Case Study: ANetworkDesignProblem

Submitted: 20 Feb 2008

Operations Research Topics:

Application Areas:

Problem Description

THE NETWORK DESIGN PROBLEM

Adapted from a real world problem

Before undertaking this case study you must (at least) read the DataNetworkFlows case study to learn about the components that make up Storage Area Networks (SANs).

The company that commissioned the initial research on routing their data (see DataNetworkFlows) has decided to add another storage device (Device C) to their network. They have also performed some extensive data traffic measurement and determined the actual data flow requirements they need to support. These flows are shown in Table 1.

Source	Destination	Requirement Mb/s
Host 1	Device A	65
Host 1	Device B	50
Host 1	Device C	30
Host 2	Device A	25
Host 2	Device B	70
Host 3	Device A	35
Host 3	Device C	65

They estimate they will need either an extra hub or an extra switch or some combination of the 3 hubs and 2 switches. They commissioned the same network consultant to design their new network for them. He finished the job, but left for his honeymoon before writing a management summary or documenting his work. The files he left are contained in:

??? LINK ??? san_design.zip

The company want to use these files to find the optimal SAN design that will support their data flow requirements.

For more detail see A Mixed-Integer Approach to Storage Area Network Design using Generic Network Components, O’Sullivan and Walker Engineering Science Technical Report 626, March 2006

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Student Tasks

STUDENT TASKS

1. Comment the AMPL files san_design_neos.mod, san_design.dat and san_design_neos.run from san_design.zip. Run these files to find the optimal SAN design to support the flow requirements. Write a management summary for your solution.

What to hand in ??? Mike to look at??? You commented AMPL files. Your management summary.

Extra for Experts' Tasks

1. One problem that often arises in network design (and other mixed-integer programming) is that of symmetry. If components in the network have the same properties, then mixed-integer programming will consider all the combinations of these components even though many combinations represent the same network. The following constraints:

subject to LinkAntisymmetry {l in LINKS} :
  card({k in LINKS : (from[k] = from[l]) and (to[k] = to[l]) and
                     (ord(k) > ord(l))}) * UseLink[l] >=
  sum {k in LINKS : (from[k] = from[l]) and (to[k] = to[l]) and
                    (ord(k) > ord(l))} UseLink[k];
  
subject to HubAntisymmetry {h in HUBS} :
  card({g in HUBS : ord(g) > ord(h)}) * UseHub[h] >=
  sum {g in HUBS : ord(g) > ord(h)} UseHub[g];

subject to SwitchAntisymmetry {s in SWITCHES : s <> last(SWITCHES)} :
  card({t in SWITCHES : ord(t) > ord(s)}) * UseSwitch[s] >=
  sum {t in SWITCHES : ord(t) > ord(s)} UseSwitch[t];

can be used to remove symmetry from the SAN design problem if all the hubs, switches and links have the same properties (i.e., bandwidth capacity, number of port slots, etc).

Add these constraints to san_design_neos.run and solve the SAN design problem again. Describe how these constraints remove symmetry. Comment on their effect on the solver's progress.

What to hand in A brief (1 page or less) summary comprised of your description of how the antisymmetry constraints work and their effect on the solver's progress.