Executando o total com em cada grupo usando o MySQL

select e.*,
       (@s := if(@id = e.id, @s + salary,
                 if(@id := e.id, salary, salary)
                )
       ) as running_salary
from (select e.*
      from employee e
      order by e.id, e.month
     ) e cross join
     (select @id := -1, @s := 0) params;

select e.*,
       (select sum(e2.salary)
        from employee e2
        where e2.id = e.id and e2.month <= e.month
       ) as running_salary
from employee e;