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As always, the correct answer is, "It depends." In this particular case, it depends on the control-plane loop-prevention algorithms (a loop in a bridged network usually causes a total network meltdown).
If you're using traditional spanning tree algorithm (in any incarnation, including MSTP), one of the links in the ring will be blocking (almost identical to the break in the ring), so you'll lose the bandwidth of that link and have a lot of traffic flowing across suboptimal paths.
If you use PBB-Traffic Engineering, you can engineer your paths according to your needs. Unless you use true 1:1 protection backed up with stringent Quality of Service guarantees, you can use most of the bandwidth available in the ring.
Last, but definitely not least, most vendors offering ring-based Carrier Ethernet solutions use their own proprietary protocols -- for example, Cisco uses Resilient Ethernet Protocol (REP). In that case, consult the vendor.
This was first published in January 2011