This paper investigates the stability characteristics of overlay networks performing switching between multiple virtual paths. A global stability condition for switched-control-systems has been applied to overlay path switching frequency, that can be incorporated into design of better routing protocols for overlay networks. Further, NS-2 based simulations have been carried out on an overlay network to evaluate the impact of round-trip-time, packet loss probability and throughput metrics on decisions regarding path selection. Throughput based switching decisions have shown to be resulting in lower number of path changes, which is desirable. Also, it has been observed that delay and loss based metrics can result into a large number of frequent path changes, which can push the overlay routing system into an instable oscillating state for a prolonged period of time.
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