With the development of multi-interface terminals, a host can connect to the Internet simultaneously by multiple access technologies. Under multi-access technology, a multi-path transmission can obtain high throughput, increased available bandwidth and enhanced reliability. However, the multi-path transmission with multi-access technology also has the problems that the packet re-ordering is unavoidable, and the fast retransmission is unnecessarily requested. Considering the stochastically varying transmission delay, the problems above may eventually result in a degradation of throughput. As a result, in this paper, we focus on the analysis of buffer overflow probability problem which is influenced by the transmission interval. First, we utilize Reinforcement Learning method to estimate the stochastic delay of end-to-end paths. Then, we discuss problems of re-sequencing buffer occupancy distribution and the overflow probability. In this paper, we model the stochastic delay as a continuous random variable, and then, discuss its mean value and variance. Simulation result shows that the re-sequencing buffer overflow probability is influenced by the transmission intervals and the variance of stochastic delay.