Power line communication (PLC) is a promising technique for information transmission using existing power lines. We analytically model a finite-source PLC network subject to channel noise (disturbance) and evaluate its call-level performance through a queueing theoretic framework. The proposed PLC network model consists of a base station (BS), which is located at a transformer station and connected to the backbone communication networks, and a number of subscriber stations that are interconnected with each other and with the BS via the power line transmission medium. An orthogonal frequency division multiplexing based transmission technique is assumed to be used for providing the transmission channels in a frequency spectrum. The channels are subject to failure during service due to disturbance. We determine the steady-state solution of the proposed model and derive a set of performance metrics of interest. Numerical and simulation results are presented to show the derived metrics with respect to different system parameters. The proposed modeling method can be used for evaluation and design of future PLC networks.