Relay Cast Scalable Multicast Routing in Delay Tolerant
Relay. Cast: Scalable Multicast Routing in Delay Tolerant Networks Uichin Lee, Soon Young Oh, Kang-Won Lee*, Mario Gerla *
DTN Multicast Routing n Delay tolerant networking: ¨ ¨ n n Provides reliable data multicast even with disruptions DTN multicast routing methods: ¨ n n Suitable for non-interactive, delay tolerant apps Ranging from connected wireless nets to wireless mobile nets with disruptions (delay tolerant networks) Tree/mesh (+ mobility), ferry/mule, epidemic dissemination DTN multicast questions: Throughput/delay/buffer bounds? Focus: dissemination; upper bound of all cases Disrupted node R 4 R 1 R 2 S R 1 Disrupted R 4 node R 1 Accessmobility Point R 2 R 3 S Bluetooth-based pocket Tree Mesh switched networking Access Point Internet S City F R 1 F Remote village R 2 mobility S Connecting villagers Ferry/mule remote Dissemination Figure from http: //www. dtnrg. org
DTN Model n Pair-wise inter-contact time: interval between two contact points T 2 T 1 T 3 Contact points between two nodes: i and j Tic(2) Tic(1) T 1 Tic(3) T 2 T 3 time Tic(n): pair-wise inter-contact time n Common assumption: exponential inter-contact time ¨ ¨ n n Random direction, random waypoint, etc. Real world traces also have “exponential” tails [Karagiannis 07] Exponential inter-contact time Inter-contact rate: λ ~ speed x radio range [Groenevelt 05] Assumption: n nodes in 1 x 1 unit area; radio range: O(1/√n) and speed: O(1/√n) meeting rate: λ=O(1/n)
2 -Hop Relay: DTN Unicast Routing n n Each source has a random destination (n source-destination pairs) 2 -hop relay protocol: 1. Source sends a packet to a relay node 2. Relay node delivers a packet to the corresponding receiver 2 -hop Relay by Grossglauser and Tse Source Relay Destination Source is also mobile
2 -Hop Relay: Throughput/Delay Throughput is determined by aggregate meeting rate ¨ n 2 -hop relay throughput: Θ(nλ) ¨ G&T’s results: Θ(nλ)=Θ(1) for λ=1/n (i. e. , speed=radio=1/√n) 2 -hop relay delay: Θ(1/λ) Avg. time for a relay to meet a dest (~exp dist!): 1/λ ¨ Ex) For λ=1/n, avg. delay is Θ(n) (Neely&Modiano) ¨ Source n [Src relay nodes], [Dest relay nodes] Agg. meeting rate: nλ Source to Relay Destination n Food (=source) Agg. meeting rate: nλ Relay to Destination Avg. (=relays) delay = Ants Avg. inter-contact time
Relay. Cast: DTN Multicast Routing D 2 D 3 n 2 -hop relay based multicast: 1. Source sends a D 1 packet to a relay node Relay 2. Relay node delivers the packet to ALL multicast receivers NB. Source & Destinations Source are also mobile Relay. Cast: 2 -hop relay based multicast
Relay. Cast: Throughput Analysis n Relay. Cast throughput: Θ(nλ/nx) ¨ ns srcs, each of which associated with nd random dests ¨ Multiple srcs may choose the same node as a dest ¨ Avg. # of competing sources per receiver: nx ns srcs dests S 1 D 1 S 2 nx competing D 2 S 3 D 3 S 4 D 4 Each src chooses 3 rand dests sources S 1 R S 2 Relay nx=ns*nd/n D 1 nx srcs to D 2 nx srcs to D 3 λ/nx λ λ To D 1 To D 2 To D 3 λ λ D 1 D 2 D 3 Relay Node in Relay. Cast
Relay. Cast: Delay Analysis n n Relay node delivers a packet to ALL destinations nx competing srcs per dest: individual rate is split to λ/nx Relay. Cast avg. delay: Θ(nx/λ(log nd+γ)) ¨ where γ = Euler constant nx srcs to D 1 nx srcs to D 2 nx srcs to D 3 nx competing srcs to D 1 n λ/nx S 1 S 2 S 3 λ λ λ To D 1 D 3 D 2 To D 3 λ/nx To D 1 λ To D 1 D 2 nd (nd-1)λ/nx nd-1 λ/nx 1 0 Markov Chain for pkt delivery * State = # of remaining nodes λ/nx To D 1 ndλ/nx D 1 To D 2 λ/nx λ λ D 1 λ/nx D 1 Avg. delay = ∑nx/kλ Destinations are also mobile nx sub-queues to D 1 = nx/λ∑ 1/k = nx/λ (log nd + γ)
Relay. Cast: Buffer Requirement n Little’s law: buffer = (rate) x (delay) Buffer per source = Θ(nnd) ¨ ¨ ¨ n Avg. sub-queue length: λ/nx*nx/λ = Θ(1) by Little’s law Each src has nd dest: packet is replicated to nd copies Per src buffer at a relay = Θ(nd) n relays: buffer = Θ(nnd) Buffer upper bound per source = Θ(n 2) nx srcs to D 1 nx srcs to D 2 nx srcs to D 3 λ/nx λ λ λ To nd dest To D 1 To D 2 To D 3 Relay Node λ λ λ D 1 D 2 D 3 nx competing srcs to D 1 n S 1 S 2 λ/nx To D 1 S 3 λ/nx To D 1 nx sub-queues to D 1
Comparison with Previous Results n n Per node throughput with ns= Θ(n) n Assumptions; n fixed, and r = √logn/n for G&K; r=1/√n for 2 -hop relay Throughput scaling with ns= Θ(n); nx = nsnd/n = nd Relay. Cast = Θ(1/ nd) Better throughput than conventional multi-hop multicast (w/ r=√logn/n) Grossglauser & Tse 2001 Delay Tolerant Networks Relay. Cast: Delay Tolerant Networks Gupta & Kumar 2001 Shakkottai, Liu, Srikant 2006 Li, Tang, & Frieder 2007 Tavli 2006 Keshavarz-Haddad, Ribeiro, Riedi 2006 # of multicast receivers (nd) per source
Simulation Results Relay. Cast throughput with varying # of relay nodes DTN with fixed λ: throughput linearly increases ¨ n Relay. Cast throughput = Θ(nλ) for nsnd ≤ n As # node increases, interference comes in; throughput is tapered off Throughput per node (Kbps) n Qual. Net v 3. 9. 5 Network: 5000 mx 5000 m Random waypoint 802. 11 b: 2 Mbps 250 m radio range Traffic : ns=1, nd=# of relay nodes Number of relay nodes in the network
Simulation Results Comparison with conventional multicast protocol n Relay. Cast is scalable; ODMRP’s throughput decreases significantly, as # sources increases But delay has significantly increased; Relay. Cast ~ 2000 s vs. ODMRP < 1 s Per node throughput (kbps) n Replication reduces delay at the cost of throughput decrement Traffic: 5 rand dest per src Total 100 nodes in the net Number of sources
Simulation Results Average delay with varying # of receivers n Relay. Cast delay = Θ(nx/λ(log nd+γ)) Delay increases as # of receivers increases Average delay (s) n 20 m/s 30 m/s Number of multicast receivers
Conclusion n Relay. Cast: ¨ Provides reliable multicast even with disruption ¨ Achieves the maximum throughput bound of DTN multicast routing n n DTN routing protocol design and comparison must consider throughput/delay/buffer trade-offs Future work ¨ Analysis of other DTN routing strategies ¨ Impact of correlated motion patterns: i. e. , power-law head and exponential tail inter-contact time distribution
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