802.11e EDCA WLN 2005 Sydney, Nov Paal E. Engelstad (presenter) UniK / Telenor R&D Olav N. sterb Telenor R&D Agenda 1.Delay and Throughput Analysis of IEEE e EDCA with Starvation Prediction Non-saturation analysis AIFS differentiation and Starvation prediction Z-tranform of the delay Virtual collision handling 2.Differentiation of Downlink e 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 Accepted) The full delay distribution (IPCCC 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 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 Before solving the equations, we first need to determine the remaining parameters , p, p*, q and q* Non-Saturation part 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, : Throughput We have shown that this expression is valid also under non-saturation Preliminary Throughput Validations: Setup I b with long preamble and without RTS/CTS Poisson distributed traffic 1024B packets Preliminary Throughput Validations: Setup II We use the recommended (default) parameter settings of e EDCA: Simulations: ns-2 with TKN implementation of e from TUB Numerical computations: Mathematica AC[3]AC[2]AC[1]AC[0] AIFSN2237 CWmin3715 CWmax Retry Limit (long/short) 7/4 Preliminary Throughput Validation: The non-saturation analysis Preliminary Throughput Validation: The starvation predictions Fixed number of nodes (n=5) 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 I Mean Medium Access Delay II... and the mean medium access delay is finally found as: Validation of Mean delay (n=5) 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: 1.The medium access delay Given by the first order moment Demonstrated in the presented paper 2.The queuing delay Given by the second order moment 3.Variation of the queuing delay Given by the third order moment 4.The full delay distribution The transform can be inverted numerically 5.All desirable delay percentiles follow... and so forth.... Agenda 1.Delay and Throughput Analysis of IEEE e EDCA with Starvation Prediction Non-saturation analysis AIFS differentiation and Starvation prediction Z-tranform of the delay Virtual collision handling 2.Differentiation of Downlink e 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 Accepted) The full delay distribution (IPCCC 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: Double derivation of the z-transform Example of queueing delay results 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: Distribution of Medium Access Delay Distribution of Queueing 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 1.Delay and Throughput Analysis of IEEE e EDCA with Starvation Prediction Non-saturation analysis AIFS differentiation and Starvation prediction Z-tranform of the delay Virtual collision handling 2.Differentiation of Downlink e 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 Accepted) The full delay distribution (IPCCC 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: Validations 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]: Validation Scenarios Throughput validations of closed form solution (Scenario 1) Throughput validations of closed form solution (Scenario 2) Validations with other scenarios Conclusion - 4 We have also derived a closed form solution for the downlink scenario Analytical results were validated and matched well with simulation results Backup slides... The effect of AIFS differentiation during countdown Packet Slots that AC[3] can use for countdown Packet Slots that AC[0] can use for countdown A higher AIFS value translates into a lower average countdown rate AC[3]s perspective: AC[0]s perspective: Medium Access Starvation Packet Slots that AC[3] can use for countdown Packet No slots for AC[0]s countdown AIFS differentiation leads to starvation at high traffic loads AC[3]s perspective: AC[0]s perspective: Packet How to incorporate this effect into the analytical model? AIFSN[0] Packet A i = AIFSN[i] - AIFSN[0] (i.e. defined such that always A 0 = 0) Packet A i blocked slots unblocked empty slots one busy slot