  Performance analysis of queueing networks is one of the most challenging
areas of queueing theory. Barring very specialized models such as product-form
type queueing networks, there exist very few results which provide provable
non-asymptotic upper and lower bounds on key performance measures. In this
paper we propose a new performance analysis method, which is based on the
robust optimization. The basic premise of our approach is as follows: rather
than assuming that the stochastic primitives of a queueing model satisfy
certain probability laws, such as, for example, i.i.d. interarrival and service
times distributions, we assume that the underlying primitives are deterministic
and satisfy the implications of such probability laws. These implications take
the form of simple linear constraints, namely, those motivated by the Law of
the Iterated Logarithm (LIL).
  Using this approach we are able to obtain performance bounds on some key
performance measures. Furthermore, these performance bounds imply similar
bounds in the underlying stochastic queueing models.
  We demonstrate our approach on two types of queueing networks: a) Tandem
Single Class queue- ing network and b) Multiclass Single Server queueing
network. In both cases, using the proposed robust optimization approach, we are
able to obtain explicit upper bounds on some steady-state performance measures.
For example, for the case of TSC system we obtain a bound of the form
$\frac{C}{1-\rho} \ln \ln(1/(1-\rho))$ on the expected steady-state sojourn
time, where C is an explicit constant and $\rho$ is the bottleneck traffic
intensity. This qualitatively agrees with the correct heavy traffic scaling of
this performance measure up to the $ln ln(1/(1-\rho))$ correction factor.
