# Delay Analysis of IEEE 802.11 in Single-Hop Networks Marcel M. Carvalho, J.J.Garcia-Luna-Aceves.

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Delay Analysis of IEEE 802.11 in Single-Hop Networks Marcel M. Carvalho, J.J.Garcia-Luna-Aceves

Outline The Distributed coordination function mechanism Service time characterization Channel probabilities Model validation Performance evaluation of DSSS and FHSS Conclusion

The Distributed coordination function(DCF) backoff DCF describes two techniques for packet transmissiom Basic access mechanism RTS/CTS access mechanism The backoff time counter is decremented if the channel is sensed idle Otherwise it is frozen in its current state until the channel is sensed idle more than a DIFS

Notation Three possible events a node can sense during its backoff = {successful transmission}, ={idle channel}, ={collision}, Let denote the backoff stage, Let,, and denote the number of idle slots, collision slots and successful transmission slots respectively, and, and denote their probabilities respectively. and is the average time the channel is sensed busy due a collision and a successful transmission respectively. is the time used when the channel is sensed idle (one backoff time) The average backoff step size is

Service time characterization At k-th backoff stage, the number of backoff steps is chosen uniformly from. The average number of backoff steps is The average time a node spends at k-th stage is Let the probability of collision. The probability of successful transmission at k-th stage is The cumulative delay of a node at k-th backoff stage is

Service time characterization The average single-hop delay considering the frame retry limit is given by the following expression Where

Channel Probabilities This model is applicable whenever,, and are known These probabilities are computed for saturated, single hop ad hoc network under ideal channel condition (i.e, no hidden terminals and capture), with fixed number of nodes This analysis is based on Bianchi framework, the probability that a node transmits in a randomly chosen slot time is Where p is the probability of a collision experienced by a transmitted packet on the channel

Channel Probabilities Let then Using the Taylor series expansion of at p=0, the first order approximation of is is approximated the following

Channel Probabilities

Probability that there is one transmission in the considered time slot is Let is the probability that a transmission occurring on the channel is successful The probability of collision is The probability of successful transmission is The probability of idle slot is

Model Validation Ns-2 simulator Network size from 8 to 56 nodes Packet size 1500 bytes Nodes randomly distributed Network area 20*20 m No mobility Performance metrics: service time and jitter

Model Validation

Performance Evaluation

Performance evaluation

Performance Evaluation

Conclusion DSSS performs better than FHSS in term of delay and jitter The higher the initial contention window size, the smaller the average service time and jitter are, especially for large networks The binary exponential backoff algorithm has negative impact if both the maximum backoff stage and the number of nodes in the network are large

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