1. 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

2. 2 Introduction Different DTN domains call for different technology –E.g., coalition operations, MESSAGE project s d (a) Coalition networks : candidate gateway location (b) Heterogeneous sensor networks

3. 3 Introduction Gateway deployment influences performance s d s d (a) (b) : gateway Q: How to deploy them?

4. 4 Domain 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.

5. 5 Outline Unified Gateway Deployment Framework (UGDF) –Utility computation –Gateway placement Context-aware utility computation Performance evaluation

6. 6 Unified Gateway Deployment Framework (UGDF) Utility computation: Decomposition + domain-specific calculation –Utility decomposition: U global = Σ domain i.j λ ij [ Σ ρ p ( Σ hop k U k )] λ ij : inter-domain traffic demand; ρ p : load factor (for inter-domain routing) –Per-hop utility calculation: domain-specific –Note: Utilities in different domains should be independent (guaranteed by networked gateways) Utility computation Gateway placement Domain knowledge, Performance criteria U(L) L* = argmax L U(L) s.t. cost(L) C Budget C

7. 7 Unified Gateway Deployment Framework (UGDF) Gateway placement: max U(L) Σ L U(l i )! (harder than knapsack problem) s.t. Σ li L cost(l i ) C Optimal alg: unequal cost – NP-hard, equal cost – O(L g ) Greedy alg: While cost less than C l (j) = argmax L\L [U(l i U L)-U(L)]/c i L L U l (j) Backward greedy alg: While cost greater than C l (j) = argmin L [U(L)-U(L \ {l i })]/c i L L \ {l (j) } Utility computation Gateway placement Domain knowledge, Performance criteria U(L) L* = argmax L U(L) s.t. cost(L) C Budget C

8. 8 Unified Gateway Deployment Framework (UGDF) 8 Gateway placement (contd): max U(L) s.t. Σ li L cost(l i ) C Performance guarantee: Under equal cost: Greedy/backward greedy solns 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 L 1 )-U(L 1 )] (1- ε) [U(l U L 2 )-U(L 2 )] for |L 1 |=|L 2 |. Utility computation Gateway placement Domain knowledge, Performance criteria U(L) L* = argmax L U(L) s.t. cost(L) C Budget C

9. 9 Unified Gateway Deployment Framework (UGDF) 9 Sketch of proof: (equal cost) -Decompose the total utility: (i: g for greedy, o for optimal) U(L i ) = U(l i 1 ) + U(l i 2 |l i 1 ) +…+ U(l i g |l i 1,…,l i g-1 ) -By definition of the greedy alg: U(l g j |l g 1,…,l g j-1 ) U(l o j |l g 1,…,l g j-1 ) -By the condition: U(l o j |l g 1,…,l g j-1 ) (1-ε) U(l o j |l o 1,…,l o j-1 ) Combining both gives U(L g ) (1- ε )U(L o ). Similarly, U(L total ) - U(L bg ) [U(L total ) - U(L o )] / (1- ε ). A similar result holds for unequal costs.

10. 10 Outline Unified Gateway Deployment Framework (UGDF) Context-aware utility computation –Results & sketch of analysis Performance evaluation

11. Context-aware Utility Computation Assume Poisson contact processes. (node- node: λ n ; node-gateway: λ l ) Source-gateway hop: Single-copy routing/forwarding: Delay: 1/λ l # replicas: 1 Unlimited replication: Delay N\logN(1/ λ l +1/ λ n ) # replicas (1+N)/2 Limited replication: Delay F(N, λ l, λ n, r) # replicas N\(r+1)(N-r/2) Other hops: Intermediate domain: (same) Destination domain: (similar but λ lλ n ) 11

12. 12 Context-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)λ n ) Conditioned on, additional delay after jth replication ~ Exp((j+1)λ l ) 2. Bound: P{} = F 1 (N,j,λ n,λ l ) F 2 (N,j,λ n,λ l ) E[Delay|] F 3 (N,j,λ n,λ l ) 3. Approximate at large N (actually close even at N=5) Similar steps for limited replication.

13. 13 Outline Unified Gateway Deployment Framework (UGDF) Context-aware utility computation Performance evaluation –Synthetic simulations –Trace-driven simulations

14. 14 Performance 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)

15. 15 Performance Evaluation Synthetic simulations (contd): End-to-end performance: –6 strategies (3 optimization algs, 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)

16. 16 Performance 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 2007http://traces.cs.umass.edu/ Mobile-mobile Mobile-AP

17. 17 Performance Evaluation Trace-driven simulations (contd): Accuracy of utility calculation: Good approximation of the trend (under constant scaling). Avg. delay (direct delivery, unlimited replication) Avg. # replicas (unlimited replication)

18. 18 Performance Evaluation Trace-driven simulations (contd): Performance of deployment: Near optimal (again) Much better (30%) than utility-agnostic deployment Minimize delay Minimize # replicas (both under unlimited replication)

19. 19 Summary 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 algs? Near-optimal performance (for scattered candidate locations) Gap with oracle? Good deployment relies on predictable mobility and representative training data