A general class of overload control mechanism for communication and switching systems is modeled and analyzed in this paper. The overload indicator is considered to be the amount of unfinished work in the system. The overload control is based on a throttling mechanism for new arriving requests when the load status of the system is above a predefined threshold. The input process, modeling the subscriber requests, is assumed to be general and can be considered under stationary or nonstationary conditions. To model the main mechanism of this class of overload control strategy, a generic queueing system of type G/G/1 with feedback, in conjunction with a workload-controlled acceptance scheme is used. The analysis method works in the discrete-time domain and allows use of efficient discrete transform algorithms [e.g., Fast Fourier Transform (FFT)] to determine the system characteristics. In discussing dimensioning aspects of the overload control strategy, numerical results are given for different types of input processes and overload threshold parameters.