Performance degradation of switching systems when the load increases above the engineered load can be caused by systemdependent and customer-dependent factors. In this paper the dependency of the service time and the call completion rate on the waiting time of a customer is investigated. The problem is modeled by means of a queueing system of typeM^{[x]}/G/1, where state-dependent batch size distributions are considered. Two analysis methods, the continuous Markov chain approach and the regenerative method, are used for Markovian and generally distributed service phases, respectively. Numerical results are given for system characteristics, in particular the call completion rate of the system. Finally, a basic overload control scheme is investigated which increases the throughput of completed calls at higher traffic levels.