Analysis of CAP of IEEE 802.15.4 Superframe

1. Analysis of CAP of IEEE 802.15.4 Superframe Iyappan Ramachandran University of Washington November 15, 2005

2. Model Assumptions • Beacon-enabled Star • M nodes attached to a coordinator • All nodes within the carrier sensing range of each other • No inactive period in the superframe, i.e. BO=SO • Contention access part (CAP) occupies active period fully • No acknowledgements • Poisson arrival of packets, i.e. probability p of packet arrival every backoff slot. • Packet length is fixed and equal to N backoff slots • No buffering at nodes • Only Uplink

3. Approximations to simplify analysis • Presence of beacons and beacon boundaries have negligible effect • Every node sees a probability pic that channel is idle in the first of two CCA backoff slots • Not slot-to-slot independence; probability that channel is idle in the second CCA backoff slot is pci|i • Independence for backoff slots separated by a backoff • Channel sees a probability ptn that a node begins transmission in any generic slot • Geometrically distributed backoff durations with same mean as original uniform distribution • Validity of approximations will be verified by simulations

4. Consequences of approximations • CAP can be simply analyzed as non-persistent CSMA • Channel and nodes have been virtually decoupled • Each node can be analyzed independent of the others • Probability pkn that node will get out of kth backoff stage

5. Node state model (see handout #1) • Node stays in IDLE state with prob. (1-p) and goes to BO1 with prob. p • BO1  CS11 with prob. p1n • CS11CS12 with prob. pic and BO2 with prob. (1-pic) • CS12TX with prob. pi|ic and CS12 with prob. (1-pi|ic) … • … and so on • TXIDLE with prob. 1 after N backoff slots • CS51IDLE and CS52 IDLE with probabilities (1-pic) and (1-pi|ic) respectively

6. Channel state model (handout #2) • Channel stays in (IDLE, IDLE) state when no node begins transmission (prob.α=(1-pt|iin)) • (IDLE, IDLE)SUCCESS when exactly one node transmits (prob. β=Mpt|iin(1-pt|iin)M-1) • (IDLE, IDLE)FAILURE when more than one node transmit (prob. δ=1-α-β) • Channel stays in SUCCESS/FAILURE state for N backoff slots • SUCCESS(IDLE,IDLE) and FAILURE(IDLE,IDLE) with probability 1

7. Calculation of channel throughput • Approximations have led to virtual decoupling of nodes’ activities • Solve node state chain to find ptn in terms of pic (1) • Solve channel state chain to find pic in terms of ptn (2) • Solve (1) and (2) numerically to find picand ptn • Aggregate channel throughput, S is the fraction of time spent in SUCCESS state

8. Calculation of average power consumption • Chipcon CC2420 radio for illustration (see handout #3) • Four energy states: shutdown, idle, transmit, receive • Included beacon receptions • Considered two cases • Stay in idle state if no packet is waiting  included idle-to-receive ramp-up for beacon reception and CCA • Shutdown node if no packet is waiting  included shutdown-idle-receive ramp-up for beacon reception and CCA

9. Simulations • All simulations were run in NS-2; used IEEE 802.15.4 module developed by J. Zheng and M. J. Lee, CUNY • Same model assumptions, but NO approximations • No. of nodes, M=12; Packet length, N=10 backoff slots • BO=6  Beacon Interval=3072 backoff slots=0.983 sec; Beacon length=2 backoff slots

10. Simulations (cont.)

11. Conclusions • Analysis predicts very accurate throughput and power consumption estimates • Although shutting down has the ramp-up overhead time, it saves considerable energy at low traffic • Analysis can be extended • Easily to include acknowledgements • With some effort to include inactive part

12. Thank you!