# The Leland & Ott 1986 Model

This is actually a model of process runtimes in an interactive
environment, rather than a model of a parallel workload.
Its distinction lies in the innovative functional form used to
describe the distribution.

### Process runtimes

The proposed distribution is valid for processes that are longer than
3 seconds.
With this restriction, the probability that a process will run for
more than *t* seconds is proportional to *t*^{k},
with *k* in the range *-1.25 < k < -1.05*.
A subsequent study by Harchol-Balter and Downey reaffirmed this model,
and provided the following formulae:

*k* in the range *-1.3 < k < -.8*, with *k = -1*
a reasonable default.
- Prob(runtime > t sec | runtime > 1 sec) = t
^{k}

For *k = -1*, this is *1 / t*.
- Prob(runtime = t sec | age = 1 sec) = -k t
^{k-1}

For *k = -1*, this is *1 / t*^{2}.

This model is described in the following papers:
[leland86] and
[harcholb97].

Parallel Workloads Archive - Models