  We present a broad literature survey of parameter and state estimation for
queueing systems. Our approach is based on various inference activities,
queueing models, observations schemes, and statistical methods. We categorize
these into branches of research that we call estimation paradigms. These
include: the classical sampling approach, inverse problems, inference for
non-interacting systems, inference with discrete sampling, inference with
queueing fundamentals, queue inference engine problems, Bayesian approaches,
online prediction, implicit models, and control, design, and uncertainty
quantification. For each of these estimation paradigms, we outline the
principles and ideas, while surveying key references. We also present various
simple numerical experiments. In addition to some key references mentioned
here, a periodically-updated comprehensive list of references dealing with
parameter and state estimation of queues will be kept in an accompanying
annotated bibliography.
