Here are two solutions... The 1st will work in 2008 & 2008R2. The 2nd will work with 2012 and above...

Note: The full script, including the creation & population of test data is attached as well.

-- ======================================================================

-- ======================================================================

-- 2008 & 2008R2 version --

IF OBJECT_ID('tempdb..#temp', 'U') IS NOT NULL

DROP TABLE #temp;

SELECT

a.ID,

a.ArrivalDateTime,

rn = ROW_NUMBER() OVER (PARTITION BY a.ID ORDER BY a.ArrivalDateTime)

INTO #temp

FROM

#Appointments a;

SELECT

t1.ID,

PrevDate = t2.ArrivalDateTime,

t1.ArrivalDateTime,

TimeSincePrevDate = DATEDIFF(hh, t2.ArrivalDateTime, t1.ArrivalDateTime)

FROM

#temp t1

JOIN #temp t2

ON t1.ID = t2.ID

AND t1.rn = t2.rn + 1

WHERE

DATEDIFF(hh, t2.ArrivalDateTime, t1.ArrivalDateTime) < 72

ORDER BY

t1.id,

t1.ArrivalDateTime;

-- ======================================================================

-- ======================================================================

-- 2012 & up version --

WITH

cte_GetPrev AS (

SELECT

a.ID,

PrevDate = LAG(a.ArrivalDateTime, 1) OVER (PARTITION BY a.ID ORDER BY a.ArrivalDateTime),

a.ArrivalDateTime,

TimeSincePrevDate = DATEDIFF(hh, LAG(a.ArrivalDateTime, 1) OVER (PARTITION BY a.ID ORDER BY a.ArrivalDateTime), a.ArrivalDateTime)

FROM

#Appointments a

)

SELECT

gp.ID,

gp.PrevDate,

gp.ArrivalDateTime,

gp.TimeSincePrevDate

FROM

cte_GetPrev gp

WHERE

gp.TimeSincePrevDate < 72;