In this paper we propose a consistent and asymptotically normal estimator (CAN) of intensities ρ₁ , ρ₂ for a queueing network with feedback (in which a job may return to previously visited nodes) with distribution-free inter-arrival and service times. Using this estimator and its estimated variance, some 100(1-α)% asymptotic confidence intervals of intensities are constructed. Also bootstrap approaches such as Standard bootstrap, Bayesian bootstrap, Percentile bootstrap and Bias-corrected and accelerated bootstrap are also applied to develop the confidence intervals of intensities. A comparative analysis is conducted to demonstrate performances of the confidence intervals of intensities for a queueing network with short run data.