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SIGNET. Special Interest Group on NEtworking & Telecommunications. Adaptive Batch Resolution Algorithm for CSMA Wireless Networks . Andrea Zanella [email protected]. Problem statement. What’s a “batch”? Set of mutually interfering nodes simultaneously solicited to send a packet - PowerPoint PPT Presentation
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Andrea [email protected]
Adaptive Batch Resolution Algorithm for CSMA Wireless Networks
Special Interest Group on
NEtworking & Telecommunications
Problem statement
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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
BRA vs MAC
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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
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
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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 (i)Feedback packet (p)
Collision (c) Successful tx (s)
C I C S S Sc p
i s
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 resolved
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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}
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 resolved
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A. Zanella - Globecom 2010
Ex: CMBTInitial batch: {1,2,3,4,5}
L= {1,2}
LL= {1,2} LR= { }
LLL= {1} LLR= {2}
1 is resolved 2 is resolved
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
4 is resolved 5 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
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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
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 frame
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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:
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€
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
scis
w*n: optimal frame length for a batch of size n
Dynamic programmi
ng optimizati
on
Batch Resolution Interval
Optimal frame length16
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ABRA’s throughput
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(n)
€
Λlimn→∞ λ n( ) = exp −μ∞( )
Case study
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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{ }
Throughput comparison Throughput gain of ~9% for
WF and ~6% for ZB wrt best competitor
High and rather constant throughput for all batch sizes
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ABRADE
ABRADE
Energy efficiency comparison Mean number of tx per
slot (proportional to energy consumption) comparable to the best performing algorithms
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ABRADE
ABRADE
Andrea [email protected]
Adaptive Batch Resolution Algorithm for CSMA Wireless Networks
Special Interest Group on
NEtworking & Telecommunications
Appendix: asymptotic throughput
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Appendix: asymptotic throughput
Taking the derivative wrt mu_infty
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