# Andrea Zanella Adaptive Batch Resolution Algorithm for CSMA Wireless Networks Special Interest Group on NEtworking & Telecommunications.

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Andrea Zanella zanella@dei.unipd.it Adaptive Batch Resolution Algorithm for CSMA Wireless Networks Special Interest Group on NEtworking & Telecommunications

Problem statement A. Zanella - Globecom 2010 2  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 A. Zanella - Globecom 2010 3  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 4 A. Zanella - Globecom 2010

Literature: immediate feedback A. Zanella - Globecom 2010 5  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) activated backlogged resolved I/S/C Idle slot (  i ) Feedback packet (  p ) Collision (  c ) Successful tx (  s ) C C I I C C S S S S S S cc pp ii s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 6 A. Zanella - Globecom 2010

Example: BT Coll Succ IdleCollIdleCollSuccCollSucc Initial 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 resolved5 is resolved 7 A. Zanella - Globecom 2010

Ex: MBT Coll Succ IdleCollIdleCollSuccCollSucc Initial 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 resolved5 is resolved 8 A. Zanella - Globecom 2010

Ex: CMBT Coll Succ IdleCollIdleCollSuccCollSucc Initial batch: {1,2,3,4,5} L= {1,2} LL= {1,2}LR= { } LLL= {1}LLR= {2} 1 is resolved 2 is resolved Clipped 9 A. Zanella - Globecom 2010

Ex: CMBT (2) CollIdleCollSuccCollSucc 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 resolved5 is resolved L= {} 10 A. Zanella - Globecom 2010

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 11 A. Zanella - Globecom 2010 In theoryIn practice Slot time durationFeedback message time duration SuccessfulTdata=1phi_s IdleBeta<<1phi_i Collisionbeta_c~1phi_c

The cost of neglecting feedback cost… 12 A. Zanella - Globecom 2010

Contribution of this work A. Zanella - Globecom 2010 13 Define a framed-based BRA that keeps into account feedback costs ABRA: Adaptive BRA Performance comparison of different BRAs in practical wireless networks

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 14 A. Zanella - Globecom 2010

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: 15 A. Zanella - Globecom 2010 Frame duration Residual batch resolution interval  s  c   i  s  s  c   i  s w* n : optimal frame length for a batch of size n Dynamic programming optimization Batch Resolution Interval

Optimal frame length 16 A. Zanella - Globecom 2010

ABRA’s throughput A. Zanella - Globecom 2010 17 (n)

Case study A. Zanella - Globecom 2010 18  Parameters set according to WiFi (WF) & ZigBee (ZB) specifications  Batch size n with Poisson distribution of parameter N  Simple batch size estimator [Schoute83]: T data [ms] bbsbs bcbc b p =w/L max 0.3990.02250.1319 w/18496 4.8960.06540.11110.0458w/944

Throughput comparison  Throughput gain of ~9% for WF and ~6% for ZB wrt best competitor  High and rather constant throughput for all batch sizes 19 A. Zanella - Globecom 2010 ABRADE

Energy efficiency comparison  Mean number of tx per slot (proportional to energy consumption) comparable to the best performing algorithms 20 A. Zanella - Globecom 2010 ABRADE

Andrea Zanella zanella@dei.unipd.it Adaptive Batch Resolution Algorithm for CSMA Wireless Networks Special Interest Group on NEtworking & Telecommunications

Appendix: asymptotic throughput 22 A. Zanella - Globecom 2010

Appendix: asymptotic throughput Taking the derivative wrt mu_infty 23 A. Zanella - Globecom 2010

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