The Queueing Rule of Thumb (QROT) is an inequality that relates the number of servers, the number of service requestors, service time per requestor per server, and the maximum time to empty the queue as: num_server > (num_requestor * service_time) / max_drain_time
Note: the servers are parallel.
Most of this rule of thumb comes from algebraically moving around common metrics like arrival rate and service rate, but the core insight is in this invariant: arrival_rate / service_rate < num_servers.
Basically, arrival_rate >= service_rate is allowed since you can process in parallel, but it must not exceed the number of servers you have; since arrival_rate >= service_rate * num_servers means that your queue will grow unboundedly.
Neat - I like this rule of thumb.
Example from the Wikipedia page:
A school of 10,000 students must set certain days for student registration. One working day is 8 hours. Each student needs about 36 seconds to be registered. How many days are needed to register all students?
Answer: 10,000 * 36 seconds < max_drain_time, so max_drain_time ~= 13 days.