Answer: A good measure (metric) for this will have to be statistical, but simple statistics like "average wait time" turn out misleading rather than meaningful. A better metric might be the percentage of voters who have to wait longer than some specified "target" wait time . The measure can be thought of as a pass/failure rate against a quality-of-service (QOS) standard. .
Resource planning for quality improvement
I know of no way to estimate a "cost of time" to voters, but choosing a target wait time leads to a more actionable metric and planning tool. The QOS standard replaces "cost" in effect. An example a QOS standard might be that at least 80% of voters every hour wait less than 5 minutes, even during peak voting hours.
This choice is motivated by the fact it may be possible to estimate the probability of waiting longer than the target amount of time, due to a model of queuing systems in telecommunications using math first worked out by Agner Krarup Erlang. The math of predicting this it is probabilistic, non-linear and frankly a bit over my head, if you are more math inclined, see this article gives formula and definitions. For non-mathematicians, there are easy to use estimating calculators are available free online. I'll illustrate using a calculator available at https://planetcalc.com/3151/; an example and screen shot appear below.
To simplify, let's assume that the only bottleneck in voting is the number of available of voting booths. (This ignores other possible sources of delay, such as the number of poll-workers needed for checking-in voters and issuing ballots; but similar service models can be generated for each resource type used in a process.)
Lets say that at a particular polling station the peak-hour arrival rate of voters is 60/hour, and that on average it takes 5 minutes (300 s) in a booth. Given these estimates, we might want to calculate: How many voting booths would I need to meet expectations?
The math of working the answer out isn't straightforward because most voters use the booth for substantially less than 5 minute; only a few go over, but those few go way over five minutes. Also the arrival time of voters won't be spaced out evenly. Both are usually modeled as probability distributions.
But to the answer, we need to specify a quality of service goal, e.g. that 80% of voters wait no more than 5 minutes (300 s.) By plugging the four numbers into the Erlang-C calculator we can estimate the minimum number of voting booths needed at that polling station is 7. See below:
Any fewer voting booths is likely result in voter delays spiraling spiral out-of-control during peak hours, like the example in Georgia. The of this simplified example math works out that within limits, quality of service be improved by increasing the number of resources (like voting booths), for example to improve and achieve 95% wait times to 5 minutes, a minimum of 8 voting booths are needed.
Like any probabilistic equation, some assumptions about distributions are made. For Erlang-C applied to voting, one of these assumptions is that the voters arrive independently of each other. If instead, voters arrive by the busload every hour, the assumption is broken. For that reason, figures the calculator produces are minimum numbers, but as a metric of results(rather than planning tool) the percentage of voters who need to wait more than 5 minutes might be a good one.