[e2e] Formal methods for simulation/analysis of network

Shivkumar Kalyanaraman shivkuma at ecse.rpi.edu
Mon Aug 11 17:49:49 PDT 2003

There is a well known area of performance analysis called "experiment
design" (a branch of statistics) that systematically develops
empirical "models" of system behavior as a function of parameters. It has
historically found only limited use in networking for reasons that are
not very clear.

See the book "The Art of Computer Systems Performance Analysis" by Raj

Perhaps we will see more usage of such techniques in the near future as we
attempt to design protocols that have to operate instantly on
large-scales and have to deal with potential feature interactions with
other existing protocols.

Shivkumar Kalyanaraman
Associate Professor, Dept of ECSE, Rensselaer Polytechnic Institute (RPI)
110, 8th Street, Room JEC 6003, Troy NY 12180-3590
Ph: 518 276 8979   Fax: 518 276 4403
WWW: http://www.ecse.rpi.edu/Homepages/shivkuma

A goal is a dream with a deadline -C. Knight

On Mon, 11 Aug 2003, Amit Prakash wrote:

> This is a research idea that has been gestating in my mind for some
> time but never got defined enough to work on it. I am looking for
> inputs from people on this idea.
> What I have in my mind is to use formal methods, or just simple
> math to write a network simulator/analyzer that can do a more
> comprehensive job than NS simulations.
> For example, earlier most circuit designers used to rely on
> simulations to verify their circuits and left many undetected bugs.
> Now increasingly they have been using more of formal verification
> tools to get a mathematical proof of the correctness of the design, or
> at least do a more comprehensive job at state space exploration by
> simulating  a set of states instead of just one. Similarly few runs
> of of NS simulation do not tell
> much about a particular protocol or routing algorithm under test.
> The problem is that even in case of circuits where state variables are
> in few thousands of bits, the verification problem  becomes
> computationally formidable. In case of networks, we have a lot more
> state to take care of, exact analysis may be impossible. Thus we have
> to look for tractable approximation models.
> There are two questions that I want your help on.
> 1) what is desired of  a network simulation/analysis tool ?
> 2) what sort of simplification assumptions can be made to make the
>    problem tractable ?
>  As for question one, You could expect to get some of the following
> answers from the tool
>  a) given a topology, fixed routing and dropping policy, congestion
>     control protocol in use,  and a set of source and a sinks,
>     what range of loads makes network unstable, or increase loss rate
>     to, say more than 90%.
> b) For what range of values of RED parameters will a certain network
>     work well (where working well needs to be defined) ?
>  c) Given a probability distributions of rate of traffic between all pairs
>     of sources and sinks in a network, what would be the probability
>     distribution of load on a certain link or a router.
> I have thought of different ideas that do not make a coherent picture
> as yet but I will try to list them.
> 1) A simulator could be built that in stead of simulating one instance
>    of traffic, simulates a range of traffic. Let A=[a_{ij}] be the
>    matrix such that a_{ij} is arrival rate of packets at input i for
>    output j.  And we are given that b_{ij} < a_{ij} < c_{ij}, where
>    b_{ij} and c{ij}s are constants. Then we can compute bounds on the
>    range of load we can see at the output links of that router using
>    simple math (assuming tail drop and a suitable arrival process). If
>    we do this computation throughout the network we can get the range
>    of loads that can be seen on any link. Then we can have
>    instantaneous rates, drop rates computed and feedbacks sent to
>    sources and rates readjusted. This way we simulate a range of loads
>    rather than one.
> 2) Have a fluid flow model, where routers are non-linear devices and
>    use techniques used in analog circuit simulation tools such as
>    SPICE.
> 3) Model network as a hybrid automaton. This blows up pretty soon.
> 4) Many papers have approximate mathematical expressions for the bandwidth
>    achieved by a TCP flow given a set of users and fixed routes in
>    a network such as Frank kelly's paper on modeling Internet. I am
>    wondering if these expressions can be used by a tool to
>    answer some of the questions that we can never hope a simulation
>    tool to answer. For example, compute what values of RED parameters
>    will optimize utility in  a
>    given network for a given probability distribution on load.
> I apologies for lack of clarity in these ideas, but I will be greatful
> if you can help me in defining this by your suggestions, pointing to
> an existing work, or otherwise.
> -regards,
> Amit

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