Enabling Inter-domain DTN Communications by

Networked Static Gateways

Ting He*, Nikoletta Sofra†, Kang-Won Lee*, and Kin K Leung†

* IBM† Imperial College

Sept. 2009

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IntroductionIntroduction

• Different DTN domains call for different technology– E.g., coalition operations, MESSAGE project

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(a) Coalition networks

: candidate gateway location

(b) Heterogeneous sensor networks

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IntroductionIntroduction

• Gateway deployment influences performance

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d

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(a) (b): gateway

Q: How to deploy them?

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Domain HeterogeneityDomain Heterogeneity

• What factors to consider:– Inter-domain factors:

• Traffic demands• Inter-domain routing scheme• Policy

– Intra-domain factors:• Mobility, channel, radio tech/range → contact patterns• Node population/density• Routing scheme:

– Replication strategy: forwarding, limited/unlimited replication

– Queue discipline– Resource assumption: unlimited/limited bandwidth/buffer– Others: data ferries, network coding, etc.

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OutlineOutline

• Unified Gateway Deployment Framework (UGDF)– Utility computation– Gateway placement

• Context-aware utility computation

• Performance evaluation

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Unified Gateway Deployment Framework (UGDF)

Unified Gateway Deployment Framework (UGDF)

Utility computation: Decomposition + domain-specific calculation

– Utility decomposition:

Uglobal = Σdomain i.j λij [Σ ρp (Σhop k Uk )] λij: inter-domain traffic demand; ρp: load factor (for inter-domain

routing)– Per-hop utility calculation: domain-specific

– Note: Utilities in different domains should be independent (guaranteed by “networked gateways”)

Utilitycomputation

Gatewayplacement

Domain knowledge,

Performance criteria

U(L’) L* = argmaxL’ U(L’) s.t. cost(L’) ≤ CBudget C

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Unified Gateway Deployment Framework (UGDF)

Unified Gateway Deployment Framework (UGDF)

Gateway placement:

max U(L’) ≠ ΣL’ U(li)! (harder than knapsack problem)

s.t. Σli∊L’ cost(li) ≤ C

• Optimal alg: unequal cost – NP-hard, equal cost – O(Lg)• Greedy alg: While cost less than C

l(j) = argmaxL\L’ [U(li U L’)-U(L’)]/ci

L’ ← L’ U l(j)

• Backward greedy alg: While cost greater than C l(j) = argminL’ [U(L’)-U(L’ \ {li})]/ci

L’ ← L’ \ {l(j)}

Utilitycomputation

Gatewayplacement

Domain knowledge,

Performance criteria

U(L’) L* = argmaxL’ U(L’) s.t. cost(L’) ≤ CBudget C

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Unified Gateway Deployment Framework (UGDF)

Unified Gateway Deployment Framework (UGDF)

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Gateway placement (cont’d): max U(L’)

s.t. Σli∊L’ cost(li) ≤ C

• Performance guarantee: Under equal cost: Greedy/backward greedy soln’s are ε-close to the optimal if [U(l U L’)-

U(L’)]’s are ε-close (for all l), i.e.

[U(l U L1’)-U(L1’)] ≥ (1- ε) [U(l U L2’)-U(L2’)]

for |L1’|=|L2’|.

Utilitycomputation

Gatewayplacement

Domain knowledge,

Performance criteria

U(L’) L* = argmaxL’ U(L’) s.t. cost(L’) ≤ CBudget C

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Unified Gateway Deployment Framework (UGDF)

Unified Gateway Deployment Framework (UGDF)

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Sketch of proof: (equal cost)- Decompose the total utility: (i: ‘g’ for greedy, ‘o’ for optimal)

U(Li) = U(li1) + U(li2|li1) +…+ U(lig|li1,…,lig-1)- By definition of the greedy alg:

U(lgj|lg1,…,lgj-1) ≥ U(loj|lg1,…,lgj-1)- By the condition:

U(loj|lg1,…,lgj-1) ≥ (1-ε) U(loj|lo1,…,loj-1)Combining both gives

U(Lg) ≥ (1- ε)U(Lo).

Similarly, U(Ltotal) - U(Lbg) ≤ [U(Ltotal) - U(Lo)] / (1- ε). □

A similar result holds for unequal costs.

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OutlineOutline

• Unified Gateway Deployment Framework (UGDF)

• Context-aware utility computation– Results & sketch of analysis

• Performance evaluation

Context-aware Utility ComputationContext-aware Utility Computation

Assume Poisson contact processes. (node-node: λn; node-gateway: λl)

Source-gateway hop:‒ Single-copy routing/forwarding:

‒ Delay: 1/λl

‒ # replicas: 1

‒ Unlimited replication:‒ Delay ≈ N\logN(1/ λl+1/ λn)‒ # replicas ≈ (1+N)/2

‒ Limited replication:‒ Delay ≈ F(N, λl, λn, r)‒ # replicas ≈ N\(r+1)(N-r/2)

Other hops:• Intermediate domain: (same)• Destination domain: (similar but λl→λn)

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Context-aware Utility ComputationContext-aware Utility Computation

Sketch of analysis: For unlimited replication:1. Decompose:E[Delay] = ∑j P{delivery between jth and (j+1)th replications}.E[Delay|▲]

(▲)E[# replicas] = ∑j P{▲} . (j+1)

Note: Period between jth and (j+1)th replications ~ Exp((j+1)(N-j-1)λn) Conditioned on ▲, additional delay after jth replication ~ Exp((j+1)λl)

2. Bound:P{▲} = F1(N,j,λn,λl)

F2(N,j,λn,λl) ≤ E[Delay|▲] ≤ F3(N,j,λn,λl)

3. Approximate at large N (actually close even at N=5)

Similar steps for limited replication. □

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OutlineOutline

• Unified Gateway Deployment Framework (UGDF)

• Context-aware utility computation

• Performance evaluation– Synthetic simulations – Trace-driven simulations

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Performance EvaluationPerformance Evaluation

Synthetic simulations: • Setup:

– Two coalition networks with different bases (localized random walks)

– Size, mobility, routing vary independently

• Calculated vs. simulated utilities:– Contact processes not Poisson– Still good approximation

(scaling needed for direct delivery)

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Performance EvaluationPerformance Evaluation

Synthetic simulations (cont’d): • End-to-end performance:

– 6 strategies (3 optimization alg’s, 2 utility computation methods)– Greedy/backward greedy alg + calculated utility is near optimal– Results robust against routing schemes and utility measure

Minimize delay Minimize # replicas

(unlimited replication in domain 1, direct delivery in domain 2)

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Performance EvaluationPerformance Evaluation

Trace-driven simulations: • Setup:

– Extracting traces from Dieselnet trace*: 4 sets of two-domain traces of mobile-to-mobile and mobile-to-AP contacts; 10 candidate gateway locations; 3 nodes per domain

– Uniform traffic: 5 packets per hour per source node

* http://traces.cs.umass.edu/, Dieselnet Fall 2007

Mobile-mobile Mobile-AP

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Performance EvaluationPerformance Evaluation

Trace-driven simulations (cont’d):• Accuracy of utility calculation: Good approximation of the trend

(under constant scaling).

Avg. delay (direct delivery, unlimited replication)

Avg. # replicas (unlimited replication)

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Performance EvaluationPerformance Evaluation

Trace-driven simulations (cont’d):• Performance of deployment:

Near optimal (again) Much better (30%) than utility-agnostic deployment

Minimize delay Minimize # replicas

(both under unlimited replication)

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SummarySummary

• Gateway deployment for inter-domain DTN – UGDF: utility computation, gateway placement– Context-aware utility computation: decomposition & domain-

specific analysis

– Observations: • Poisson contacts? → Robust to mobility models (up to

scaling)• Suboptimal alg’s? → Near-optimal performance (for

scattered candidate locations)• Gap with oracle? → Good deployment relies on predictable

mobility and representative training data