Multi-Hop Networking with Hard Delay Constraints

Multi-Hop Networking with Hard Delay Constraints

Michael J. Neely, University of Southern CaliforniaDARPA IT-MANET Presentation, January 2011

PDF of paper at: http://www-bcf.usc.edu/~mjneely/

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http://www-rcf.usc.edu/~mjneely

•Non-Equilibrium Networking for MANETS•Delay Guarantees•Optimization of Throughput-Utility

M. J. Neely, “Opportunistic Scheduling with Worst Case Delay Guarantees in Single and Multi-Hop Networks,” Proc. IEEE INFOCOM 2011.

This work builds on: i) “Universal Scheduling” (Neely, Proc. IEEE CDC 2010)• ARL CTA Task.• Social Networks extensions:

M. J. Neely, L. Golubchik, “Utility Optimization for Dynamic Peer-to-Peer Networks with Tit-for-Tat Constraints,” Proc. IEEE INFOCOM 2011.

ii) “Hop Count Limited Networking” (IT-MANET, PI Shakkottai) L. Ying, S. Shakkottai, A. Reddy, “On Combining Shortest Path And Back-pressure Routing over Multihop Wireless Networks,” Proc. IEEE INFOCOM 2009.

IT-MANET Topics:

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Want to optimally react to unexpected events.Example 1: Failure at Node B

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Example 2: Opportunity via Mobility

mobile node

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mobile node

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mobile node

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mobile node

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Assumptions and Main Questions:

Assumptions:•Arbitrary mobility, traffic, channels.•Little or no probability models known in advance.•Any sample path is possible (non-ergodic).•Future is unknown.

Questions:•Can we develop math for non-equilibrium networks? •Can we optimize without knowing the future?•Can we make worst-case delay guarantees?

Main Results:

•We use a backpressure/max-weight algorithm that does not know future.

•Design a novel “ε-persistent service” virtual queue for delay guarantees.

•Use “T-Slot Lookahead Utility” defined by an “ideal” alg. that has perfect knowledge of the future up to T slots.

•For any T, our algorithm can achieve utility that is arbitrarily close to the T-slot Lookahead utility, with tradeoff in worst case delay.

Problem Formulation:•Timeslotted system, slots t = {0, 1, 2, …}.•N node MANET.•M data flows (each with source-destination).•No pre-specified routes (we learn them).


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Nodes: N = 8


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Nodes: N = 8Flows: M = 3


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1 Nodes: N = 8Flows: M = 3• Flow 1: 13

Problem Formulation:•Timeslotted system, slots t = {0, 1, 2, …}.•N node MANET. •M data flows (each with source-destination).•No pre-specified routes (we learn them).

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Nodes: N = 8Flows: M = 3• Flow 1: 13• Flow 2: 73


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3 Nodes: N = 8Flows: M = 3• Flow 1: 13• Flow 2: 73• Flow 3: 56


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3 Nodes: N = 8Flows: M = 3• Flow 1: 13• Flow 2: 73• Flow 3: 56

•S(t) = “Topology State” observed on slot t.•(μij

(c)(t)) = Transmission Decisions (in set Γ(S(t))

State Information and Network Decisions:

Sij(t)

Sik(t)

How to enforce delay guarantees?(1) Allow Packet Dropping at Source Flow Control:

(2) Allow Packet Dropping at in-Network Queues:

arrivalsj(t)

Dj(t)

μj(t)

Source node m

Qj(t)

Am(t)Rm(t)

Maximize: ∑ gm(rm – dm) Subject to: Net. Stability

Maximize: ∑ [gm(rm) – νmdm] Subject to: Net. Stability

rm = time avg admission rate of flow mdm = time avg packet drops of flow m

This transformation separates out the variables, and is useful for distributed implementation.

How to enforce delay guarantees?(1) Allow Packet Dropping at Source Flow Control:

(2) Allow Packet Dropping at in-Network Queues:

arrivalsj(t)

Dj(t)

μj(t)

Source node m

Qj(t)

Am(t)Rm(t)

Maximize: ∑ gm(rm – dm) Subject to: Net. Stability

Maximize: ∑ [gm(γm) – νmdm] Subject to: rm ≥ γm

Net. Stabilityrm = time avg admission rate of flow mdm = time avg packet drops of flow m

This transformation turns a maximization of a function of a time average into a maximizationof a pure time average.

How to enforce delay guarantees?(3) Use New Virtual Queue for ε-Persistent Service:

Theorem: If Qj(t) ≤ Qmax, Zj(t) ≤ Zmax, then:

Worst Case Delay in Node j ≤ (Qmax + Zmax)/ε

a(t)

tQ(t

) ≤ Q

max

t+MaxDelay

arrivalsj(t) μj(t)+Dj(t)Qj(t)Actual Queue:

Virtual Queue: Zj(t) μj(t)+Dj(t)ε 1{Qj(t)>0}

•Segment timeline into T-slot frames.

•φopt[r] = optimal sum utility over frame r, assuming future is known in frame!

Utility Maximization with T-Slot Lookahead:

Frame 0 Frame 1 Frame 2

•Value of φopt[r] can be written as a non-linear program (assuming future arrivals, channels, and topology states are known)…

Analytical Approach:•Lyapunov Function for queues: L(Q(t)) = ∑ [Qi(t)2 +Zi(t)2 + Yi(t)2]•New sample path “T-slot” Lyapunov Drift:

ΔT(t) = L(Q(t+T)) – L(Q(t))

•Every slot “greedily” minimize 1-slot drift-plus-penalty:

Δ1(t) + V x Penalty(t) , Penalty(t) = -φ(γ(t))+νmDm(t) •Results in a joint backpressure, flow control, packet dropping alg with modified backpressure weights:

Qj(t) + Zj(t)1{Qj(t)>0}

Performance ResultTheorem: Arbitrary Traffic, Mobility. For any R>0, T>0:

(ii) Worst Case Queue Delay = B3V/ε

•B1 , Β2 , Β3 are known constants. •V = “knob” to turn to affect the tradeoff•R = Running Time (number of T-slot frames)

V RT

(i) “Fudge Factor” = B1T + B2V

O(1/V), O(V) utility-backlog tradeoff when time horizon R infinity

Achieved Utility over RT slots ≥ (1/R)∑r=0 φopt[r] – “Fudge Factor”R-1

Conclusions:•Arbitrary Traffic, Mobility (can be “non-ergodic”).

•New Math for “Non-Equilibrium” Networking.

•O(V), O(1/V) tradeoff between worst case queue delay and network utility.

•Easily extends to worst-case end-to-end delay via: (i) Restrict routing paths to H hops.

(ii) Use PI Shakkottai result on H-hop limited Queueing.

New Book Advertisement: M. J. Neely, Stochastic Network Optimization with Application to Communication and Queueing Systems. Morgan & Claypool, 2010.

PDF available from “Synthesis Lecture Series” (on digital library), linkon Neely homepage (for PDF and/or order form for hardcopy)

Extra Detail Slides: •Network Transmission Model•Some Simulations for “Universal Scheduling” in the presence of non-ergodic traffic and jamming.

Network Queueing:

a b a

•Each node keeps queues for each separate commodity (“commodity” = “destination”).•For commodity c (say, green commodity):

Qa(c)(t+1) = Qa

(c)(t) – Transmit out + Endogenous Arrivals + Exogenous Arrivals

Example Mobile Network:

Five Mobility Groups: •10 nodes Group 1 (upper left) •10 nodes Group 2 (upper right)•10 nodes Group 3 (lower right)•10 nodes Group 4 (lower left)•1 node Group 5

Group 1 nodes: Random Walk on Upper Left Region

S1

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Group 2 nodes: Random Walk on Upper Right Region

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Group 3 nodes: Random Walk on Lower Right Region

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Group 4 nodes: Random Walk on Lower Left Region

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Group 5 node: Periodically cycles about the clockwise orbit

Social Contacts:•Source 1: S1D1 (constant rate = 0.07 packets/slot) •Source 2: S2 S1 (for first half of simulation) S2 D1 (for second half of simulation)Goal: Maximize Throughput of Source 2 subject to stabilityUse V=10, so guarantee no more that 11 source 2 packetsin any queue!

S1

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D1

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Backlog Bound for D1 in a sample RED node

Backlog Bound for S1 in a sample RED node

Example Mobile Network: Sim. 1– Change Social Contacts

Social Contacts:•Source 1: S1D1 (constant rate = 0.07 packets/slot) •Source 2: S2 S1 (for first half of simulation) S2 D1 (for second half of simulation)Goal: Maximize Throughput of Source 2 subject to stabilityUse V=10, so guarantee no more that 11 source 2 packetsin any queue!

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Moving Average thruput:S2D1

Moving Average thruput:S2S1

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Moving Average thruput:S2D1

Moving Average thruput:S2S1

Overall Performance is Seamless: •Backlog no more than 11 packets in any queue for Source 1 data•Backlog no more than 15 packets in any queue for Source 2 data•Overall Thruput of Source 2 is maintained at near-optimal over the change, even though the routes must fundamentally change!

S1

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Example Mobile Network: Sim. 2– Intermittent Jamming

Social Contacts:•Source 1: S1D1 (constant rate = 0.07 packets/slot) •Source 2: S2 S1 (Goal to maximize its throughput)Intermittent Interference during 2 intervals of the simulationThat completely cut interaction between the groups 1-4.Can only use the cyclic mobile node at these times!Max Thruput of Source 2 during interference ~= 0.03.

Time

JAM! JAM!

S1

S2

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Example Mobile Network: Sim. 2– Intermittent Jamming

Social Contacts:•Source 1: S1D1 (constant rate = 0.07 packets/slot) •Source 2: S2 S1 (Goal to maximize its throughput)Intermittent Interference during 2 intervals of the simulationThat completely cut interaction between the groups 1-4.Can only use the cyclic mobile node at these times!Max Thruput of Source 2 during interference ~= 0.03.

Time

JAM! JAM!

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Conclusion Slide:

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Backlog Bound for D1 in a sample RED node

Backlog Bound for S1 in a sample RED node

Moving Average Thruput of Source 2

•Overall Seamless Operation•Throughput During Jamming goes down, but is close to optimal value of 0.03. •Fudge Factor = BT/V + CV/RT•Worst Case Queue Backlog = O(V)•Framework useful for stock market trading! (Thursday @ 10:20am)

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Multi-Hop Networking with Hard Delay Constraints