Transcript O3: Optimized Overlay Based Opportunistic Routing Mi Kyung Han, Apurv Bhartia, Lili Qiu and Eric Rozner The University of Texas at Austin Presented by: Apurv.

O3: Optimized Overlay Based
Opportunistic Routing
Mi Kyung Han, Apurv Bhartia, Lili Qiu and Eric Rozner
The University of Texas at Austin
Presented by:
Apurv Bhartia
[email protected]
ACM Mobihoc 2011
1
Wireless Mesh Networks (WMN)
Internet
Gateway
Gateway
Router
Router
WiFi Network
Campus LAN
2
Routing Schemes in WMN
• Traditional routing
– Develops a variety of routing metrics to select the
best path
• Hop counts, ETX (expected # transmissions), ETT
(expected transmission time), RSS, …
• Opportunistic routing
• Routing with inter-flow coding
3
Motivating Example (1/7)
B
F1: A→D
F2: D→A
50%
50%
A
D
50%
50%
C
Routing Scheme
No. of transmissions
Traditional Routing
Opportunistic Routing
Inter-flow Coding
Opportunistic Routing +
Inter-flow Coding
4
Motivating Example (2/7)
2 xmits
F1: A→D
F2: D→A
B
50%
2 xmits
50%
A
D
50%
2 xmits
Routing Scheme
Traditional Routing
50%
C
2 xmits
No. of transmissions
8
Opportunistic Routing
Inter-flow Coding
Opportunistic Routing +
Inter-flow Coding
5
Motivating Example (3/7)
B
F1: A→D
F2: D→A
50%
2 xmits
50%
A
D
50%
1.33 xmits
Routing Scheme
Traditional Routing
Opportunistic Routing
50%
C
No. of transmissions
8
6.66
Inter-flow Coding
Opportunistic Routing +
Inter-flow Coding
6
Motivating Example (4/7)
F1: A→D
F2: D→A
P
B
2 xmits
P
Q
50%
A
50%
P XOR Q
2 xmits
50%
D
Q
50%
C
Routing Scheme
Traditional Routing
Opportunistic Routing
No. of transmissions
8
6.66
Inter-flow Coding
Opportunistic Routing +
Inter-flow Coding
7
Motivating Example (5/7)
B
F1: A→D
F2: D→A
50%
2 xmits
A
P
P XOR Q
50%
D
P XOR Q
50%
Q
50%
P XOR Q
C
Routing Scheme
Traditional Routing
Q
P
No. of transmissions
Opportunistic Routing
8
6.66
Inter-flow Coding
6
Opportunistic Routing +
Inter-flow Coding
8
Motivating Example (6/7)
B
F1: A→D
F2: D→A
50%
50%
A
D
50%
1.33 xmits
Routing Scheme
Traditional Routing
50%
1.33 xmits
C
No. of transmissions
Opportunistic Routing
8
6.66
Inter-flow Coding
6
Opportunistic Routing +
Inter-flow Coding
9
Motivating Example (7/7)
B
F1: A→D
F2: D→A
50%
2 xmits
A
50%
50%
D
50%
C
Routing Scheme
Traditional Routing
No. of transmissions
Opportunistic Routing
8
6.66
Inter-flow Coding
6
Opportunistic Routing +
Inter-flow Coding
4.66
Significant Performance Gains Possible!
10
The Big Question!
How to achieve this opportunistic
routing + inter-flow coding gain in
practice?
11
Related Work
• Protocols [Biswas05, Chachulski07]
• Optimization frameworks [Lun06, Radunovic2008, Soldo10, Ho06]
Opportunistic Routing
• Co-ordinate to select forwarders [Koutsonikolas03, Yan08, Zhang08]
• Evaluate only on toy topologies
• Optimization framework ?
• Practical protocol ?
Opportunistic Routing + Inter-flow Coding
• Protocols [Katti06, Das08, Le10]
• Optimization frameworks [Chaporkar07, Scheuermann07]
• Coding-aware traditional routing [Sengupta07]
Inter-flow Coding
12
Challenges
• Strong tension between opportunistic routing and
inter-flow coding
– Opportunistic routing spreads information across
multiple nodes
– Inter-flow coding opportunity decreases
• Node itself receives less traffic ⇒ limited coding choices
• Next-hop receive less traffic ⇒ hard to decode
13
Our Approach
• Decouple the strong interactions between
opportunistic routing and inter-flow coding
• Solution lies in “abstraction”
– Overlay Nodes → inter-flow coding
• Reduce amount of overlay traffic generated
– Underlay Nodes → opportunistic routing
• Combat wireless losses ⇒ provide reliable overlay links
14
O3: Understanding by Example
Physical Node
F1: A→D
F2: D→A
Underlay Node
B
Overlay Node
Overlay Plane
D
A
C
B
D
A
Opportunistic Routing
C
Underlay Plane
15
O3: Understanding by Example
Physical Node
Underlay Node
B
Overlay Node
Overlay Plane
D
A
C
B
D
A
Opportunistic Routing
C
Underlay Plane
Inter-flow Coding
16
Contributions
• Decouple the strong interdependency between
opportunistic routing and inter-flow coding
• Jointly optimize inter-flow coding, opportunistic
routing, and rate limiting
• Practical inter-flow coding aware opportunistic
routing protocol; O3
• Study benefits of O3 and individual benefit of
inter-flow coding, opportunistic routing and rate
limiting
17
O3: The Big Picture…
Topology details,
traffic demands
Overlay nodes and
overlay paths
Overlay-underlay
link mapping
O3 Optimization
Framework
Input
Output
Source Rate
Limiting
Underlay opportunistic
forwarding
Overlay node
forwarding
Protocol Implementation
18
O3: Optimization Framework
• Objective: Maximize total network throughput
subjected to – Overlay network constraints
• Flow conservation constraints
– Underlay network constraints
• Flow conservation constraints
• Opportunistic constraints
– Overlay <-> underlay mapping constraints
– Wireless interference constraints
19
Overlay Network Constraints (1/2)
Σ 𝑒1,𝑒2,𝑛 𝜖𝐶𝑆 𝑥𝑖 𝐶𝑆
𝑘
≤ Σ𝑘𝜖𝐷 Σ𝑒1𝑒2𝜖𝑃,𝑃𝜖𝑃𝑆 𝑘 𝑧𝑡 𝑒1 𝑃
Flow conservation
constraint for native traffic
involved in coding
Σ 𝑒1,𝑒2,𝑐 𝜖𝐶𝑆 𝑥𝑖 𝐶𝑆
≤ Σ𝑘𝜖𝐷 Σ𝑒1𝑒2𝜖𝑃,𝑃𝜖𝑃𝑆 𝑘 𝑓 𝑘 𝑃
Flow conservation
constraint for coded traffic
involved in coding
𝒆𝟏, 𝒆𝟐, 𝒏 : native-received traffic over 𝑒1 that can participate in
coding and sent over 𝑒2
𝒆𝟏, 𝒆𝟐, 𝒄 : same as above but with coded-received traffic
𝑪𝑺 : set of coding structures
𝒛𝒌𝒊 (𝑷): traffic transmitted by node 𝑖 for flow 𝑘 over path 𝑃
20
Overlay Network Constraints (2/2)
Σ𝑘𝜖𝐷 Σ𝑒1𝑒2𝜖𝑃,𝑃𝜖𝑃𝑆 𝑘 𝑓 𝑘 𝑃
= Σ𝑘𝜖𝐷 Σ𝑒1𝑒2𝜖𝑃,𝑃𝜖𝑃𝑆 𝑘 𝑧𝑖𝑘 𝑃
+ Σ 𝑒1,𝑒2,𝑛 𝜖𝐶𝑆 𝑥𝑖 𝐶𝑆
+ Σ 𝑒1,𝑒2,𝑐 𝜖𝐶𝑆 𝑥𝑖 𝐶𝑆
𝑘
𝑧𝑠𝑟𝑐
𝑘
𝑃 = 𝑓𝑘
𝑃
∀ 𝑃 𝜖 𝑃𝑆 𝑘
Flow conservation constraint
for total traffic received on 𝑒1
and transmitted on 𝑒2
𝑠𝑟𝑐 𝑓 transmits all traffic as
native over all paths
Flow conservation on total
𝑧𝑖𝑘 𝑃
native traffic tx by transit node
≤ 𝑓 𝑘 𝑃 𝑤ℎ𝑒𝑟𝑒 𝑖 𝜖 𝑃
− 𝑠𝑟𝑐 𝑘 , 𝑑𝑠𝑡 𝑘 ; 𝑃 𝜖 𝑃𝑆 𝑘
𝒆𝟏, 𝒆𝟐, 𝒏 : native-received traffic over 𝑒1 that can participate in
coding and sent over 𝑒2
𝒆𝟏, 𝒆𝟐, 𝒄 : same as above but with coded-received traffic
𝑪𝑺 : set of coding structures
21
𝒛𝒌𝒊 (𝑷): traffic transmitted by node 𝑖 for flow 𝑘 over path 𝑃
Underlay Network Constraints (1/2)
Underlay Node
𝒗𝒍
Overlay Node
flow1
j
i
flow1
Underlay Link
Overlay Link
𝒑𝒇 (inter-coded or native)
𝑰𝒏𝒇𝒐(𝒗𝒍, 𝒑𝒇, 𝒊 → 𝒋) : information from 𝑖 to 𝑗 for virtual flow (𝑣𝑙, 𝑝𝑓)
𝑻(𝒗𝒍, 𝒑𝒇, 𝒊) : traffic transmitted from node 𝑖 for (𝑣𝑙, 𝑝𝑓)
𝑵𝑹(𝒗𝒍, 𝒑𝒇) : traffic demand of virtual flow (𝑣𝑙, 𝑝𝑓)
𝑺 𝒊, ℵ 𝒊 : probability of successfully transmission to node in ℵ 𝑖
𝑻𝒎𝒂𝒙 𝒑𝒇, 𝒊 : total overlay traffic 𝑖 sends for 𝑝𝑓 over all paths
22
Underlay Network Constraints (2/2)
Σ𝑘𝜖𝑖𝑛
𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑘 → 𝑠𝑟𝑐(𝑣𝑙) = 0
𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑑𝑒𝑠𝑡 𝑣𝑙 → 𝑘 = 0
𝑖 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑘 → 𝑖 ≥ Σ𝑗𝜖𝑜𝑢𝑡 𝑖 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑗
Σ𝑘 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑠𝑟𝑐 𝑣𝑙 → 𝑘 ≤ 𝑁𝑅 𝑣𝑙, 𝑝𝑓
Flow
Conservation
Constraints
𝑆 𝑖, ℵ 𝑖 𝑇 𝑣𝑓, 𝑖 ≥ Σ𝑘𝜖ℵ 𝑖 𝑌 𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘
Opportunistic
𝑆 𝑖, 𝑘 𝑇𝑚𝑎𝑥 𝑝𝑓, 𝑖 ≥ Σ 𝑖,∗ 𝜖𝑣𝑙 𝑌 𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘
constraints
𝑆 𝑖, ℵ 𝑖 𝑇𝑚𝑎𝑥 𝑝𝑓, 𝑖 ≥ Σ𝑘𝜖ℵ 𝑖 Σ 𝑖,∗ 𝜖𝑣𝑙 𝐼𝑛𝑓𝑜(𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘)
𝑰𝒏𝒇𝒐(𝒗𝒍, 𝒑𝒇, 𝒊 → 𝒋) : information from 𝑖 to 𝑗 for virtual flow (𝑣𝑙, 𝑝𝑓)
𝑻(𝒗𝒍, 𝒑𝒇, 𝒊) : traffic transmitted from node 𝑖 for (𝑣𝑙, 𝑝𝑓)
𝑵𝑹(𝒗𝒍, 𝒑𝒇) : traffic demand of virtual flow (𝑣𝑙, 𝑝𝑓)
𝑺 𝒊, ℵ 𝒊 : probability of successfully transmission to node in ℵ 𝑖
𝑻𝒎𝒂𝒙 𝒑𝒇, 𝒊 : total overlay traffic 𝑖 sends for 𝑝𝑓 over all paths
23
Underlay Network Constraints (2/2)
f1
j
i
ℵ 𝒊
f1
k
𝑆 𝑖, ℵ 𝑖 𝑇 𝑣𝑙, 𝑝𝑓, 𝑖 ≥ Σ𝑘𝜖ℵ 𝑖 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘
Opportunistic
𝑆 𝑖, 𝑘 𝑇𝑚𝑎𝑥 𝑝𝑓, 𝑖 ≥ Σ 𝑖,∗ 𝜖𝑣𝑙 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘
constraints
𝑆 𝑖, ℵ 𝑖 𝑇𝑚𝑎𝑥 𝑝𝑓, 𝑖 ≥ Σ𝑘𝜖ℵ 𝑖 Σ 𝑖,∗ 𝜖𝑣𝑙 𝐼𝑛𝑓𝑜(𝑣𝑙, 𝑝𝑓, 𝑖 → 𝑘)
𝑰𝒏𝒇𝒐(𝒗𝒍, 𝒑𝒇, 𝒊 → 𝒋) : information from 𝑖 to 𝑗 for virtual flow (𝑣𝑙, 𝑝𝑓)
𝑻(𝒗𝒍, 𝒑𝒇, 𝒊) : traffic transmitted from node 𝑖 for (𝑣𝑙, 𝑝𝑓)
𝑵𝑹(𝒗𝒍, 𝒑𝒇) : traffic demand of virtual flow (𝑣𝑙, 𝑝𝑓)
𝑺 𝒊, ℵ 𝒊 : probability of successfully transmission to node in ℵ 𝑖
𝑻𝒎𝒂𝒙 𝒑𝒇, 𝒊 : total overlay traffic 𝑖 sends for 𝑝𝑓 over all paths
24
Overlay <-> Underlay Constraints
𝑘
𝑁𝑅 𝑣𝑙, 𝑝𝑓 = Σ𝑣𝑙𝜖𝑃 𝑧𝑠𝑟𝑐
𝑣𝑙 (𝑃)
𝑁𝑅 𝑣𝑙, 𝑝𝑓 = Σ𝑣𝑙𝜖𝑃 𝑥𝑠𝑟𝑐 𝑣𝑙 𝐶𝑆
𝑁𝑅 𝑣𝑙, 𝑝𝑓 = Σ𝑘𝜖𝑖𝑛 𝑑𝑒𝑠𝑡 𝑣𝑙 𝐼𝑛𝑓𝑜(𝑣𝑙, 𝑝𝑓, 𝑘 → 𝑑𝑒𝑠𝑡 𝑣𝑙 )
• The overlay traffic demand is imposed on the underlay
• Native traffic
• Coded traffic
• The underlay honors the demand imposed by the overlay
𝑴𝑻 : total traffic from node 𝑖
𝑰𝒏𝒇𝒐(𝒗𝒍, 𝒑𝒇, 𝒊 → 𝒋) : information from 𝑖 to 𝑗 for virtual flow (𝑣𝑙, 𝑝𝑓)
𝑻(𝒗𝒍, 𝒑𝒇, 𝒊) : traffic transmitted from node 𝑖 for (𝑣𝑙, 𝑝𝑓)
𝑵𝑹(𝒗𝒍, 𝒑𝒇) : traffic demand of virtual flow (𝑣𝑙, 𝑝𝑓)
𝑻𝒎𝒂𝒙 𝒑𝒇, 𝒊 : total overlay traffic 𝑖 sends for 𝑝𝑓 over all paths
25
Interference Constraints
• Interfering transmitters should not tx together
• Overlay nodes broadcast over multiple overlay
links simultaneously
• Underlay nodes forward for a specific overlay link
• Independent set constraints: nodes belonging to
an independent set can be active simultaneously
[Jain05]
26
O3: Revisiting the Big Picture...
Topology details,
traffic demands
Overlay nodes and
overlay paths
Overlay-underlay
link mapping
O3 Optimization
Framework
Input
Output
Source Rate Limiting
Underlay opportunistic
forwarding
Overlay node
forwarding
Protocol Implementation
27
Protocol Implementation
• Packet encoding and decoding algorithm
• Flow source and destination
• Forwarders
28
Packet Encoding and Decoding
• 𝑠𝑟𝑐 𝑓 divides packets into batches of size K
– Intra-coded packet
• Random linear combination of all packets from a batch
– Inter-coded packet
• Random linear combination of 2 different flows
• Destination performs Gaussian elimination
R1
P1
A
P2
αP1+ ßP2
γP1+ δP2
λP
+ ξQ
λP11++μP
μP22 + νQνQ
1 +1ξQ2 2
κP1+ θP2
+ ρQ2
κP1+ θP2 + ζQ1ζQ
+ 1ρQ
2
B
Q1
Q2
R2
α‘Q1+ ß’Q2
λ'P
λ’P11++μ’P
μ’P22 + ν’Q
νQ1 1++ξ’Q
ξ’Q2 2
γ‘Q1+ δ’Q2
κ'P
ζ’Q
ρ’Q
κ'P11++θ’P
θ’P22 + ζ’Q
ρ’Q
1+
1+
22
29
Flow Source and Destination
• Flow Source, 𝑠𝑟𝑐(𝑓)
– Never performs inter-flow coding
– Includes all overlay paths the pkt may traverse
– Multiple outstanding small-size batches
• Support inter-flow coding
• Reduce wait-time overhead
• Flow Destination, 𝑑𝑠𝑡(𝑓)
– Generates ACK when entire batch is rx or threshold
number of packets rx since last ACK
30
Forwarder Operation
• Which flow-batch combination to forward?
• Credits → number of transmissions to generate [MORE]
– Flow credits: tx rate for flow on a given overlay path
– Batch credits: tx rate for batch within a given flow
• Pick flow with max flow credit
• Pick batch with max batch credit within the flow!
31
Evaluation Methodology
• Qualnet Simulation for both (11a and 11b)
• Protocols compared w/ O3
– Shortest-path routing (SPP) w/ ETX
– SPP w/ rate limit (SPP-RL)
– COPE; state of art inter-flow coding protocol
– COPE w/ rate limit (COPE-RL)
– MORE; state of art opportunistic routing protocol
– O3-Intra (O3 w/o inter-flow coding)
• Different topologies studied
– Canonical, grid, random, testbeds ..
32
Canonical Topologies
50%
A
100%
B
2-hop
50%
100%
C
B
50%
A
D
50%
C
50%
Diamond
(Mbps)
O3 O3-Intra MORE COPE-RL COPE SPP-RL SPP
2-hop
3.45
2.98
2.78
2.95
2.84 2.56 1.78
Diamond 1.50
1.11
0.91
0.54
0.47 0.47 0.40
O3 significantly outperforms all the other
protocols!
33
Synthetic Topologies (802.11a)
3
2.2
2
2.5
1.8
High Loss
1.6
2
1.4
1.2
1.5
Throughput
(Mbps)
1
1
Throughput
0.8
(Mbps)
0.6
Low Loss
0.4
0.5
0.2
2
4
6
8
Number of flows
12
16
2
4
6
8
12
Number of flows
16
• 25 nodes placed in a random setting
• UDP, bi-directional flows selected randomly
• Loss distributed uniformly 0-30% (Low Loss) and 0-80% (High
34
Loss)
Synthetic Topologies (802.11a)
3
2.2
2
2.5
1.8
High Loss
1.6
2
1.4
1.2
1.5
Throughput
(Mbps)
1
1
Throughput
0.8
(Mbps)
0.6
Low Loss
0.4
0.5
0.2
2
4
6
8
Number of flows
12
16
2
4
6
8
12
Number of flows
16
• O3 outperforms state-of-art protocols in all scenarios
• Rate limiting is important: O3-Intra > MORE (18-286%), COPE-RL >
COPE (6-239%), SPP-RL > SPP (45-211%)
• High loss rate: Benefits of inter-flow coding decrease, OR increase35
Testbed Topologies
0.5
0.45
0.4
0.35
0.3
0.25
0.2
Throughput 0.15
(Mbps) 0.1
0.05
0
2
4
3.5
3
2.5
2
Roofnet (11b)
1.5
Throughput
1
(Mbps)
0.5
0
6
8 12 16
2
Number of flows
UW (11a)
4
6
8
Number of flows
10
• Testbed traces depicting realistic scenarios
• Random bi-directional flows
• Roofnet (MIT) testbed – 35 nodes, UW testbed – 19 nodes
36
Testbed Topologies
0.5
0.45
0.4
0.35
0.3
0.25
0.2
Throughput 0.15
(Mbps) 0.1
0.05
0
2
4
3.5
3
2.5
2
Roofnet (11b)
1.5
Throughput
1
(Mbps)
0.5
0
6
8 12 16
2
Number of flows
UW (11a)
4
6
8
Number of flows
10
• O3 > O3-Intra (14-30%), COPE-RL (11-83%), SPP-RL (21- 46%),
MORE (48-1000%), COPE (41-6100%), SPP (87-32600%)
• O3-Intra > MORE ( 15-696%), COPE-RL > COPE (1-617%).
37
Future Work
• Plan to explore other wireless applications
where ‘overlay abstraction’ can be used
• Solve linear constraints incrementally on slight
network changes
• Solve optimization based on decentralized
information to enhance scalability
38
Conclusion
• Optimize inter-flow coding in context of
opportunistic routing
• Jointly optimize opportunistic routing, rate
limiting and inter-flow coding
• Practical network protocol that achieves it
• Reveal relative benefit of different schemes
39
Thank You!
Questions?
[email protected]
40
Effects of Network Density
O3
0.9
0.8
0.7
0.6
0.5
Throughput 0.4
(Mbps)
0.3
0.2
0.1
0
O3-Intra
MORE
COPE
COPE-RL
SPP
SPP-RL
1000x1000
1750x1750
2000x2000
3250x3250
Area (sq. m)
8 flows, high loss
O3 out-performs the other protocols across all network densities
41
Complexity Analysis
• Inputs
– traffic demands, 𝑂(𝐹)
– link loss rates, 𝑂(𝐸) and
– conflict graph, 𝑂 𝐸 2
• Outputs
– Overlay credits, 𝑂(𝑂𝑁. 𝐹. 𝑃)
– Underlay credits, 𝑂 𝑁. 𝐷. 𝐹. 𝑂𝐸 + 𝑂(𝑁. 𝐷. 𝑂𝐸 2 )
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Optimization Objective
• Maximizing Total throughput
𝑘
Σ𝑘𝜖𝐷 Σ𝑃𝜖𝑃𝑆 𝑘 𝑓 𝑃
where
𝐷: set of traffic demands
𝑓 𝑘 𝑃 : 𝑘-th flow’s throughput over path 𝑃
𝑃𝑆 𝑘 : set of paths used by 𝑘-th flow
Alternatively, we can also support other objectives,
like proportional fairness, etc.
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Interference Constraints
𝑀𝑇𝑖 = Σ𝑝𝑓 𝑀𝑎𝑥𝑇(𝑣𝑙, 𝑝𝑓, 𝑖); 𝑖: 𝑜𝑣𝑒𝑟𝑙𝑎𝑦
𝑀𝑇𝑖 = Σ𝑝𝑓 Σ𝑣𝑙 𝑇 𝑣𝑙, 𝑝𝑓, 𝑖 ; 𝑖: 𝑢𝑛𝑑𝑒𝑟𝑙𝑎𝑦
𝑀𝑇𝑖 ≤ 𝐶𝑎𝑝𝑖 Σ𝑘𝜖𝐼𝑖 𝜆𝑘
Σ 𝑘 𝜆𝑘 ≤ 1
• Overlay nodes broadcast over multiple overlay links simultaneously
• Underlay nodes forward for a specific overlay link
• Independent set constraints: nodes belonging to an independent
set can be active simultaneously
𝑴𝑻 : total traffic from node 𝑖
𝑻(𝒗𝒍, 𝒑𝒇, 𝒊) : traffic transmitted from node 𝑖 for (𝑣𝑙, 𝑝𝑓)
𝑵𝑹(𝒗𝒍, 𝒑𝒇) : traffic demand of virtual flow (𝑣𝑙, 𝑝𝑓)
𝑴𝒂𝒙𝑻 𝒑𝒇, 𝒊 : total overlay traffic 𝑖 sends for 𝑝𝑓 over all paths
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Using Credits in O3 (1/2)
• Underlay Credits
Fraction of useful information
contained in each transmission
from upstream node
𝐶 × 𝑅
Amount of information received
𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑗, 𝑖
𝐶=
𝑇𝐶 𝑣𝑙, 𝑝𝑓, 𝑗 ∗ (1 − 𝑙𝑜𝑠𝑠 𝑗, 𝑖 ) Amount of traffic received
Redundancy ‘i’
should include to
compensate loss
to it’s forwarders
𝑇 𝑣𝑙, 𝑝𝑓, 𝑖
𝑅=
Σ𝑘 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑖, 𝑘
Desirable sending rate
Total information
successfully delivered
to all forwarders
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Using Credits in O3 (2/2)
• Underlay Credits
𝐶 × 𝑅
𝐶 = 𝐼𝑛𝑓𝑜(𝑣𝑙, 𝑝𝑓, 𝑗, 𝑖)/(𝑇𝐶 𝑣𝑙, 𝑝𝑓, 𝑗 ∗ (1 − 𝑙𝑜𝑠𝑠 𝑗, 𝑖 )
𝑇 𝑣𝑙, 𝑝𝑓, 𝑖
𝑅=
Σ𝑘 𝐼𝑛𝑓𝑜 𝑣𝑙, 𝑝𝑓, 𝑖, 𝑘
• Overlay Credits
– On receiving an native packet
𝑝𝑓
𝑇 𝑣𝑙, 𝑝𝑓, 𝑖 ∗
𝑧𝑖
Σ𝑃
𝑃
𝑝𝑓
𝑖:𝑣𝑙𝜖𝑃𝑖 𝑧𝑖 (𝑃𝑖)
– On receiving an inter-coded packet
𝑝𝑓
𝑧𝑠𝑟𝑐
𝑝𝑓
𝑝𝑓
𝑃 − 𝑧𝑖
𝑃
∗ 𝑁𝑆𝑅(𝑖, 𝑣𝑙)
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