This thesis addresses a method of deducing the statistical upper and lower bounds associated with the cell-transfer delay variations (CDVs) encountered by the cells transmitted in the asynchronous transfer mode (ATM) networks due to cell losses. This study focuses on: (1) Estimating CDV arising from multiplexing/switching for both constant bit rate and variable bit rate services via simulations. (2) Deducing an information-theoretics based new technique to get an insight of the combined BER-induced and multiplexing/switching-induced CDVs in ATM networks. Algorithms on the CDV statistics are derived and the lower and upper bounds of the statistics are obtained via simulations in respect of CBR and VBR traffics. These bounds bounds are useful in the cell-admission control (CAC) strategies adapted in ATM transmissions. Inferential remarks indicating the effects of traffic parameters (such as bandwidth, burstiness etc.) on the values of the statistical bounds are presented, and scope for further work is indicated.