Globus toolkit is widely used Grid middleware for implementing Grid computing concepts. You should visit http://www.globus.org/

I think, building a grid environment, require more computational power, more than just two computers! unless you may want to use some visualization technique to create a test-bed for Grid component. I advice you, run the Rocks Cluster Manager on Vmware or VirtualBox, In order to construct a grid, at least one two WNs(worker node) and one CE(Computing element or head) is required

Globus toolkit is one middleware for grid computing. However, my group uses OurGrid middleware (much easier to learn and to use) - see: http://www.ourgrid.org/ (see also: http://en.wikipedia.org/wiki/OurGrid)

make a look on these documents. they might help https://www.researchgate.net/project/Build-a-small-grid-for-tests

Grid computing system is a widely distributed resource for a common goal. It is Brother of Cloud Computing and Sister of Supercomputer. We can think the grid is a distributed system connected to a single network. This types of computing work with the large volume of files. Basically, it is a cluster types system. So people call it cluster computing.

Source: https://www.cloudwebhostingtips.com/grid-computing-vs-cloud-computing-supercomputer/

Grid computer tends to be more geographically disperse and heterogeneous by nature. Grid network also has various types. A single grid is like dedicated connection but a common grid perform multiple tasks.

The size of the grid is large. So grid computing is like supercomputing. It consists of many network, computer, and middleware. Grid computer is dedicated to some specific function of the large volume of data. In the grid process, each task divided into a various process. All the process starts execution simultaneously on a different computer. As a result, very few seconds needs to execute and enjoy the flavor of supercomputing.

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It depends on your requirements b put simply, Globus is a widely used middleware for the purpose.

But connecting two computers doesn't lead to a grid implementation, even a small test-bed. Consider adding more computation power, and also take a look at Condor g.