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The domain name system (DNS) is critical to Internet functionality. The availability of a domain name refers to its ability to be resolved correctly. We develop a model for server dependencies that is used as a basis for measuring availability. We introduce the minimum number of servers queried (MSQ) and redundancy as availability metrics and show how common DNS misconfigurations impact the availability of domain names. We apply the availability model to domain names from production DNS and observe that 6.7% of names exhibit sub-optimal MSQ, and 14% experience false redundancy. The MSQ and redundancy values can be optimized by proper maintenance of delegation records for zones.