In this paper a new non-switching type reaching law for sliding mode control of discrete time systems is proposed and applied to the problem of flow regulation in a class of data transmission networks. The reaching law proposed in this paper is inspired by the significant `constant plus proportional' reaching law of Gao, Wang and Homaifa, however, in our work the original formulation is refined in order to avoid chattering and to ensure fast convergence with limited control signal. These improvements are possible due to the application of a modified definition of the quasi-sliding mode, and also because of the introduction of adaptive, state dependent sliding variable decrease rate factor. In the second part of the paper the proposed reaching law is employed for the purpose of congestion control in a single virtual circuit of connection oriented (e.g. Multi Protocol Label Switching) networks. Several important properties of the proposed reaching law based control scheme are proved.