"Col. Shaw / Col. Risdon, 2nd Brig./3rd. Brig XVII Corps on 5.15 camped E. and S. of Ft. Derussy...the area from Marksville - De Russy was covered with Federal soldiers. They rejoined A.J, Smith near Marksville at 3 a.m. (5.16.64.)
This must br the time in which A.J. arrived."

After Gen. Smith told Col Shaw to "go to hell," Shaw set off for Fort DeRussy. Col. Risdon's brigade had been following Shaw all day, so when Shaw left, they followed. Both brigades arrived at Fort DeRussy, only to find that the transports they had hoped to find in the river there had already left. There being no alternative, they headed back toward Marksville and arrived there around 3 AM, rejoining Smith and the main column, which had been at Marksville since earlier that evening.

Not sure what you mean by "the time in which A. J. arrived." A. J. Smith was already in Marksville when Shaw arrived. Nothing concerning Shaw's arrival at Marksville would have any bearing on when Smith arrived.