Vijay's scores this season are 56, 100, 85, and 80.
Vijay had scored 56 and 100 on County debut, against Nottinghamshire. This is his second match.
Former England stumper James Foster is set to leave Essex at the end of the 2018 County Championship season announcing his retirement.
Vijay, who was dropped after poor run of form that included a pair in the 2nd Test against England at Lord’s, had signed with Essex a week earlier and became the first Essex player to score a century on debut after Hashim Amla achieved the feat against Glamorgan in 2009.
Set a target of 282, the defending champions were 147/1 at stumps against Nottinghamshire.
On the eve of the squad selection for the Pakistan tour, coach Langer has assured Siddle that age will not be a barrier.
With fellow opener Nick Browne, Vijay put on 56 for the first wicket against Nottinghamshire
The 33-year-old seamer has taken 37 wickets in seven County Championship First Division matches this year, convincing Essex chiefs to bring him back next season.
Burns is 174 ahead of Vince of Hampshire, the second name on the list.
Cook holds numerous records for England, and is 146 short of Sangakkara's record for most Test runs for a left-hander.