1. Congestion Control and AQM
Congestion Control, Efficiency and Fairness
Analysis of TCP Congestion Control
A simple TCP throughput formula
RED and Active Queue Management
How RED works
Other AQM mechanisms
TCP and ECN
Readings: please do required!
And optional readings if interested
CSci5221: congestion control and AQM

2. Why Congestion Control
Inefficiency and Congestion Collapse
“self-interest” vs. “social welfare”
Inefficiency: a simple “artificial” example s1 s2 x y d1 d2
C3 =110kb/s
C4 =100kb/s
C5 =10kb/s
C1 =100kb/s
C2 =1000kb/s
source 1 rate
l1 =100kb/s
source 2 rate
l2 =1000kb/s
source 1 throughput
m1 =10kb/s !
source 2 throughput
m2 =10kb/s
Assumption: when total offered traffic exceeds link capacity, all sources see their traffic reduced in proportion of their offered traffic (e.g., when FIFO is used)
CSci5221: congestion control and AQM

3. Why Congestion Control (cont’d)
Congestion Collapse: another “artificial” example
link i+1
link i-1
node i
node i+1
source i
link i
Each source i traverses two links:
link i and link i+1
source i input rate li
actual rate on link i:
CSci5221: congestion control and AQM

4. CSci5221: congestion control and AQM
Fairness
Consider a simple scenario:
N users want to transit data over a link of bandwidth C
Each user i wants ri bandwidth
If ri <C, no problem!
But if ri >C, what should we do?
Suppose all users are of equal “importance”:
To be fair, allocate the same share, C/N, to each user
Ok, if ri > C/N; what if there exists ri, ri < C/N
i.e., some users want less than that their “fair share”
how do we allocate the “residue” bandwidth of these users?
the “Fair Queuing” algorithm: WFQ where wi =1 for all i’s
If not all users are equal: importance denoted by wi
weighted fair queueing
CSci5221: congestion control and AQM

5. CSci5221: congestion control and AQM
Max-Min Fairness
Network scenario: A simple line network example
First, maximize thruput at each router/link (or total network thruput) may lead to unfair bw allocation
How to allocate bw fairly?
let x ij be a “feasible” bw share of user i at link j
Bw allocation to user i: xi = minj xij
Ideally, we want to max xi =max minj xij , for all users
Max-min fairness:
Let {xj} be a bw allocation vector (bav), it is max-min fair if
for any other bav y, if yi > xi, then there exists j, xj <= xi and yj < xj
Unfortunately, such max-min fair bav may not always exist!
user 0
user i
link i bw Ci
CSci5221: congestion control and AQM

6. CSci5221: congestion control and AQM
Fairness (cont’d)
(Abstract) Network model: S sources and L links (cl)
Al,s (routing matrix): fraction of traffic of source s on link l
feasible (rate) allocation:
formal def of “bottleneck” link (with respect to source s)
Some Facts (Theorems)
A feasible rate allocation is max-min fair if and only if every source has a bottleneck link
Under network model and assuming routing matrix fixed, there exists a unique max-min fair allocation !
Fair Queueing implements max-min fairness
Other definitions of fairness (optional material!)
proportional fairness: there exists a unique prop. fair allocation!
utility approach to fairness:
“utility-fair”:
CSci5221: congestion control and AQM

7. TCP Congestion Control Behavior
TCP runs at end-hosts
congestion control:
decrease sending rate when loss detected, increase when no loss
routers
discard, (or mark packets if ECN is available),
when congestion occurs
interaction between end systems (TCP) and routers?
want to understand (quantify) this interaction
congested router drops packets
CSci5221: congestion control and AQM

8. Generic TCP CC Behavior: Additive Increase
Congestion Window Adaption Algorithm (window W )
up to W packets in network
return of ACK allows sender to send another packet
cumulative ACKS
increase window by one per RTT
W:= W +1/W per ACK
=> W :=W +1 per RTT
seeks available network bandwidth
Ignoring the “slow start” phase during which window increased by one per ACK
W := W +1 per ACK
=> W :=2W per RTT
CSci5221: congestion control and AQM

9. CSci5221: congestion control and AQM
receiver W
sender
CSci5221: congestion control and AQM

10. Generic TCP CC Behavior: Multiplicative Decrease
Congestion Window Adaption Algorithm (window W)
increase window by one per RTT
W :=W +1/W per ACK
Packet loss: indication of congestion
Upon receiving triple duplicate ACKs,
decrease window by half, W :=W/2
CSci5221: congestion control and AQM

11. CSci5221: congestion control and AQM
receiver TD
sender
CSci5221: congestion control and AQM

12. Generic TCP CC Behavior: After Time-Out (TO)
Congestion Window Adaption Algorithm (window W)
increase window by one per RTT
W :=W +1/W per ACK
halve window on detection of loss (triple duplicate ACKs): W := W/2
timeouts due to lack of ACKs:
window reduced to one, W :=1
CSci5221: congestion control and AQM

13. CSci5221: congestion control and AQM
receiver
sender TO
CSci5221: congestion control and AQM

14. Generic TCP Behavior: Summary
Congestion Window Adaption Algorithm (window W)
increase window by one per RTT (or one over window per ACK, W :=W +1/W)
halve window on detection of loss (triple duplicate ACKs), W :=W/2
timeouts due to lack of ACKs, W:= 1
successive timeout intervals grow exponentially long up to six times
CSci5221: congestion control and AQM

15. Understanding TCP Behavior
can simulate (ns-2)
+ faithful to operation of TCP
- expensive, time consuming
deterministic approximations
+ quick
- ignore some TCP details, steady state
fluid models
+ transient behavior
- ignore some TCP details
CSci5221: congestion control and AQM

16. TCP Throughput/Loss Relationship
loss occurs
Idealized model:
W is maximum supportable window size (then loss occurs)
TCP window starts at W/2 grows to W, then halves, then grows to W, then halves…
one window worth of packets each RTT
to find: throughput as function of loss, RTT W
TCP
window
size
W/2
time (rtt)
CSci5221: congestion control and AQM

17. TCP Throughput/Loss Relationship
# packets sent per “period” = W
TCP
window
size
W/2
period
time (rtt)
CSci5221: congestion control and AQM

18. TCP Throughput/Loss Relationship
# packets sent per “period” = W
TCP
window
size
W/2
period
time (rtt)
CSci5221: congestion control and AQM

19. TCP Throughput/Loss Relationship
# packets sent per “period”
1 packet lost per “period” implies:
ploss
or: W
TCP
window
size
W/2
period
B throughput formula can be extended
to model timeouts and slow start [PFTK’98]
(see slide 59 for details)
time (rtt)
CSci5221: congestion control and AQM

20. Drawbacks of FIFO with Tail-drop
Sometimes too late a signal to end system about network congestion
in particular, when RTT is large
Buffer lock out by misbehaving flows
Synchronizing effect for multiple TCP flows
Burst or multiple consecutive packet drops
Bad for TCP fast recovery
CSci5221: congestion control and AQM

21. FIFO Router with Two TCP Sessions
CSci5221: congestion control and AQM

22. Active Queue Management
Dropping/marking packets depends on average queue length -> p = p(x)
Advantages:
signal end systems earlier
absorb burst better
avoids synchronization
Examples:
RED
REM …
tmin
tmax
pmax 1
2tmax
Marking probability p
average queue length x
CSci5221: congestion control and AQM

23. CSci5221: congestion control and AQM
RED: Parameters
min_th – minimum threshold
max_th – maximum threshold
avg_len – average queue length
avg_len = (1-w)*avg_len + w*sample_len
Discard Probability 1
min_th
max_th
queue_len
Average
Queue Length
CSci5221: congestion control and AQM

24. RED: Packet Dropping If (avg_len < min_th)  enqueue packet
If (avg_len > max_th)  drop packet
If (avg_len >= min_th and avg_len < max_th)  enqueue packet with probability P
Discard Probability (P) 1
min_th
max_th
queue_len
Average
Queue Length
CSci5221: congestion control and AQM

25. RED: Packet Dropping (cont’d)
P = max_P*(avg_len – min_th)/(max_th – min_th)
Improvements to spread the drops
P’ = P/(1 – count*P), where
count – how many packets were consecutively enqueued since last drop
Discard Probability
Average
Queue Length 1
min_th
max_th
queue_len
avg_len P
max_P
CSci5221: congestion control and AQM

26. RED Router with Two TCP Sessions
CSci5221: congestion control and AQM

27. CSci5221: congestion control and AQM
Issues with RED
Parameter sensitivity
how to set minth, maxth, and maxp
Goal: maintain avg. queue size below midpoint between min_{th} and max_{th}
maxth needs to be significantly smaller than max. queue size to absorb transient peaks
maxp determines drop rate
In reality, hard to set these parameters
RED uses avg. queue length, may introduce large feedback delay, lead to instability
CSci5221: congestion control and AQM

28. CSci5221: congestion control and AQM
Other AQM Mechanisms
Adaptive RED (ARED)
BLUE
Virtual Queue
Random Early Discard (REM)
Proportional Integral Controller
Adaptive Virtual Queue
Improved AQMs are designed based on control theory to provide better faster response to congestion and more stable systems
CSci5221: congestion control and AQM

29. Explicit Congestion Notification (ECN)
Standard TCP:
Losses needed to detect congestion
Wasteful and unnecessary
ECN (RFC 3168):
Routers mark packets instead of dropping them
Receiver returns marks to sender in ACK packets
Sender adjusts its window accordingly
Need to make “changes” to both IP and TCP headers
two bits (ECT and CE bits) in the IP header (“TOS” field)
two bits (CWR and ECE) bits in TCP header (two unused “reserved” bits in the standard TCP header)
assume cooperation of sender/receiver and routers
CSci5221: congestion control and AQM

30. TCP with ECN: How It Works
Use of ECT and CE bits (in “TOS” field) in the IP header
ECT CE
non-ECT capable (set by sender)
ECT(1), endpoints ECT-capable (set by sender)
ECT(0), endpoints ECT-capable (set by sender)
CE, set by routers indicating congestion!
Use of in CWR and ECE in the TCP header
Receiver: if CE, set ECE (explicit congestion echo) bit in ACK
What about receiver cheating?! See RFC 3540
Sender: sets CWR in next data packet to ack receipt of ECE!
why does sender needs to indicate receipt of ECE-set ACK?
During TCP set-up, sender and receiver negotiate ECT
If using ECT, sender sets both CWR and ECE in the SYN packet
receiver sets ECE (but not CWR), if also ECT-capable
CSci5221: congestion control and AQM

31. Generalization of TCP AIMD
AIMD in Standard TCP:
If no packet lost during the round,
CongWin: = CongWin +1;
If packet losses encountered during the round,
CongWin: = CongWin/2
Generalization of AIMD
CongWin: = CongWin + \alpha;
CongWin: = CongWin/\beta
where \alpha (>=1) and \beta (>1)
CSci5221: congestion control and AQM

32. Other Issues/Extension of TCP
When most flows are “short” (i.e., consist of 1 or few packets), TCP slow start cannot ramp up fast enough to the available bw
persistent TCP connections
TCP splitting via “TCP proxies”, etc.
TCP and congestion issues in data centers
e.g., the “TCP incast” problem which may cause throughput collapse!
Multi-path TCP (mTCP): esp. useful in data centers
TCP under large delay-bandwidth product
e.g., XCP: eXplicit congestion Control Protocol (a “research” protocol – optional material follows!)
CSci5221: congestion control and AQM