AbstractSome general results are derived for single‐channel queues with Poisson input and state‐dependent Erlang service times in view of the possible use of this model to approximate arbitraryM/G/1‐like state‐dependent queues in a manner similar to that suggested by Rosenshine, and by Kendall, and Kotiah, Thompson, and Waugh for theM/G/1. Numerical procedures are indicated for the evaluation of stationary state probabilities, expected system sizes and waiting times, and parameter est