enabling inter-domain dtn communications by networked static gateways ting he*, nikoletta sofra,...
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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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(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
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