Select rows starting from specified value until another specified value

A suggestion that should work in 2008 version.

Tested at rextester.com:

with 
  end_points as                       -- find start and end points
    ( select id, time, value
      from table_x
      where value in (15, 16)
    ), 
  start_points as                     -- only the start points
    ( select id, time, value
      from end_points
      where value = 15
    )
select 
    t.id, t.time, t.value
from
    start_points as s
  outer apply                         -- find where each island ends
    ( select top (1) ep.* 
      from end_points as ep
      where s.id   = ep.id
        and s.time < ep.time
      order by ep.time
    ) as e
  cross apply                         -- and run through each island
    ( select p.id, p.time, p.value, 
             rn = row_number() over (order by p.time) 
      from table_x as p
      where s.id   = p.id
        and s.time <= p.time
        and         ( p.time < e.time
                   or p.time = e.time and e.value = 16
                   or          e.time is null)
    ) as t
where 
    t.rn <= 100
order by
    t.id, t.time  ;

More info:

• Using Common Table Expressions
• Using APPLY
• ROW_NUMBER (Transact-SQL)