Taylor-series approximations for queues with arrival correlation

•We propose a queueing model with session-based arrivals, where sessions are not always active.•We analyse the system in the light traffic regime, by Taylor series expansion techniques.•We find explicit expressions for the 3rd order expansions of the first two moments of the queue content.•Combining light and heavy traffic approximations covers a large part of parameter space.•We formally prove the existence of the Taylor series expansions.