Buffer size of router

Data buffer

 

Buffers are typically used when there is a difference between the rate at which data is received and the
rate at which it can be processed, or in the case that these rates are variable.
A buffer often adjusts timing by implementing a queue algorithm in memory, simultaneously writing
data into the queue at one rate and reading it at another rate.

 

Bufferbloat

 

Bufferbloat is a phenomenon in a packet-switched computer network whereby excess buffering of packets
inside the network causes high latency and jitter, as well as reducing the overall network throughput.
This problem is caused mainly by router and switch manufactures making incorrect assumptions and
buffering packets for too long in cases where they should be dropped.
On older routers, buffers were fairly small so they filled quickly and therefore pakcets began to drop shortly
after the link became saturated.

 

High-Speed Routers

 

Loss can be reduced by making buffers large enough.
jitter：fluctuation in buffer size.
The buffer size in core Internet routers is typically chosen according to a rule of thumb which says:
provide at least one round trip time's worth of buffering.
Recent theoretical work has challenged the rule of thumb: it seems that a buffer of just 20 packets
should be sufficient.
The buffer in an Internet router has serveral roles. It accommodates transient bursts in traffic,
without having to drop packets. It keeps a reserve of packets, so that the link doesn't go idle.
It also introduces queueing delay and jitter.
The network model comprises two parts: one part describing the dynamics of TCP, another
describing the dynamics of the queue. [1]

 

Optimal choice of the buffer size

 

Data packets of an Internet connection travel from a source node to a destination node via a
series of routers. Some routers, particularly edge routers, experience periods of congestion
when packets spend a non-negligible time waiting in the router buffers to be transmitted
over the next hop.
Congestion signals can be either packet losses or Explicit Congestion Notifications.
At the present state of the Internet, nearly all congestion signals are generated by packet losses.
Packets can be dropped either when the router buffer is full or when Active Queue Management
(AQM) scheme is employed. Given an ambiguity in the choice of the AQM parameters, so far
AQM is rarely used in practice. On the other hand, in the basic Drop Tail routers, the buffer size
is the only one parameter to tune apart of the router capacity.
The first proposed rule of thumb for the choice of the router buffer size was to choose the buffer
size equal to the Bandwidth-Delay Product (BDP) of the outgoing link.
It was observed that the utilization of a link improves very fast with the increase of the buffer size
until a certain threshold value. After that threshold value the further increase of the buffer size
does not improve the link utilization but increases the queueing delay. [2]

 

Sizing Router Buffer

 

A link with n flows requires no more than ：

for long-lived or short lived TCP flows.
The consequences on router design are enormous: a 2.5Gbps link carrying 10,000 flows
could reduce its buffer by 99% with negligible difference in throughput, and a 10Gbps link
carrying 50000 flows requires only 10Mbits of  buffering, which can easily be implemented
using fast, on-chip SRAM.
If these buffers fill up, they cause queueing delay and delay-variance; when they overflow they
cause packet loss, and when they underflow they can degrade throughput.
Router buffers are sized today based on a rule-of-thumb commonly attributed to a 1994 paper
by Villamizar and Song. Network operators follow the rule-of-thumb and require that router
manufacturers provide 250ms (or more) of buffering.

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按照rule-of-thumb：

a 10Gbps router linecard  needs buffers — 20万个包，300MB
a 1Gbps router linecard needs buffers — 2万个包，30MB
a 100Mbps router linecard needs buffers — 2千个包，3MB

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Today（2005）backbone links commonly operate at 2.5Gbps or 10Gbps and carry over
10000 flows. We believe that significantly smaller buffers could be used in backbone routers
(e.g., by removing 99% of the buffers) without a loss in network utilization.
With declining memory prices, why not just overbuffer routers ?
First, it complicates the design of high-speed routers, leading to higher power consumption,
more board space, and low density. Second, overbuffering increases end-to-end delay in the
presence of congestion. Large buffers conflict with the low-latency needs of real time application. 

中心极限定理：设从均值为u、方差为Q^2的任意一个总体中抽取样本量为n的样本，当n充分大时，
样本均值的抽样分布近似服从均值为u、方差为Q^2/n的正太分布。 

We know from the central limit theorem that the aggregate window size does converge to a
Gaussian process.

The graph above shows the probability distribution of the sum of the congestion windows of all
flows, with different propagation times and start times.
How does the shape of the Gaussian, and thus our buffer, depend on the number of flows?
If we have more flows, we would expect more statistical multiplexing and thus a narrower
Gaussian. In fact, the central limit theorem tells us that if we increase the number of flows n,
the width of the Gaussian (or, more formally, its standard deviation) should decrease with

The role of the buffer is to absorb the fluctuation in the total window size. If the standard deviation
of the total window size decrease with 1/ root(n), we would expect the required amount of buffer
to do the same.

For short flows — the size of the buffer does not depend on the line-rate, the propagation delay of
the flows, or the number of flows; it only depends on the load of the link, and length of the bursts.

Our model predicts that for 98% utilization a buffer of RTT * C / sqrt(n) should be sufficient.
Decreasing the latency of a TCP flow will always increase the loss rate.The loss rate of a TCP flow
is a function of the flow's window size and can be approximated to l = 0.76/w^2. If we reduce buffers,
we decrease the RTT of the flow, therefore decrease the average W and thus increase loss.

 

Rule-of-thumb

 

The rule of thumb for buffer sizing derives from the following goal: If capacity is limited, it's
desirable to make sure the link never goes idle. Therefore there should always be some
packets in the buffer. By reasoning about how TCP responds to loss, we can work out how
big the buffer needs to be.
The buffer needs to be at least Wmax/2 to avoid going empty during the pause. The key to
sizing the buffer is to make sure that while the sender pauses, the router buffer doesn't go
empty and force the bottleneck link to go idle.(原来链路是满的，在流出Wmax/2的数据后，
路由器至少需要补充Wmax/2的数据量，才能保持链路被完全利用) It turns out that this is equal
to the distance (in bytes) between the peak and trough of the "sawtooth" representing the TCP
window size.
Bursts from short flows do have an effect. However it is very small, and that the buffer size is,
in fact, dictated by the number of long flows.
If the buffer never goes empty, the router must be sending packets onto the bottleneck link at
constant rate C. This in turn means that ACKs arrive to the sender at rate C. The sender therefore
pauses for exactly (Wmax/2)/C seconds for the Wmax/2 packets to be acknowledged. It then resumes
sending, and starts increasing its window size again.
The buffer will just avoid going empty if the first packet from the sender shows up at the buffer just as
it hits empty, i.e., (Wmax/2)/C <= B/C or B >= Wmax/2

 

拥塞阈值

 

当diff >= beta时，我们判断路由器拥塞。
在vegas中，beta=5。
在veno中，beta=3。
A 2.5Gbps link typically carries over 10000 flows at a time.
Network operators follow the rule-of-thumb and require that router
manufacturers provide 250ms (or more) of buffering. [3]
所以对于一条2.5Gbps的链路，它的路由器缓存大小大概为5万个数据包，75MB。
因为在链路上大约有1万条连接，所以当路由器发生拥塞时，每条连接平均占用路由器缓存为：5个包。
当然，由于Internet上的tcp连接不是同步的，所以在发生拥塞时beta的取值还有待研究。

 

Synchronization

 

Flows are not synchronized in a backbone router carrying thousands of flows with varying RTTs.
Small variations in RTT or processing time are sufficient to prevent synchronization; and the absence
of synchronization has been demonstrated in real networks.Likewise, we found in our simulations
and experiments that while in-phase synchronization is common for under 100 concurrent flows,
it is very rare above 500 concurrent flows.

 

Reference

 

[1]《Buffer Requirements for High-Speed Routers》
[2]《Optimal Choice of the Buffer Size in the Internet Routers》
[3]《Recent Result on Sizing Router Buffers》