RFC970 - On packet switches with infinite storage

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　　Network Working Group John Nagle
Request for Comments: 970 FACC Palo Alto
December 1985

On Packet Switches With Infinite Storage

Status of this Memo

The purpose of this RFCis to focus discussion on particular problems
in the ARPA-Internet and possible methods of solution. No proposed
solutions in this document are intended as standards for the
ARPA-Internet at this time. Rather, it is hoped that a general
consensus will emerge as to the appropriate solution to such
problems, leading eventually to the adoption of standards.
Distribution of this memo is unlimited.

Abstract

Most prior work on congestion in datagram systems focuses on buffer
management. We find it illuminating to consider the case of a packet
switch with infinite storage. Such a packet switch can never run out
of buffers. It can, however, still become congested. The meaning of
congestion in an infinite-storage system is explored. We demonstrate
the unexpected result that a datagram network with infinite storage,
first-in-first-out queuing, at least two packet switches, and a
finite packet lifetime will, under overload, drop all packets. By
attacking the problem of congestion for the infinite-storage case, we
discover new solutions applicable to switches with finite storage.

Introduction

Packet switching was first introduced in an era when computer data
storage was several orders of magnitude more expensive than it is
today. Strenuous efforts were made in the early days to build packet
switches with the absolute minimum of storage required for operation.
The problem of congestion control was generally considered to be one
of avoiding buffer exhaustion in the packet switches. We take a
different view here. We choose to begin our analysis by assuming the
availablity of infinite memory. This forces us to look at congestion
from a fresh perspective. We no longer worry about when to block or
which packets to discard; instead, we must think about how we want
the system to perform.

Pure datagram systems are especially prone to congestion problems.
The blocking mechanisms provided by virtual circuit systems are
absent. No fully effective solutions to congestion in pure datagram
systems are known. Most existing datagram systems behave badly under
overload. We will show that substantial progress can be made on the

RFC970 December 1985
On Packet Switches With Infinite Storage

congestion control problem even for pure datagram systems when the
problem is defined as determining the order of packet transmission,
rather than the allocation of buffer space.

A Packet Switch with Infinite Storage

Let us begin by describing a simple packet switch with infinite
storage. A switch has incoming and outgoing links. Each link has a
fixed data transfer rate. Not all links need have the same data
rate. Packets arrive on incoming links and are immediately assigned
an outgoing link by some routing mechanism not examined here. Each
outgoing link has a queue. Packets are removed from that queue and
sent on its outgoing link at the data rate for that link. Initially,
we will assume that queues are managed in a first in, first out
manner.

We assume that packets have a finite lifetime. In the DoD IP
protocol, packets have a time-to-live field, which is the number of
seconds remaining until the packet must be discarded as
uninteresting. As the packet travels through the network, this field
is decremented; if it becomes zero, the packet must be discarded.
The initial value for this field is fixed; in the DoD IP protocol,
this value is by default 15.

The time-to-live mechanism prevents queues from growing without
bound; when the queues become sufficiently long, packets will time
out before being sent. This places an upper bound on the total size
of all queues; this bound is determined by the total data rate for
all incoming links and the upper limit on the time-to-live.

However, this does not eliminate congestion. Let us see why.

Consider a simple node, with one incoming link and one outgoing link.
Assume that the packet arrival rate at a node exceeds the departure
rate. The queue length for the outgoing link will then grow until
the transit time through the queue exceeds the time-to-live of the
incoming packets. At this point, as the process serving the outgoing
link removes packets from the queue, it will sometimes find a packet
whose time-to-live field has been decremented to zero. In such a
case, it will discard that packet and will try again with the next
packet on the queue. Packets with nonzero time-to-live fields will
be transmitted on the outgoing link.

The packets that do get transmitted have nonzero time-to- live
values. But once the steady state under overload has been reached,
these values will be small, since the packet will have been on the
queue for slightly less than the maximum time-to-live. In fact, if

RFC970 December 1985
On Packet Switches With Infinite Storage

the departure rate is greater than one per time-to-live unit, the
time-to-live of any forwarded packet will be exactly one. This
follows from the observation that if more than one packet is sent per
time-to-live unit, consecutive packets on the queue will have
time-to-live values that differ by no more than 1. Thus, as the
component of the packet switch that removes packets from the queue
and either sends them or discards them as expired operates, it will
either find packets with negative or zero time to live values (which
it will discard) or packets with values of 1, which it will send.

So, clearly enough, at the next node of the packet switching system,
the arriving packets will all have time-to-live values of 1. Since
we always decrement the time-to-live value by at least 1 in each
node, to guarantee that the time-to-live value decreases as the
packet travels through the network, we will in this case decrement it
to zero for each incoming packet and will then discard that packet.

We have thus shown that a datagram network with infinite storage,
first-in-first-out queuing, and a finite packet lifetime will, under
overload, drop all packets. This is a rather unexpected result. But
it is quite real. It is not an artifact of the infinite-buffer
assumption. The problem still occurs in networks with finite
storage, but the effects are less clearly seen. Datagram networks
are known to behave badly under overload, but analysis of this
behavior has been lacking. In the infinite-buffer case, the analysis
is quite simple, as we have shown, and we obtain considerable insight
into the problem.

One would expect this phenomenon to have been discovered previously.
But previous work on congestion control in packet switching systems
almost invariably focuses on buffer management. Analysis of the
infinite buffer case is apparently unique with this writer.

This result is directly applicable to networks with finite resources.
The storage required to implement a switch that can never run out of
buffers turns out to be quite reasonable. Let us consider a pure
datagram switch for an ARPANET-like network. For the case of a
packet switch with four 56Kb links, and an upper bound on the
time-to-live of 15 seconds, the maximum buffer space that could ever
be required is 420K bytes <1>. A switch provided with this rather
modest amount of memory need never drop a packet due to buffer
exhaustion.

This problem is not just theoretical. We have demonstrated it
experimentally on our own network, using a supermini with several
megabytes of memory as a switch. We now have experimental evidence
that the phenomenon described above occurs in practice. Our first

RFC970 December 1985
On Packet Switches With Infinite Storage

experiment, using an Ethernet on one side of the switch and a 9600
baud line on the other, resulted in 916 IP datagrams queued in the
switch at peak. However, we were applying the load over a TCP
transport connection, and the transport connection timed out due to
excessive round trip time before the queue reached the time to live
limit, so we did not actually reach the stable state with the queue
at the maximum length as predicted by our analysis above. It is
interesting that we can force this condition from the position of a
user application atop the transport layer (TCP), and this deserves
further analysis.

Interaction with Transport Protocols

We have thus far assumed packet sources that emit packets at a fixed
rate. This is a valid model for certain sources such as packet voice
systems. Systems that use transport protocols of the ISO TP4 or DoD
TCP class, however, ought to be better behaved. The key point is
that transport protocols used in datagram systems should behave in
such a way as to not overload the network, even where the network has
no means of keeping them from doing so. This is quite possible. In
a previous paper by this writer [1], the behavior of the TCP
transport protocol over a congested network is explored. We have
shown that a badly behaved transport protocol implementation can
cause serious harm to a datagram network, and discussed how such an
implementation ought to behave. In that paper we offered some
specific guidance on how to implement a well-behaved TCP, and
demonstrated that proper behavior could in some cases reduce network
load by an order of magnitude. In summary, the conclusions of that
paper are that a transport protocol, to be well behaved, should not
have a retransmit time shorter than the current round trip time
between the hosts involved, and that when informed by the network of
congestion, the transport protocol should take steps to reduce the
number of packets outstanding on the connection.

We reference our earlier work here to show that the network load
imposed by a transport protocol is not necessarily fixed by the
protocol specification. Some existing implementations of transport
protocols are well-behaved. Others are not. We have observed a wide
variability among existing TCP implementations. We have reason to
suspect that ISO TP4 implementations will be more uniform, given the
greater rigidity of the specification, but we see enough open space
in the TP4 standard to allow for considerable variability. We
suspect that there will be marginal TP4 implementations, from a
network viewpoint, just as there are marginal TCP implementations
today. These implementations will typically work quite well until
asked to operate over a heavily loaded network with significant
delays. Then we find out which ones are well-behaved.

RFC970 December 1985
On Packet Switches With Infinite Storage

Even if all hosts are moderately well-behaved, there is potential for
trouble. Each host can normally obtain more network bandwidth by
transmitting more packets per unit time, since the first in, first
out strategy gives the most resources to the sender of the most
packets. But collectively, as the hosts overload the network, total
throughput drops. As shown above, throughput may drop to zero.
Thus, the optimal strategy for each host is strongly suboptimal for
the network as a whole.

Game Theoretic Aspects of Network Congestion

This game-theory view of datagram networks leads us to a digression
on the stability of multi-player games. Systems in which the optimal
strategy for each player is suboptimal for all players are known to
tend towards the suboptimal state. The well-known prisoner's dilemma
problem in game theory is an example of a system with this property.
But a closer analogue is the tragedy of the commons problem in
economics. Where each individual can improve their own position by
using more of a free resource, but the total amount of the resource
degrades as the number of users increases, self-interest leads to
overload of the resource and collapse. Historically this analysis
was applied to the use of common grazing lands; it also applies to
such diverse resources as air quality and time-sharing systems. In
general, experience indicates that many-player systems with this type
of instability tend to get into serious trouble.

Solutions to the tragedy of the commons problem fall into three
classes: cooperative, authoritarian, and market solutions.
Cooperative solutions, where everyone agrees to be well-behaved, are
adequate for small numbers of players, but tend to break down as the
number of players increases. Authoritarian solutions are effective
when behavior can be easily monitored, but tend to fail if the
definition of good behavior is subtle. A market solution is possible
only if the rules of the game can be changed so that the optimal
strategy for players results in a situation that is optimal for all.
Where this is possible, market solutions can be quite effective.

The above analysis is generally valid for human players. In the
network case, we have the interesting situation that the player is a
computer executing a preprogrammed strategy. But this alone does not
insure good behavior; the strategy in the computer may be programmed
to optimize performance for that computer, regardless of network
considerations. A similar situation exists with automatic redialing
devices in telephony, where the user's equipment attempts to improve
performance over an overloaded network by rapidly redialing failed
calls. Since call-setup facilities are scarce resources in telephone
systems, this can seriously impact the network; there are countries

RFC970 December 1985
On Packet Switches With Infinite Storage

that have been forced to prohibit such devices. (Brazil, for one).
This solution by administrative fiat is sometimes effective and
sometimes not, depending on the relative power of the administrative
authority and the users.

As transport protocols become more commercialized and competing
systems are available, we should expect to see attempts to tune the
protocols in ways that may be optimal from the point of view of a
single host but suboptimal from the point of view of the entire
network. We already see signs of this in the transport protocol
implementation of one popular workstation manufacturer.

So, to return to our analysis of a pure datagram internetwork, an
authoritarian solution would order all hosts to be "well-behaved" by
fiat; this might be difficult since the definition of a well-behaved
host in terms of its externally observed behavior is subtle. A
cooperative solution faces the same problem, along with the difficult
additional problem of applying the requisite social pressures in a
distributed system. A market solution requires that we make it pay
to be well-behaved. To do this, we will have to change the rules of
the game.

Fairness in Packet Switching Systems

We would like to protect the network from hosts that are not
well-behaved. More specifically, we would like, in the presence of
both well-behaved and badly-behaved hosts, to insure that
well-behaved hosts receive better service than badly-behaved hosts.
We have devised a means of achieving this.

Let us consider a network that consists of high-bandwidth
pure-datagram local area networks without flow control (Ethernet and
most IEEE 802.x datagram systems are of this class, whether based on
carrier sensing or token passing), hosts connected to these local
area networks, and an interconnected wide area network composed of
packet switches and long-haul links. The wide area network may have
internal flow control, but has no way of imposing mandatory flow
control on the source hosts. The DoD Internet, Xerox Network Systems
internetworks, and the networks derived from them fit this model.

If any host on a local area network generates packets routed to the
wide area network at a rate greater than the wide area network can
absorb them, congestion will result in the packet switch connecting
the local and wide area networks. If the packet switches queue on a
strictly first in, first out basis, the badly behaved host will
interfere with the transmission of data by other, better-behaved
hosts.

RFC970 December 1985
On Packet Switches With Infinite Storage

We introduce the concept of fairness. We would like to make our
packet switches fair; in other words, each source host should be able
to obtain an equal fraction of the resources of each packet switch.
We can do this by replacing the single first in, first out queue
associated with each outgoing link with multiple queues, one for each
source host in the entire network. We service these queues in a
round- robin fashion, taking one packet from each non-empty queue in
turn and transmitting the packets with positive time to live values
on the associated outgoing link, while dropping the expired packets.
Empty queues are skipped over and lose their turn.

This mechanism is fair; outgoing link bandwidth is parcelled out
equally amongst source hosts. Each source host with packets queued
in the switch for the specified outgoing link gets exactly one packet
sent on the outgoing link each time the round robin algorithm cycles.
So we have implemented a form of load-balancing.

We have also improved the system from a game theory point of view.
The optimal strategy for a given host is no longer to send as many
packets as possible. The optimal strategy is now to send packets at
a rate that keeps exactly one packet waiting to be sent in each
packet switch, since in this way the host will be serviced each time
the round-robin algorithm cycles, and the host's packets will
experience the minimum transit delay. This strategy is quite
acceptable from the network's point of view, since the length of each
queue will in general be between 1 and 2.

The hosts need advisory information from the network to optimize
their strategies. The existing Source Quench mechanism in DoD IP,
while minimal, is sufficient to provide this. The packet switches
should send a Source Quench message to a source host whenever the
number of packets in the queue for that source host exceeds some
small value, probably 2. If the hosts act to keep their traffic just
below the point at which Source Quench messages are received, the
network should run with mean queue lengths below 2 for each host.

Badly-behaved hosts can send all the datagrams they want, but will
not thereby increase their share of the network resources. All that
will happen is that packets from such hosts will experience long
transit times through the network. A sufficiently badly-behaved host
can send enough datagrams to push its own transit times up to the
time to live limit, in which case none of its datagrams will get
through. This effect will happen sooner with fair queuing than with
first in, first out queuing, because the badly- behaved host will
only obtain a share of the bandwidth inversely proportional to the
number of hosts using the packet switch at the moment. This is much

RFC970 December 1985
On Packet Switches With Infinite Storage

less than the share it would have under the old system, where more
verbose hosts obtained more bandwidth. This provides a strong
incentive for badly-behaved hosts to improve their behavior.

It is worth noting that malicious, as opposed to merely
badly-behaved, hosts, can overload the network by using many
different source addresses in their datagrams, thereby impersonating
a large number of different hosts and obtaining a larger share of the
network bandwidth. This is an attack on the network; it is not likely
to happen by accident. It is thus a network security problem, and
will not be discussed further here.

Although we have made the packet switches fair, we have not thereby
made the network as a whole fair. This is a weakness of our
approach. The strategy outlined here is most applicable to a packet
switch at a choke point in a network, such as an entry node of a wide
area network or an internetwork gateway. As a strategy applicable to
an intermediate node of a large packet switching network, where the
packets from many hosts at different locations pass through the
switch, it is less applicable. The writer does not claim that the
approach described here is a complete solution to the problem of
congestion in datagram networks. However, it presents a solution to
a serious problem and a direction for future work on the general
case.

Implementation

The problem of maintaining a separate queue for each source host for
each outgoing link in each packet switch seems at first to add
considerably to the complexity of the queuing mechanism in the packet
switches. There is some complexity involved, but the manipulations
are simpler than those required with, say, balanced binary trees.
One simple implementation involves providing space for pointers as
part of the header of each datagram buffer. The queue for each
source host need only be singly linked, and the queue heads (which
are the first buffer of each queue) need to be doubly linked so that
we can delete an entire queue when it is empty. Thus, we need three
pointers in each buffer. More elaborate strategies can be devised to
speed up the process when the queues are long. But the additional
complexity is probably not justified in practice.

Given a finite buffer supply, we may someday be faced with buffer
exhaustion. In such a case, we should drop the packet at the end of
the longest queue, since it is the one that would be transmitted
last. This, of course, is unfavorable to the host with the most
datagrams in the network, which is in keeping with our goal of
fairness.

RFC970 December 1985
On Packet Switches With Infinite Storage

Conclusion

By breaking away from packet switching's historical fixation on
buffer management, we have achieved some new insights into congestion
control in datagram systems and developed solutions for some known
problems in real systems. We hope that others, given this new
insight, will go on to make some real progress on the general
datagram congestion problem.

References

[1] Nagle, J. "Congestion Control in IP/TCP Internetworks", ACM
Computer Communications Review, October 1984.

Editor's Notes

<1> The buffer space required for just one 10Mb Ethernet with an
upper bound on the time-to-live of 255 is 318 million bytes.

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