a finite set of vertices,
E ⊆ V×ΣE×V is the set of labeled edges,
ℓV:V→ΣV is a function that maps vertices to labels and,
ΣV and ΣE are alphabets of the labels that can be assigned to vertices and edges, respectively
Problem formulation
ΣE={0}, ΣV=ℕ, and ℓV:V→ΣV is injective
The image of ℓV is I
The only restriction over paths is that they must be simple
Minimum structure
Semigroup (S, ⊗b) where the set S is the image of I under some function f.
What we gain:
Proofs are well structured and simpler; start of a sound taxonomy!
Show that condition(s) for path selection are correct and that signaling satisfied conditions at any time.

8. From Routing Algebras to Algorithms
All we need is simple paths, and our algorithm must search for such paths
Two extremes:
Breath-first search (BFS): Traditional approach (on-demand, proactive, epidemic routing); network-wide dissemination must be used [flooding or incremental dissemination]
Depth-first search (DFS): No network-wide dissemination of information; search packets establish walks in the network
Approaches:
BFS: Reduce signaling by establishing areas of interest where signaling disseminates.
DFS: Eliminate flooding completely with “ordered walking plus learning” (OWL) to improve over random walking.

9. BFS: Distributed Ordering in Routing
MAX
ordering sequence
(2) i
(3)
(4) u R g
(5) k f
(1)
(2) p h j e
(3)
MIN
(0)
(4) m
RREQ,
Update,
Subscription,
Interest c d
(1) b
(3) R v
(5)
(3)
(2)
(4) a
Nodes are ordered for each destination, which can be a node, a service, content or a role.
Ordering is maintained as nodes move around carrying content. Ordering of nodes forms a directed acyclic graph (DAG) independently of any routing metric used

10. BFS: Distributed Ordering in Routing
MAX
ordering sequence
(2) i
(3)
(4) u R g
(5) k f
(1)
(2) p h j e
(3)
MIN
(0)
(4) m
RREQ,
Update,
Subscription,
Interest c d
(1) b
(3) R v
(5)
(3)
(2)
(4) a
Load balancing and constraints (e.g., end-to-end delay and jitter) used for forwarding over DAG.
Paper in ICCCN 2007 & MS Thesis

11. BFS: Proactive Routing
Too many nodes are forced to know about how to
reach each destination! Does not work well with random partitions
Path first, then data forwarding c f D D h e a S
Information about D propagates away from D in a circle of radius r b

12. BFS: On-Demand Routing
Too many nodes are forced to help find or repair ways to reach a few destinations! (RREQ flooding). Does not work with partitioned networks!
Path first, then data forwarding
Nodes with paths to D reply to S.
Information from S propagates away from S in a circle of radius r c f D h e a S S
Too few nodes keep state for D.
So too many nodes try to fix broken paths b

13. BFS: Epidemic Routing
Too many nodes are forced to relay data from S to D.
Does not work with partitioned networks, unless infinite storage is assumed.
Data create paths
Information from S propagates away from S in a circle of radius r c f D h e a S S b

14. EDIT: Elliptic Demarcation of Information Transfer (BFS)
Limit the number of nodes that incur signaling and forwarding overhead between S and D c f
Region of interest is a function of the source and destination! D h e a S b

15. EDIT Routing entries are based on [S,D] pair, not just D.
Distance from S to D, and distance to S and to D at R decides whether R forwards signaling packet c f D h e a S b

16. EDIT ✖ [S,D] ellipse changes as D and S move or relays move
Routing information for [S,D] pairs (many forms!) is sent proactively within elliptical region of interest c f h ✖ e D a S

17. EDIT
Qualnet simulator. Simulation scenario with 100 nodes in 1500x1500 area, MAC, 10% or 30% of nodes with active 1pps flows, speed of 1 to 10 m/s uniformly distributed, different pause times, 900 sec of simulation time, 10 seeds per run.
Performance over all pause times is almost as good as having geo-location information!
Far better than traditional on-demand and proactive schemes.

18. EDIT
Performance over all pause times is almost as good as having geo-location information!
Far better than traditional on-demand and proactive schemes.

19. DFS: OWL Minimum structure other than random walk with memory.
Define semi-group based on the operation:
i.e., “pick the next node whose ID is closest to destination ID.”
Carry path traversed in walk, and leave lessons learned behind at each node visited.

20. DFS: OWL Example
Ongoing work: Use learning from prior walks to shorten search & reduce the need to backtrack
Is there a major advantage over BFS?
Are DTNs a good application for OWL?

21. More Ongoing Work Analytical models for routing protocols
Preliminary results on proactive routing in MASS 2007
Working on on-demand routing and comparison between on- demand and proactive schemes
Extend EDIT to routing on n-ary relations and lexicographic ordering constraints.
Describe DFS and BFS approaches using the routing algebra.
Approaches to integrate BFS and DFS (i.e., “OWL” and EDIT) applied to addresses, object names, roles, and any “many-casting”
Approaches to integrate routing and channel access.

22. Questions?