1. WiFi Models EE 228A Lecture 5 Teresa Tung and Jean Walrand
Department of EECS
University of California at Berkeley

2. Overview: Contents WiFi models via an example of QoS over 802.11
DCF
Extension for e EDCF

3. Overview: Scenario 802.11 Network What is the throughput?
Can we provide QoS? D1 S1 A1
5.5 Mbps … Am Sm Dm
2 Mbps AP V1 H1 H1
11 Mbps … Vn Hn Hn
5.5 Mbps

4. Overview: 802.11 MAC Point Coordination Function (PCF)
Not implemented
Simple to analyze TDMA
Distributed Coordination Function (DCF)
Implemented
More difficult to analyze CSMA/CA
Ex: b (11 Mbps)
Data only: 6 Mbps
VoIP: 12 connections  64 kbps/direction  1.5 Mbps

5. Overview: DCF review … … S1 Sm AP H1 Hn D1 A1 5.5 Mbps Am Dm 2 Mbps V1Vn Hn Hn
5.5 Mbps V1
V’n V1 A1 Dm Dm

6. VoIP only … Hope to send V1,V2,…,Vn in 20 ms
Time depends on n and rates
Given rates, there is a maximum n feasible V1 H1 H1
11 Mbps AP … Vn Hn Hn
5.5 Mbps … V1
V’2 V1 Vn
V’1

7. QoS criterion: ave delay < 20 ms
VoIP only: approach
Observation: Bottleneck at the AP
# voice connections
Bianchi’s model
M/G/1 model at the AP
QoS criterion: ave delay < 20 ms
Pr(AP senses channel busy)
E[transmission delay]
Call capacity

8. Bianchi model Discrete model with variable slot size Idle slot
Success = VoIP + SIFS + ACK + DIFS
Collision = VoIP + EIFS
VoIP = (RTP + UDP + IP + MAC + payload)/rate

9. Bianchi: 802.11b Markov chain16 32

10. Bianchi: simplification
Markov chains coupled
Ex: 2 stations state (CW1,m1,CW2,m2)
c1 = 1 –  i 1 (1 – pi) pn p2 … 1 p1
Simplification: Assume independence 1 2

11. Bianchi: background N2 N1 A C B
Circuit switched networks [Erlang fixed point]
Pr(A blocked) depends on (#A,#B,#C)
Simplification: Assume each call blocked independently by different links
Ex: Arrival rate at 1: 1 = A (1 – b2) + B
Pr(blocked at 1): b1 = (N1) M/M/1/N1
Packet switched network [Kleinrock independence approximation]: M/M/1 queuing model
Interacting particle systems [Gibbs] N2 N1 A C B
Not independent, capacity at 2 dependent on whether 1 blocks A
Actual blocking probability for A is the fraction of time in all states (#A,#B,#C) that result in busy for adding a new flow A
Kleinrock: We know from the special case of two tandem queues that even if the packet streams are Poisson with independent packet lengths at their point of entry into the network, this property is lost after the first transmission line. To resolve the dilemma, it was suggested by Kleinrock that merging several packet streams on a transmission line has an effect akin to restoring the independence of interarrival time and packet lengths. It was concluded that it is often appropriate to adopt an M/M/1 queueing model for each communication link regardless of the interaction of traffic on this link with traffic on other links. This is known as Kleinrock independence approximation and seems to be a reasonably good approximation for systems involving Poisson stream arrivals at the entry points, packet lengths that are nearly exponentially distributed, a densely connected network and moderate-to-heavy traffic load.

12. Find fixed point solution (e.g. voice only)
Bianchi: fixed point
Node n
Find fixed point solution (e.g. voice only)
Markov chain

13. M/G/1 review
Little’s formula: The average number of customers in a stable system (over some time interval) is equal to their average arrival rate, multiplied by their average time in the system

14. 802.11: Comparison with ns-2
802.11b network, G.711 codec (160 byte/D)

15. 802.11: results Maximize throughput by
Limiting the number of contending stations
Using large packet payload
Not suitable for VoIP

16. 802.11e: EDCF review Voice has edge over data (waits less)
Chooses random back-off from smaller interval
Waits less time after busy period to operate
AIFS V = DIFS
AIFS D = AIFS V + 2 IDLE
However, may still be pre-empted by data
AIFS V
Backoff V V1 D1
AIFS D
Backoff D
AIFS D
Backoff D

17. 802.11e: approach Classify slots by two types
Type A
AIFS D = AIFS V + 2 IDLE
Type B 1
Classify slots by two types
A reserved for VoIP transmissions
B for all types of transmissions
Changes fixed point equations
e.g. AP

18. 802.11e results
Cannot guarantee service
Ex.

19. Why 802.11e is not enough Not enough transmission attempts for VoIP
AP admits too many data packets

20. Enabling QoS over WiFi Ideal solution: PCF
Requires changes of AP and wireless clients
DCF solution using existing WiFi clients
Requires changes at the AP
Estimate capacity
Admission control for VoIP and video
Traffic shaping for TCP
PCF on downlink via NAV vector

21. References
G. Bianchi, “Performance analysis of the IEEE distributed coordination function,” IEEE J. Select Areas Communications, vol. 18, no. 3, pp , 2000.
N. Hedge, A. Proutiere, and J. Roberts, “Evaluating the voice capacity of WLAN under distributed control,” Proc. LANMAN, 2005.