1. Open Problems in the Design of Distributed Algorithms for Wireless Networks
R. Srikant
CSL & ECE
University of Illinois at Urbana-Champaign
(based on discussions with Bin Li and Ning Lu)

2. Scheduling Algorithms: An Example
Web Server
client 1
client 2
“Get Page”
“Get Video”
client 1000
“Get Audio”
Internet
Scheduling Algorithm: Server has to decide how much service to provide to each request in each time slot
Wireline (e.g., web server): the amount of available service in each time slot is constant

3. Scheduling Example client 1
Web Server
client 1
client 2
“Get Page”
“Get Video”
client 1000
“Get Audio”
Wireless Network
Scheduling Algorithm: Server has to decide how much service to provide to each request in each time slot
Wireless: available service is time-varying due to channel variations

4. Outline of this Talk
Consider three widely studied scheduling algorithms: Round Robin, Earliest Deadline First, and Shortest-Remaining-Time-First
Discuss wireless analogues of these scheduling algorithms, and their limitations
Open Problems
Web Server
client 1
client 2
“Get Page”
“Get Video”
client 1000
“Get Audio”
Wireless Network

5. Short-Term Fairness: Round Robin

6. Round-Robin Scheduling
Flows (file requests) in the system are served in a cyclic, or round-robin order
Each flow gets the same amount of service when it is served
server

7. Round-Robin Scheduling
Flows in the system are served in a cyclic, or round-robin order
One packet from each flow is served, during each service instant
server

8. Round-Robin Scheduling
Flows in the system are served in a cyclic, or round-robin order
One packet from each flow is served, during each service instant
server

9. Properties of Round-Robin Scheduling
Fairness
If there are n flows in the system, each of them is served at rate 1 𝑛
Maximum Throughput
The server is always working, thus no other algorithm can do better
Insensitivity
Mean response time (delay) of a request depends only on the mean of the file-size distribution
Non-trivial, follows from studying the relationships between a Markov chain and its reversed version (Kelly, 1979; Ross, 1996; and Gallager, 2013)
Does there exist a scheduling algorithm that has these three desirable properties in wireless networks?

10. Wireless Fading
ON-OFF fading: the channel rates for each user are i.i.d. over time with Bernoulli distribution
General fading: different channel rates for different users and follows a general distribution.

11. Round Robin in Cellular Networks
mobile 1
mobile 2
flow 1
flow 2
Consider a downlink cellular network with two mobiles
Each mobile has independent ON- OFF channels
Assume that the transmitter knows the channel states at the beginning of each time slot
RR serves ON channels in cyclic order

12. More General Channel Models
The channel states may not just be ON and OFF
In each time slot, the number of bits transmitted over the channel varies
The channels can have widely different statistics
One cannot generalize round robin by simply skipping a transmission when a channel is OFF
mobile 1
mobile 2
flow 1
flow 2

13. A Commonly Used Algorithm
Let 𝑥 𝑖 be the throughput available to mobile 𝑖 at a time instant.
Let 𝑥 𝑖 be the average throughput realized so far
Scheduling Algorithm (Tse, 1996): Transmit to the user which solves
max 𝑖 𝑥 𝑖 𝑥 𝑖
mobile 1
mobile 2
flow 1
flow 2

14. Achieves Proportional Fairness
The previous algorithm achieves proportional fairness
Gives different throughputs for different 𝑤 𝑖 ′ 𝑠
Fairness is achieved asymptotically
But, fixed throughput per user: not adaptive
mobile 1
mobile 2
flow 1
flow 2
max 𝑖=1 𝑁 𝑤 𝑖 log 𝑥 𝑖

15. Adaptive Throughput Maximization: MaxWeight Scheduling
At each time t, serve mobile 𝑖 ∗ such that
It achieves maximum throughput when the number of mobiles is fixed (Tassiulas-Ephremides, 1992)
mobile 1
mobile 2
flow 1
flow 2
𝑖 ∗ ∈ arg max i 𝑞 𝑖 𝑡 𝑐 𝑖 (𝑡)

16. Deficiency of MaxWeight Scheduling
In the presence of dynamic mobiles, it is not even throughput optimal
An example (Borst & van de Ven, 2009):
Flows arrives arrive according to a Bernoulli process with probability λ having an arrival
All flows have the same size of 3
The channel rate of each flow is either 2 with prob. 𝑝, or 3 with prob. 1−𝑝
What is the throughput of this algorithm under these conditions?

17. Deficiency of MaxWeight Scheduling
Key observation: MaxWeight always serves newly arriving flows.
A newly arrived flow has 3 packets: so its weight is 4 or 6
An existing flow has at most one packet, so its weight is 2 or 3
So a flow is either served in one time slot, or it requires an additional time slot with probability 𝑝
So the throughput of this algorithm is 𝜆 1+𝑝 1+𝑝 <1
Channel can serve 2 packets with probability p or 3 packets with probability 1-p

18. An Alternative Policy
Always serve the flow with the maximum channel rate
When the number of waiting flows is large, there is at least one channel which can serve 3 packets
So a flow (which has 3 packets in this example) can be served in one time slot
So max throughput is 𝜆<1
But not insensitive

19. Wireless Ad Hoc Networks: Interference
Wireless interference
A subset of users can be served at each time
Interference models
Link contention-based model
SNR-based model
(SINR: signal-to-interference-and- noise ratio)

20. Wireless Ad Hoc Networks
Wireless interference
A subset of users can be served at each time
Interference models
Link contention-based model
SINR-based model
(SINR: signal-to-interference-and- noise ratio)

21. Distributed Solution Assuming No Fading
Flow-aware CSMA algorithm (Bonald and Feuillet, 2010)
Each flow generates an exponentially distributed timer with mean 1
Start transmission after backoff timer expires if it does not sense any transmission
Suspend its backoff timer, otherwise, and resume the backoff after the completion of transmission
One transmission per region; neighboring regions interfere with each other

22. Distributed Solution Assuming No Fading
Flow-aware CSMA algorithm (Bonald and Feuillet, 2010)
Achieves maximum throughput: Why? Because the mean backoff time in each region is the inverse of the number of flows in that region
Thus, more heavily backlogged regions get more priority: similar to MaxWeight
But fails in the presence of wireless fading
One transmission per region; neighboring regions interfere with each other

23. Open Problems in Wireless Ad Hoc Networks
Develop a robust scheduling algorithm that achieves
Maximum throughput
Fairness
Insensitivity
Our model for fading is an abstraction:
Power control, modulation schemes, multiple antennas, multiple channels, etc.?
Distributed Implementation
Known with interference only
But not with fading

24. Enforcing Deadlines: EDF

25. Real-time Application
Vehicle platooning on highway
Timely information delivery (position, speed, deceleration, etc.)
Violating the time limitations beyond certain thresholds is unacceptable
Scheduling real-time traffic over wireless links is an important task to provide quality of service (QoS) guarantees for mission-critical systems. Consider the scenario where vehicles are platooning on highways. Vehicles in each platoon exchange up-to-date driving status (i.e., position, speed, deceleration, etc.) wirelessly to maintain a small inter-vehicle distances for fuel economy. The data of driving status needs to be delivered in a timely manner, otherwise the data becomes outdated, which could lead to disturbance in the platooning system.

26. Handling Deadlines in Wireline Networks
Deadline associated with each packet
Earliest Deadline First (EDF) Scheduling
Priority-based scheduling
Highest priority gives to the packet with the earliest deadline
When job sizes are variable, and interruptions are allowed, then it produces a feasible schedule if one exists
Stronger guarantees for fixed job sizes 9 5
Packet arrivals 10
Server 2 3
Packets missing the deadline are discarded

27. EDF May Not be Optimal for Wireless Networks
Link 1
Key Issue: Interference
In this example, if link 2 transmits, other two links must remain silent
In general, there exists a tradeoff between transmitting multiple packets versus choosing one with the smallest deadline
Link 2
Link 3

28. A More Modest Goal: A Frame-based Framework
Consider an ad hoc network consisting of 𝑙 links
Time is divided into frames of 𝑇 slots each (Hou, Borkar, Kumar, 2009)
QoS (Quality-of-Service) requirement for link 𝑙: fraction of packets lost due to deadline expiry has to be less than or equal to 𝑝 𝑙
Frame
…….. 1 2 T
Packets not served by the end of the frame are lost
All arrivals occur here

29. Schedule for Each Frame
In each time slot, select a set of links to be ON, while satisfying interference constraints
Thus, a schedule is an fffffffmatrix of 1s and 0s
Time Slot 1
Time Slot 2 .
Time Slot T
Link 1 1
(ON)
Link 2
0 (OFF)
Link L
Problem: Find a schedule in each frame such that the QoS constraints are satisfied for each link

30. Deficit Counter Upon each packet Remove a token arrival to link ,
add a token to
this counter with
prob.
Remove a token
from the counter
every time a packet
is transmitted
Deficit counter:
Keeps track of deficit in QoS

31. Schedule for Each Frame
Associate a weight equal to the number of tokens in the deficit counter for each link included in the schedule
Pick the schedule with the largest weight
Computationally infeasible
Time Slot 1
Time Slot 2 .
Time Slot T
Link 1 1
(ON)
Link 2
0 (OFF)
Link L
Problem: Find a schedule in each frame such that the QoS constraints are satisfied for each link

32. Distributed Implementation
Existing designs are for special cases
Full Interference
Periodic traffic flow, general interference
Greedy Solution: Add the link with the largest weight to the schedule (Jaramillo, S., Ying, 2011 and Li, Eryilmaz, 2012)
Glauber Dynamics: Instead of finding the MaxWeight schedule, the probability of choosing a schedule is proportional to exp⁡(𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐ℎ𝑒𝑑𝑢𝑙𝑒)
(Lu, Li, S., Ying, 2016)
Frame k
Frame k+2
Frame k+1
Link l
The same number of packet arrivals

33. Glauber dynamics
Let S be a schedule (collection of non-interfering links). Let 𝑙 be another link that doesn’t interfere with 𝑆
The stationary distribution of this Markov chain has the desired exponential form
𝑒 𝑤 𝑙 1

34. Open Problems
Distributed implementation remains open for general cases
General network topology and traffic models
Short-term QoS
Existing algorithms only ensure long-term QoS performance
Short-term guarantee is also important
e.g., Long-term QoS: up to 10% packet dropping rate
Case 1: the first 1000 packets are dropped and the next 9000 packets are delivered, and so on
Case 2: the first packet is dropped, the next 9 packets are delivered, and so on
The same long-term QoS, but prefer case 2 since it has better short-term QoS

35. Minimizing Delays: SRPT

36. Scheduling in a Single Wireline Server
Non-Size-Based Policies
FCFS (First-Come-First-Served, non-preemptive)
PS (Processor-Sharing, preemptive)
LAS (Least Attained Service, preemptive)
Size-Based Policies
SJF (Shortest-Job-First, non-preemptive)
SRPT (Shortest-Remaining-Processing-Time, preemptive)
Load 𝜌<1
Poisson
arrival
process
Large Variance
File size distribution
Which policy has the smallest mean response time?

37. Mean Response Time Comparison
LOW E[T] HIGH E[T]
SRPT < LAS < PS < SJF < FCFS
OPT for all
arrival
sequences
[Schrage 67]
Requires D.F.R.
[Righter,
Shanthikumar89]
Insensitive
to E[X2]
Still bad:
(E[X2] term)
~E[X2]
(shorts caught
behind longs)
Slide from Harchol-Balter’s Notes

38. Fairness of SRPT Fairness: All jobs have the same slowdown
The slowdown of a job is its response time divided by its size
All-can-win-theorem [Bansal, Harchol-Balter, Sigmetrics 2001]
With Poisson arrivals, for all job size distributions, if r < 0.5,
E[T(x)]SRPT < E[T(x)]PS for all job size x.
For heavy-tailed distributions, holds for r < 0.95.

39. Wireless Networks with Dynamic Flows
In the presence of dynamic mobiles, develop a scheduling algorithm that not only achieves maximum throughput but also minimizes mean delay??
Existing work mainly focus on the transient setting where all jobs are available at time 0 and no new jobs arrive thereafter (Sadiq & de Veciana, 2010)

40. Conclusions
What are the equivalent of RR, EDF, SRPT in wireless networks?
Partial progress in each case (but in decreasing order: RR, EDF, SRPT)
Even centralized algorithms with all the desired properties are unknown
When algorithms with certain desirable properties exist, there are still many open questions in the design of their distributed counterparts