Estimating the demands placed by services on physical resources is an essential step for the
definition of performance models. For example, scalability analysis relies on these parameters to
predict queueing delays under increasing loads. In this paper, we investigate maximum likelihood
(ML) estimators for demands at load-independent and load-dependent resources in systems with
parallelism constraints. We define a likelihood function based on state measurements and derive
necessary conditions for its maximization. We then obtain novel estimators that accurately and
inexpensively obtain service demands using only aggregate state data. With our approach, and
also thanks to approximation methods for computing marginal and joint distributions for the
load-dependent case, confidence intervals can be rigorously derived, explicitly taking into account
both topology and concurrency levels of the services. Our estimators and their confidence intervals
are validated against simulations and real system measurements for two multi-tier applications,
showing high accuracy also in the presence of load-dependent resources.