Design of a supercomputing network infrastructure

A distributed computing server has been created with N=2^n=8192 computing nodes, and needs a good network connection to allow for fast data exchange. These N nodes are subdivided in racks of 256 nodes each, all of which share a connection. Our task is that of creating another network that connects all racks (there are \frac{N}{256} = 2^{n-8} in total) so that very strict connectivity and speed constraints are met:

  • Any two racks must have a total connection speed of 10Mb/s available at all times
  • There are two types of interconnecting technology:
    1. one that has a speed of 2.5Gb/s, with maximum length of 5 meters and a cost per cable (independent of the length) of $2000;
    2. another one that has a speed of 32Gb/s, with maximum length of 10 meters and a cost per cable (independent of the length) of $12,000;
  • Due to delay constraints, There can be no more than three hops when connecting any two nodes

In order to keep an orderly arrangement of the racks, they are placed in a room in a matrix 4\times 8 and there are two ample corridors (two meters) that cross the matrix at the middle row and the middle column, respectively. Each rack occupies a square meter.

Notice that the set of potential edges of the network, which can be in theory between any two nodes i,j\in V, can be reduced before applying an Optimization approach given that not all pairs of nodes satisfy the connection/distance constraints for each technology.

Formulate and solve an Optimization model for the problem of minimizing the total installation cost.

Simulate the obtained system by introducing packets into random nodes of the network with increasing arrival rate, and observing the behavior of the system when each packet is sent from a node to another (random) node for k=1 times. The packet input rate should match that of the total throughput of the network. Simulate the behavior when k increases to 2 and then 3.