In communication networks that span large geographical regions, transfer of bulk data is often costly and hard to manage. One prominent reason for that is bandwidth contention among long-lasting flows, and between long-lasting and short-lived ones on inter-datacenter links. Delaying the transfer of bulk data to off-peak hours by temporarily storing transfer at edge of the network can help reduce bandwidth contention during peak hours, and improve overall bandwidth utilization and network utility. Although extensive research has been conducted on its use, to date no model has been developed to quantify the performance of storage assisted bulk transfers across multiple congested links. This research gap has limited our understanding of the operation of storage assisted transfer under different network conditions. In this paper, we model bulk data transfer in inter-datacenter optical networks with edge storage, and derive closed-form equations for bulk data transfer on inter-DC links that exhibit diurnal traffic patterns and varying peak hours. Our study reveals that when the data transfer requests arrive uniformly in a day, the probability of a successful transfer increases linearly with the time data is allowed to wait in edge storage. Our study also shows that this probability decreases linearly with β+D, where β and D are the durations of background traffic peak and size of data transfers, respectively, when the network is moderately loaded. And, the benefit of storage will barely increase when the allowed waiting time goes beyond β+D.