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Overview This simulation enables comparison of latency and network investment tradeoffs between point-to-point and hub-and-spoke random networks. Pairs of points are randomly generated on a unit disc (circle). Each pair may be directly connected, or may be connected via a central hub. Generally, for n nodes, the benefit of a hub-and-spoke or "star" network is that the number of connections to a hub is order (n), whereas in a fully-connected point-to-point network on n nodes the number of connections is order (n*n), namely 1/2n(n-1). However, while the number of connections is decreased, latency is increased. Specifically, the expected value of the distance between two points selected at random on a unit disc is 128/45PI, or roughly .909. The expected value of the distance of a point selected at random on a unit circle to the center of the circle is 2/3, making the latency penalty roughly an additional 47% (1.333 / .909).
Basic Flow First, select the desired graphical view: hub-and-spoke, point-to-point, both, or neither.

Second, run any number of random trials, one at a time up through a thousand at a time. For each trial, a random pair of points is generated, and calculations are made regarding the distance between the points via either strategy.

Lastly, view the results. The average point-to-point distance should converge to .909=128/(45PI), whereas the hub-and-spoke distance should converge to 1.333=4/3.

About This model was written by Joe Weinman in about 200 lines of code, which are a mixture of HTML, DHTML, ASP.NET 2.0 / Visual Basic, stylesheets, and JavaScript, using Microsoft Visual Web Developer 2010. It has been tested using a variety of browsers, smartphones, and tablets.
© 2005-2012 Joe Weinman