Net2Plan

Example: Capacity assignment minimizing network delay, with concave cost constraints

ca_minAvDelayConcaveCost

This algorithm obtains the capacity assignment that minimizes the average network delay in the network, so that the network cost is limited to a maximum budget $C_{max}$ .

Average network delay considers the queueing delay and the transmission delay. Propagation delay is not included since it is not affected by the link capacities. Average network delay is estimated as:

$T = frac{L}{sum_d h_d} sum_e frac{rho_e}{1 - rho_e}$

Where:

is the offered traffic in bps of demand
: is the average packet length in bits
: is the utilization of link

The network cost is the sum of the costs of the links C_e , where the cost in a link grows in a concave form respect to capacities:

$C_e = (alpha + d_e beta ) sqrt{u_e}$

Where:

, : are cost factors, input parameters to the problem.
: is the length in km of link
: is the link capacity in Erlangs

The algorithm solves the following formulation:

Decision variables:

: Utilization in the links

$min sum_e frac{rho_e}{1 - rho_e}$

$sum_e (alpha + d_e beta ) sqrt{y_e} frac{1}{sqrt{rho_e}} leq C_{max}$

Although the cost function is concave with respect to the u_e variables, it is convex with respect to rho_e variables. Then, the previous formulation is a convex program respect to the rho_e variables, and is solved using CVX. The algorithm requires CVX solver installed and running.

Download .m file: ca_minAvDelayConcaveCost.m