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## 802.11e EDCA

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**802.11e EDCA**WLN 2005 Sydney, Nov. 15 2005 Paal E. Engelstad (presenter) UniK / Telenor R&D Olav N. Østerbø Telenor R&D http://www.unik.no/~paalee/research.htm**Agenda**• ”Delay and Throughput Analysis of IEEE 802.11e EDCA with Starvation Prediction” • Non-saturation analysis • AIFS differentiation and Starvation prediction • Z-tranform of the delay • Virtual collision handling • ”Differentiation of Downlink 802.11e Traffic in the Virtual Collision Handler” • Downlink UDP scenario • Virtual collision handling (demonstration) • Closed-form solution to this scenario • Follow-up work • The queueing delay (WONS 2006 - Accepted) • The full delay distribution (IPCCC 2006 - Pending)**Recap EDCA: 4 Access Categories (AC)**• AC[0] (AC_BK) • AC[1] (AC_BE) • AC[2] (AC_VI) • AC[3] (AC_VO) • 4 queues on each station • ... and Virtual Collision Handling (VCH) between the queues**EDCA channel Access**• Differentiation parameters: • Contention Windows: • Arbitration IFS (AIFS): • (TXOP lengths)**Markov Chain**• The utilization factor ρ balances between saturation and non-saturation • Collision prob.: p • Other parameters: • p*, q and q* • Drop probability: • Transmission in (i,j,0) states, with distribution:**... some calculations ...**• The transmission probablity • From chain regularities... • ... and after normalization:**The transmission probability**Non-Saturation part • Before solving the equations, we first need to determine the remaining parameters • ρ, p, p*, q and q***The collision probability**• The probability of a busy slot: • The collision probability of AC[i]: • (Here: Without Virtual Collisions) • The probability of blocking of the countdown, p*, is distinguished from the collision probablity, p. • Gives much flexibility • p* = 0 (similar to the original Bianchi model) • p* = p (similar to the model of Xiao / Ziouva) • In this paper, we propose to incorporate AIFS differentiation into p*...**AIFS Differentiation**• We “scale down” the collision probability during countdown, depending on the AIFS setting: • Starvation is thus predicted to occur when: where:**Determining the remaining parameters:**• The pdf of the length of a slot: • Thus, assuming Poisson traffic: • And from the general result regarding the utilization factor, ρ:**Throughput**• We have shown that this expression is valid also under non-saturation**Preliminary Throughput Validations: Setup I**• 802.11b with long preamble and without RTS/CTS • Poisson distributed traffic – 1024B packets**AC[3]**AC[2] AC[1] AC[0] AIFSN 2 2 3 7 CWmin 3 7 15 15 CWmax 15 31 1023 1023 Retry Limit (long/short) 7/4 7/4 7/4 7/4 Preliminary Throughput Validations: Setup II • We use the recommended (default) parameter settings of 802.11e EDCA: • Simulations: • ns-2 • with TKN implementation of 802.11e from TUB • Numerical computations: • Mathematica**Preliminary Throughput Validation: The non-saturation**analysis**Preliminary Throughput Validation: The starvation**predictions**The delay analysis**• The major contribution of this paper is probably that the Medium Access Delay (”MAC delay”) is expressed in terms of the z-transform...**z-tranform of the MAC delay**s=1 s=0**z-transform of the medium access delay (cntd.)**• The mean medium access delay is found by derivation of the z-transform and by letting z=1 • Obtain a delay expression that can easily be verified directly...**Mean Medium Access Delay II**• ... and the mean medium access delay is finally found as:**Conclusion - 1**• An analytical model is found that also describes non-saturation conditions • We propose a new model, leading to a relatively simple set of equations • AIFS differentiation is incorporated into the model • We propose a new approach • Starvation prediction follows • Virtual collision handling is incorporated • Demonstrated in our downlink work (next paper) • Most importantly: The z-transform of the medium access delay was found • Our analytical findings seem to be supported by simulation results**The z-transform is an important contribution...**...because it encompasses a full description of the delay in the system: • The medium access delay • Given by the first order moment • Demonstrated in the presented paper • The queuing delay • Given by the second order moment • Variation of the queuing delay • Given by the third order moment • The full delay distribution • The transform can be inverted numerically • All desirable delay percentiles follow ... and so forth ....**Agenda**• ”Delay and Throughput Analysis of IEEE 802.11e EDCA with Starvation Prediction” • Non-saturation analysis • AIFS differentiation and Starvation prediction • Z-tranform of the delay • Virtual collision handling • ”Differentiation of Downlink 802.11e Traffic in the Virtual Collision Handler” • Downlink UDP scenario • Virtual collision handling (demonstration) • Closed-form solution to this scenario • Follow-up work • The queueing delay (WONS 2006 - Accepted) • The full delay distribution (IPCCC 2006 - Pending) A small side-step:**Queueing Delay**• Assuming a M/G/1 system the queueing delay is expressed as: • The second order of the delay is found by double derivation of the z-transform and by letting z=1:**The full delay distribution**• The z-transform of the delay • For the tail probabilities • then: • and can be expressed by the Cauchy contour integral:**Approximation: Trapezodial Rule**• The Cauchy contour integral can be approximated using the trapezodial rule with stepsize • Hence: • It can be shown that the accuracy is bounded by:**Same method to find distribution of the queueing delay**• Pollaczek-Khinchin formula (discrete time): • Thus, the tail probability of the • Queueing Delay: • Total Delay:**Conclusion - 2**• The z-transform of the delay was found • Derived the mean medium access delay (as before) • It is so important because, it can be used to find: • the mean medium access delay, its variation, etc... • the mean queueing delay, its variation and so forth • the full delay distribution • all desirable delay percentiles • Our analytical findings seem to be supported by simulation results**Agenda**• ”Delay and Throughput Analysis of IEEE 802.11e EDCA with Starvation Prediction” • Non-saturation analysis • AIFS differentiation and Starvation prediction • Z-tranform of the delay • Virtual collision handling • ”Differentiation of Downlink 802.11e Traffic in the Virtual Collision Handler” • Downlink UDP scenario • Virtual collision handling (demonstration) • Closed-form solution to this scenario • Follow-up work • The queueing delay (WONS 2006 - Accepted) • The full delay distribution (IPCCC 2006 - Pending)**Background: Downlink Analysis**• Unlike most related work, we also put focus on the downlink scenario**Assumption**• All traffic are downlink! • E.g. downlink video streaming over UDP • The AP has full control over the wireless medium • Collision primarily happens in the virtual collision handler**Core idea of Downlink Analysis**• Treat the Virtual Collision Handler as a ”virtual channel” and disregard the wireless medium as a channel • Re-use the Markov model • Introduce Virtual Collision Handling into the model • Set the number of nodes to 1**Virtual Collision Handling – 1 node**• The probability of a busy slot: • The collision probability of AC[i]: • Without Virtual Collisions: • With Virtual Collisions:**Throughput – 1 node**• Generally: • But for 1 node: • Using the above, we have – quite interestingly - proved by induction that: • Hence, the throughput becomes:**Conclusion - 3**• We have shown that the Bianchi model can be extended to also cover downlink traffic • All collisions in the virtual collision handler of the AP. It is treated as a virtual channel. • Need a model that incoporates virtual collision handling. • Set n=1 • The approach was validated, and numerical results matched well with simulations.**Closed-form solution under saturation conditions**• We show that the downlink model can be expressed ON CLOSED FORM... • ...under saturation conditions:**Recursive solution method**• Start with the highest priority ACs: • For lower priority ACs • etc.... • Use , , or (starvation)**Example of solution for the second highest priority AC**• Note that it is expressed in terms of the transmission probability of the highest priority AC, AC[3]. • This is why a ”recursive” solution method is required.**Closed form delay expression**• Using these expressions, the delay can be found on closed form, e.g. for AC[3]: