Waiting for Erlang Buses

A bus line's inter-arrival gaps are independent, and each gap is the sum of two independent exponential random variables with mean 1 minute apiece (an Erlang-2 gap, mean 2 minutes). You arrive at a time chosen uniformly over a very long stretch of the schedule, with no knowledge of the history. What is your expected wait for the next bus, in minutes? Give a reduced fraction.

• bias
• distributions
• graph theory

Source: Inspection paradox / residual life in renewal theory, as in Feller vol. 2 and Ross, Stochastic Processes. Statement written for AxiomIQ.