Biàn (便), jiù (就) and jí (即) all can serve as temporal adverbs. Jiù (就) and biàn (便) both can reinforce a relationship of sequence between two actions or situations that occur in series, but biàn (便) is largely restricted to more formal and literary contexts.
tā yī xià kè jiù /biàn qù le tú shū guǎn.
She went to the library right after the class.
Jiù (就) can indicate that some situations will occur in a short time, which conveys a sense of immediacy in terms of time. In contrast to jiù (就), biàn (便) must be bounded in a sequence relationship between two actions or situations.
fàn jiù hǎo le, zài děng yī xià.
fàn biàn hǎo le, zài děng yī xià.
The meal will be ready soon, hold on.
When serving as a temporal adverb, jiù (就) also implies that the action or the situation happens/ happened earlier than assumed or expected. Biàn (便) usually doesn’t have this kind of semantic effect without specific contexts.
tā zuó tiān jiù huí lái le.
He came back (as early as) yesterday.
The temporal adverb jí (即) can be regarded as the formal vision of jiù (就) when indicating that the action will be taken in a short time or under certain circumstance. Jí (即) mainly appears in literary or formal contexts.
kāi dài jí shí.
Ready to enjoy when opened.
fú yào sān tiān hòu jí kě jiàn xiào.
The drug will take effect in three days.
Reference: Modern Mandarin Chinese Grammar: A Practical Guide
Claudia Ross，Jing heng Sheng Ma