1. Wireless Scheduling

2. Puzzle Monty Hall Problem
You are a contestant on a game show. In front of you are three closed doors. The game show host informs you that behind one of these doors is the motor car of your dreams, but behind the other two doors lies a peanut (which you're allergic to anyway!).
The quiz-master asks you to select a door. After you have selected, he then opens one of the other two doors that does not contain the car. He does this every week to build up the suspense for the watching millions. He asks if you would like to open the door you originally selected and take home that prize, or switch to the remaining door and go home with that prize. 
Is it in your best interests to switch, or to remain with your original selection ?

3. Generic Wireless FS Model
Error free service
Lead/lag/in-sync
Compensation model
Channel monitoring and prediction

4. Instantiations Channel state dependent packet scheduling (CSDPS)
Idealized wireless fair queuing (IWFQ)
Wireless packet scheduling (WPS)
Channel-condition independent fair queuing (CIFQ)
CBQ-CSDPS
Server based fairness approach (SBFA)
Wireless fair service (WFS)

5. CSDPS
CSDPS allows for the use of any error-free scheduling discipline – e.g. WRR with WFQ spread
When a flow is allocated a slot and is not able to use it, CSDPS skips that flow and serves the next flow
No measurement of lag or lead
No explicit compensation model

6. CSDPS (Contd.)
Lagging flows can thus make up lags only when leading flows cease to become backlogged or experience lossy channels sometime
No long-term or short-term fairness guarantees

7. IWFQ WFQ is used for the error free service
Packets tagged as in WFQ. Of the flows observing a clean channel, the flow with the minimum service tag packet is served
Tags implicitly capture the service differences between flows (lagging flows will have a smaller service and hence will be scheduled earlier)

8. IWFQ (Contd.)
Channel capture by lagging flows possible resulting in short term unfairness and starvation
Even in-sync flows can become lagging during such capture periods
Coarse short-term fairness guarantees because of possible starvation
Provides long-term fairness

9. WPS WRR with WFQ spread used for error free service
A frame of slot allocations generated by WPS based on WRR (with WFQ spread)
Intra frame swapping attempted when a flow is unable to use a slot
If intra-frame swapping is not possible lag incremented as long as another flow can use the slot

10. WPS (Contd.)
At the beginning of next frame, weights for calculating spread readjusted to accommodate lag and lead
If intra-frame swapping succeeds most of the time, in-sync flows not affected
Complete channel capture prevented as each flow has a non-zero weight when frame spread is calculated
No short-term fairness guarantees, but provides long-term fairness

11. CIFQ STFQ (Start time fair queuing) used for the error free service
Lag or lead computed as the difference between the actual service and the error free service
A backlogged leading flow relinquishes slot with a probability p, a system parameter
A relinquished slot is allocated to the lagging flow with the maximum normalized lag

12. CIFQ (Contd.)
In-sync flows not affected since lagging flows use slots given up by leading flows
Lagging flows can still starve leading flows under pathological scenarios
Provides both short-term and long-term fairness

13. CBQ-CSDPS
Same as IWFQ except that no explicit error free service is maintained
Rather, lead/lag is measured based on the actual number of bytes s transmitting during each time window
A flow with normalized rate r is leading if it has received channel allocation in excess of s*r, and lagging if it has received channel allocation less than s*r
Lagging flows are allowed precedence

14. CBQ-CSDPS
Same problem as in IWFQ – lagging flows given precedence, and hence can capture channel
Short term fairness is thus not guaranteed
Additionally, leads and lags are computed not based on error-free service, but based on a time window of measurement … performance sensitive to the time window

15. SBFA Any error free service model can be used
SBFA reserves a fraction of the channel bandwidth statically for compensation by specifying a virtual compensation flow
When a flow is unable to use a slot, it queues a slot-request to the compensation flow
Scheduler serves compensation flow just as other flows
When the compensation flow gets a slot, it turns the slot over to the flow represented by the head-of-line slot-request

16. SBFA (Contd.) Scheduled to Tx F1 Cannot transmit because of error
Slot queued
into compensation flow
Cannot transmit
because of error
Compensation Flow of weight w
Slot scheduled for
Tx and handed over to F1

17. SBFA (Contd.) No concept of a leading flow
All bounds supported by SBFA are only with respect to the remaining fraction of the channel bandwidth
Performance of SBFA is sensitive to the statically reserved fraction
No short-term fairness
Long-term fairness dependent upon the reserved fraction

18. Wireless Fair Service
Uses an enhanced version of WFQ in order to support delay-bandwidth decoupling
Lag of a flow incremented only if there is a flow that can use the slot
Both lead and lag are bounded by per-flow parameters
A leading flow with a lead of L and a lead bound of Lmax relinquishes a fraction L/Lmax of the slots allocated to it by the error-free service
This results in an exponential reduction in the number of slots relinquished

19. WFS (Contd.) Service degradation is graceful for leading flows
In-sync flows are not affected
Tightest short-term fairness among all algorithms discussed
Compensation for lagging flows can take up more time than other algorithms

20. Recap Wireless Fair Scheduling Why wireline algorithms cannot be used
Key components of a a wireless fair scheduling algorithm
Different approaches for wireless fair scheduling

21. Puzzle Man in a boat floating in a swimming pool 
He has a large solid iron ball
If he drops the ball into the water, what happens to the level of water in the swimming pool? (increases, decreases, stays the same?)