Appendix A. Lyapunov Analysis

This appendix provides an outline of the mathematical proof that shows why the least connections server load balancing (SLB) algorithm is inherently stable. This means that over a long period of time, the system will ensure that the load is evenly balanced. This analysis can be used to model and verify the stability of any network design, which may be of tremdous value if you are an advanced network architect.

Building on what was discussed in Chapter 3, we will extend the model of the single queue to that of the entire system and then show that the entire system is stable. The entire system consists of an aggregate ingress load of l, N server processes of varying service rates µ1, µ2, . . .µn, hence we get the following ...

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