adaptive batch resolution algorithm for csma wireless networks

Andrea [email protected]

Adaptive Batch Resolution Algorithm for CSMA Wireless Networks

Special Interest Group on

NEtworking & Telecommunications

A. Zanella - Globecom 2010

2

Problem statement What’s a “batch”?

Set of mutually interfering nodes simultaneously solicited to send a packet RF tags illuminated by a reader Wireless nodes that reply to neighbour-discovery request Mobile terminals that compete to reserve a channel slot

What’s the “Batch resolution problem”? Simultaneous transmissions by multiple nodes result into

collision all packets are lost! Nodes need to arbitrate the channel access in order to

transmit their packet avoiding collisions A node that successfully transmits is said to be resolved

What’s a “Batch Resolution Algorithm” (BRA)? The BRA arbitrates the channel access in order to minimizing

the batch resolution interval, ie, the mean time required to resolve all the nodes in the batch

Broadcast inquiry message

Inquirer

Solicited nodes form the “batch”

Unicast reply messages


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BRA vs MAC The batch resolution problem looks like the MAC

problem but… MAC protocols generally look at the channel contention as

a steady-state phenomenon BRAs address scenarios where contention has a bursty

nature BRAs can be applied as MAC protocol, called obvious

MAC nodes with pending packets form a batch batch is resolved using BRA

one pck delivered per node No other nodes is admitted into the batch till the end of the BRA

Process starts over again, with a new batch formed by nodes with still pending packets

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Performance measures Batch resolution interval (BRI)

Tau(n) = E[time required to resolve a batch of size n]

Batch Throughput

Asymptotic throughput Corresponds to the maximal sustainable

arrival rate when BRA is used as obvious MAC



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Literature: immediate feedback Feedback (idle, successful, collision) is returned after

each slot Collisions are recursive resolved by random binary

splitting Nodes are randomly split in two subsets: Left and Right Left subset is activated first (nodes transmit)

Collision? apply recursively the algorithm from step (1) Idle or successful slot? activate Right subset & goto step (3)

activatedbackloggedresolved

I/S/C

Idle slot (ti)Feedback packet (bp)

Collision (tc) Successful tx (ts)

C I C S S Stc bp

ti ts

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Splitting-tree BRAs Time is slotted

Slots may have unequal duration in CSMA networks In each slot, some nodes are “activated”, that is to say,

enabled to transmit Feedback is returned after each slot

Idle slot: no nodes transmit Successful slot: a single node transmit Collided slot: two or more nodes transmit

BRA works recursively, driven by feedback, as follows Idle: activate nodes in the next slot Successful: activated node is resolved and leaves the batch Collision: activated nodes are randomly split in left (L) and right (R)

subgroups BRA is applied to L first Once L is resolved, BRA is applied to R


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Example: BTInitial batch: {1,2,3,4,5}

L= {1,2}

LL= {1,2} LR= { }

R= {3,4,5}

LLL= {1} LLR= {2}

1 is resolved 2 is resolved

RL= {} RR= {3,4,5}

RRL= {3} RRR= {4,5}

RRRL= {4} RRRR= {5}

3 is resolved

4 is resolved 5 is resolvedA. Zanella - Globecom 2010

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Ex: MBTInitial batch: {1,2,3,4,5}

L= {1,2}

LL= {1,2} LR= { }

R= {3,4,5}

LLL= {1} LLR= {2}


RL= {} RR= {3,4,5}

RRL= {3} RRR= {4,5}

RRRL= {4} RRRR= {5}

3 is resolved

4 is resolved 5 is resolvedA. Zanella - Globecom 2010

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Ex: CMBTInitial batch: {1,2,3,4,5}

L= {1,2}

LL= {1,2} LR= { }

LLL= {1} LLR= {2}


Clipped


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Ex: CMBT (2)Clipped batch: {3,4,5}

R= {3,4,5}

RL= {3}

RR= {4,5}

RRR= {4,5}

RRL= {4} RRR= {5}3 is resolved


L= {}


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Shortcomings of existing solutions

Slots are assumed to have constant time duration

Feedback overhead is negligible

Maximizing the per-frame throughput will minimize the batch resolution time

In CSMA systems, slots duration depends on the channel status

Each transmission brings along a certain overhead

Maximizing per-frame throughput does not necessarily minimize the overall batch resolution interval

In theory In practice

Slot time duration Feedback message time duration

Successful Tdata=1 phi_sIdle Beta<<1 phi_iCollision beta_c~1 phi_c

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The cost of neglecting feedback cost…


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Contribution of this work


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ABRA: principles

ABRA works in successive resolution rounds At each round, unresolved nodes transmit their packets in a random slot in the

frame Slotted CSMA ALOHA

At the end of the contention frame, the inquirer broadcasts a probe message that contains: aggregate feedback field frame length w to be used in the next round

ACKed nodes leave ABRA, the other keep competing in the next frameA. Zanella - Globecom 2010

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ABRA core: frame size optimization!

We assume that the inquirer perfectly knows the number “n” of still unresolved nodes at the end of each round

The frame size w(n) of the next round is selected in order to minimize the BRI for the residual batch:


€

wn* = argmin

w

β p +w −w 1− 1w

⎛ ⎝ ⎜

⎞ ⎠ ⎟n−1

1−β( ) + ps r( )r=1

min w,n{ }

∑ T n − r( )

1− ps 0( )

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪

€

T n( ) = β p +E sτ s + cτ c + iτ i + T n − s( )w,n[ ]

= β p +w −w 1− 1w

⎛ ⎝ ⎜

⎞ ⎠ ⎟n

1−β( ) + Pr s = r w,n[ ]r=0

min w,n{ }

∑ T n − r( )

Frame duration Residual batch resolution interval

ts=tc=1b=ti/ts

w*n: optimal frame length for a batch of size n

Dynamic programming optimization

Batch Resolution Interval

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Optimal frame length


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ABRA’s throughput


l(n)

€

Λ=limn→∞ λ n( ) = exp −μ∞( )


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Case study Parameters set according to WiFi (WF) & ZigBee

(ZB) specifications Batch size n with Poisson distribution of

parameter N Simple batch size estimator [Schoute83]:

Tdata [ms] b bs bc bp=w/Lmax

0.399 0.0225 0.1319 0.1319 w/184964.896 0.0654 0.1111 0.0458 w/944

€

ˆ n = max ˆ n ,s +2c{ }

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Throughput comparison Throughput gain of ~9% for

WF and ~6% for ZB wrt best competitor

High and rather constant throughput for all batch sizes

ABRADE

ABRADE

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Energy efficiency comparison Mean number of tx per

slot (proportional to energy consumption) comparable to the best performing algorithms


ABRADE

ABRADE

Andrea [email protected]

Adaptive Batch Resolution Algorithm for CSMA Wireless Networks

Special Interest Group on

NEtworking & Telecommunications

22

Appendix: asymptotic throughput


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Appendix: asymptotic throughput

Taking the derivative wrt mu_infty


adaptive batch resolution algorithm for csma wireless networks

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