Modeling Per-flow Throughput and Capturing Starvation in CSMA Multi-hop Wireless Networks

Rice Networks Grouphttp://www.ece.rice.edu/networks

Michele GarettoTheodoros Salonidis Edward W. Knightly

Modeling Per-flow Throughput and Capturing Starvation in CSMA

Multi-hop Wireless Networks

INFOCOM 2006

Garetto, Salonidis, Knightly

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Saturated traffic

802.11 DCF (CSMA/CA)

Ideal channel


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A few rich flows

Many starving flows !


Our contributions

We develop an analytical model to compute per-flow throughput in arbitrary network topologies employing 802.11 DCF

We explain the origin of starvation in CSMA-based wireless mesh networks

We propose metrics to quantify starvation due to the MAC


The model The channel “private view” of a node:

… …

successful transmission idle slot collision

t

busy channel due to activity of other nodes

Modelled as a renewal-reward process

Throughput (pkt/s) = P [event Ts occurs]

Average duration of an event (s)


Single cell: DCF can coordinate the nodes


Mesh Network : DCF cannot coordinate the nodes


The model

Event probabilities:

… …t

Define, for each node, the probabilities = probability that the node sends out a packet in a slot= conditional collision probability= conditional busy channel probability


The unknown variables for each node are:

Analysis (for backlogged flows)

(a decreasing function of p ) [Bianchi ’00]

The throughput of a node decreases if either: is large (large collision probability) is large (large fraction of busy time)

Throughput formula:


The origin of starvation

A node “starves” if either: – the conditional packet loss probabilityor – the fraction of time sensed busy (or both)

are “disproportionally” large as compared to its neighbors

(which are expected to have similar throughput)


How can p be disproportionally large ?

bB

aA

The “information asymmetry” scenario


How can bTb be disproportionally large ?

The “flow-in-the-middle” scenario

a

A

b

B C

cFlow Aa starves due to large fraction of busy time

idle time of A

busy time of A

channel at node A:


Incorporates known starvation effects due to the MAC protocol and predict their impact in the presence of many nodes

Requires solving a coupled non-linear multivariate system of equations

System is very sensitive to local perturbations (chaotic system ?)

Can analyze arbitrary topologies Predicts individual flow throughput Has been extended to non-saturated flows

The model


Model vs Sim – 50-nodes example

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How to measure starvation ?

We must separate out starvation due to MAC from natural throughput unbalance due to topology (different number of contenders)

We take a reference system in which starvation due to MAC is structurally eliminated :– Slotted aloha (proportional fairness can be

achieved by properly setting nodes’ transmission probabilities [Kar ’04])

We compare the two system using various metrics– aggregate metrics are not adequate– we consider how individual flows are treated in

the two systems


Disproportionality index

802.11

Aloha prop. fair.

Provides a measure of starvation which is independent of aggregate network throughput 50-nodes example: D = 0.39


Conclusions Multi-hop wireless networks employing 802.11

(or other variants of CSMA) are subject to severe starvation (under heavy load)

This is a fundamental problem due to lack of coordination between out-of-range transmitters

System performance strongly depends on network topology

We developed an analytical model to predict per-flow throughput in arbitrary topologies and characterize starvation

Thanks !


Propagation effects

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12 flows

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Tx Range = 200 m50 tx-rx pairs

Example : 50 nodes


Model vs simulation – 50 nodes

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Analysis of Asymmetric Incomplete State scenarios (AIS)

Flow A a does not know when to contend: it has to discover an available gap in the activity of flow B b randomly, where to place an entire RTS or DATA packet

B b…t

…B b B b B b

A a ?RTS/DATA

A a

B baA

b

B


Analysis of Asimmetric Incomplete State scenarios (AIS)

B bA a

B b B b

B bA a

B b B b

B b A a B b B b

• The collision probability of flow A a can be accurately computed assuming that the first packet arrives at a random point in time • The collision probability of flow B b is zero


Addressing Starvation

Structural approach : a slotted system with global synchronization (e.g. Slotted Aloha) eliminates starvation due to lack of coordination

Rate-limiting approach : sources are appropriately rate-limited to leave sufficient “air time” to flows subject to starvation

MAC-based approach : enhanced coordination mechanisms on top of existing MAC protocols: – receiver-initiated random access– schedule advertisement– orthogonal access

3 approaches: (within family of random access protocols)


System comparison

It is essential to:– Consider how individual flows are treated in

two different systems– Separate out unbalance due to topology

(number of contenders) and starvation due to the MAC protocol

We take as reference system: Slotted Aloha– Starvation structurally eliminated – Attempt probabilities can be set to achieve

proportional fairness:K. Kar, S. Sarkar, L. Tassiulas, Achieving Proportional Fair Rates using Local Information in Aloha Networks, IEEE Transactions on Automatic Control, Vol . 49, No. 10, October 2004


Lorentz curve and Gini index

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802.11Aloha prop fair

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Gini 802.11 = 0.76

Gini Aloha = 0.33


Lorentz curve and Gini index

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Modeling Per-flow Throughput and Capturing Starvation in CSMA Multi-hop Wireless Networks

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