Agenda

1. The Delay Distribution of IEEE 802.11e EDCA and 802.11 DCFIPCCC 2006 April 10 - 12, 2006 - Phoenix, ArizonaPaal E. EngelstadUniK / Telenor R&DOlav N. Østerbø (presenter)Telenor R&D

2. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

3. Wireless Channel Introduction • Fact 1: IEEE 802.11 WLAN standard widely deployed as wireless access technology in • office environments • public hot-spots • in the homes. • Fact 2: WLAN easily becomes bottleneck for communication. (shared medium with limited capacity, overhead etc..) • Fact 3: Standard IEEE 802.11 WLAN lacks QoS differentiation • Fact 4: IEEE 802.11e Enhanced Distributed Channel Access (EDCA) allows for differentiation between four different access categories (ACs) at each station • relative QoS differentiations between ACs

4. Why is the queueing delay so important? • Delay consists of two major parts: • Queuing Delay • Transmit queues • IP buffering • Medium Access Delay (”MAC delay”) AC[1] (AC_BE) AC[0] (AC_BK) AC[3] (AC_VO) AC[2] (AC_VI)

5. The problem... • Analytical work on the performance of 802.11e EDCA (Bianchi models) assume saturation conditions and focuses on predicting the • throughput • mean delay of the medium access • Current analytical Bianchi models assume saturation conditions • The queue lengths and the queueing delay are assumed to be infinite ! • Not a realistic transmission scenario • No protocols will work under those circumstances! • A non-saturation model is needed

6. The objective... • Finding the MAC delay, by itself, is normally not so interesting • The queueing delay can be significant • moments of the delay • full distribution of the delay, for instance to obtain various delay percentiles • Important is to find the point when saturation occurs, i.e. when: • the queueing delay goes to infinity, and • the transmission of the flow breaks down

7. AC[3] (AC_VO) QAP QAP AC[2] (AC_VI) QSTA 1 QSTA 1 QSTA 1 QSTA 5 QSTA 5 QSTA 5 AC[1] (AC_BE) AC[0] (AC_BK) QSTA 2 QSTA 2 QSTA 2 QSTA 4 QSTA 4 QSTA 4 QSTA 3 QSTA 3 QSTA 3 Uplink throughput example

8. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

9. IEEE 802.11e EDCA channel access • Differentiation parameters: • Contention Windows: • Arbitration IFS (AIFS): • (TXOP lengths)

10. A bi-dimensional Markov chain representing backoff stage and backoff counter • Embedded Markov chain • Post-backoff included • Adding “extra” row representing the case where the post-backoff starts with an empty queue • The state space where • representing the backoff stage • is the backoff counter

11. -the probability that there is a packet waiting in the transmission queue at the time a transmission is completed -the collision probability -the probability that there is at least one packet arrives in the idle state (-1,0) during a generic time slot -the countdown blocking probability -the probability that at one packet arrives during the time the system is in post-backoff state (-1,j) Markov chain- parameters

12. ... some calculations ... - the steady state distributions, Chain regularities gives a power-law expression - probability of a transmission attempt in a generic time slot Solving for bijk gives

13. The transmission probability Non-Saturation part • Before solving the equations, we first need to determine the remaining parameters • ρi*, pi, pi*, qi and qi* in terms ofti

14. The collision probabilities pi, pi* • The probability of a busy slot: • The collision probability of AC[i]- pi : • Without Virtual Collisions: • With Virtual Collisions: • Countdown blocking probability: • Bianchi: • pi*= 0 • Xiao: • pi*= pi • Incorporating AIFS differentiation:

15. Expressions for qi and qi* Assuming Poisson arrivals of packets with rate li • qi –prob. that at least one packet will arrive in the transmission queue during generic time slot • ps -prob. that a time slot contains a successfully transmitted packet with • pb -prob. of busy channel • Te duration of an empty slot, • Ts a slot containing a successfully transmitted packet and • Tc of a slot containing two or more colliding packets • qi* -prob. that a packet arrives during countdown blocking.

16. Expressions for the load ri and ri* • Backoff instance is busy: • while contending for channel access ("CA") • while the packet is being transmitted ("Tr"), • and during post-backoff ("PB") of the packet. • The post-backoff period should be associated as part of the processing of the packet that has been transmitted, and not the next packet to be transmitted and therefore • represents the mean service time (including CA,TR and PB) • The following relation yields: • PiPB-prob. of not receiving any packets in the transmission queue while performing a complete empty-queue post-backoff procedure.

17. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

18. s=1 s=0 z-tranform of the MAC delay

19. Exact form of the z-transform of the MAC delay by considering three cases: • The queue is non-empty when the post-backoff starts. • Exact form of the z-transform of the MAC delay by considering three cases: • The queue is non-empty when the post-backoff starts. • The queue is empty when the post-backoff starts and with no arrivals during the whole post-backoff period. • Exact form of the z-transform of the MAC delay by considering three cases: • The queue is non-empty when the post-backoff starts. • The queue is empty when the post-backoff starts and with no arrivals during the whole post-backoff period. • The queue is empty when the post-backoff starts, there is at least one packet arrival during the post-backoff period. where z-transform of the MAC delay • With post-backoff (Saturation case) • Without post-backoff (Non-saturation case)

20. Mean Medium Access Delay • Diffrentiation of z-tramsforms gives: • Mean Medium Access Delay: • Higher order moments may also be found (e.g second order) (+ should be – in paper)

21. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

22. Z-transform of the queueing delay • Queueing delay is obtained by consider an M/G/1 queue with DiSAT as service time with z-transform Dsati(z): • Total delay is sum of queueing delay and MAC delay • z-transforms of complementary (tail) distributions obtain through

23. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

24. Numerical procedure for obtaining tail distributions • Inversion of the z-transforms by applying Cauchys integral formula • By using the trapezoidal rule with step size p/m of the inversion integral becomes: • Discretization error:

25. Agenda • Introduction • A non-saturation model for 802.11e EDCA • ... and for 802.11 DCF as a special case • Finding the z-transform of the MAC delay • Deriving the z-transform of queueing delay from the z-transform • Finding the delay distribution and precentiles • Numerical examples

26. Numerical parameters • Numerical computations in Mathematica. • Applying 802.11b with long preamble and without the RTS/CTS-mechanism with time parameters • Parameters CWmin and CWmax are overridden using 802.11e values • Five different stations, QSTAs, contending for channel access. • Each QSTA uses all four ACs, and virtual collisions therefore occur. • Poisson distributed traffic consisting of 1024-bytes packets was generated at equal amounts to each AC.

27. The complimentary distribution of the MAC delay of AC[3] at a generated traffic rate of 1250 kbps

28. The complimentary distribution of the queueing delay of AC[3] at 1250 kbps

29. The complimentary distribution of the total delay of AC[3] at 1250 kbps

30. The complimentary distribution of the MAC delay of AC[3] at a generated traffic rate of 1750 kbps

31. Percentiles of the MAC

32. Percentiles of the queueing delay

33. Percentiles of the total delay

34. Summary • We have argued why the queuing delay is important. • Describing the queueing delay requires a non-saturation model • Based on an analytical model for the IEEE 802.11e the z-transform of the MAC delay is obtained in closed form • The queueing delay and total delay is obtained by applying a slotted version of Pollaczek-Khintchine formula. • The corresponding distributions are obtained by numerical inversion (by applying the trapezoidal rule), and different percentiles are calculated. • The numerical results show that the complementary distribution of the MAC delay has a typical stepwise form where the levels of the steps are related to the probability and duration of a transmission. • In a following up paper "Analysis of the Total Delay of IEEE 802.11e EDCA", Accepted for IEEE International Conference on Communication (ICC'2006), Istanbul, June 11-15, 2006 the mean and second order moments of the MAC delay and mean queueing delay is obtained

35. Backup slides...

36. Throughput • We have shown that this expression is valid also under non-saturation

37. AIFS Differentiation • We “scale down” the collision probability during countdown, depending on the AIFS setting: • Starvation is thus predicted to occur when: where:

38. Preliminary Throughput Validations: Setup I • 802.11b with long preamble and without RTS/CTS • Poisson distributed traffic – 1024B packets

39. 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

40. Preliminary Throughput Validation: The non-saturation analysis

41. Preliminary Throughput Validation: The starvation predictions

42. Fixed number of nodes (n=5)

43. A higher AIFS value translates into a lower average countdown rate The effect of AIFS differentiation during countdown Slots that AC[3] can use for countdown AC[3]’s perspective: Packet Packet AC[0]’s perspective: Packet Packet Slots that AC[0] can use for countdown

44. AIFS differentiation leads to starvation at high traffic loads Medium Access Starvation Slots that AC[3] can use for countdown AC[3]’s perspective: Packet Packet Packet AC[0]’s perspective: Packet Packet Packet No slots for AC[0]’s countdown

45. How to incorporate this effect into the analytical model? AIFSN[0] Packet Packet Ai = AIFSN[i] - AIFSN[0] (i.e. defined such that always A0 = 0) unblocked empty slots one busy slot Packet Packet Ai blocked slots