For networks providing a specific level of service
guarantees, capacity planning is an imperative part of
network management. Accurate dimensioning is especially
important in DiffServ networks, where no per-flow signaling
or control exists.  In this paper, we address the problem of
capacity planning for DiffServ networks with only Expedited
Forwarding (EF) and best effort (BE) traffic classes. The
problem is formulated as an optimization problem, where the
total link cost is minimized, subject to the performance
constraints of both EF and BE classes. The variables to be
determined are the routing of EF tra±c, and the discrete
capacities of the links.  We show that Lagrangean Relaxation
and subgradient optimization methods can be used to solve
the problem. Computational results show that the solution
quality is verifiably good while the running time remains
reasonable on practical-sized networks. This represents the
first work for capacity planning of multi-class IP networks
with convex performance constraints.