SQL count number of time series events, with some some start or stop entries missing - sql

Question

I have some start/stop events and I need to count the number of total events but sometimes a start or stop is missing, for example:
Time Event
10:50 START
10:52 STOP
10:59 START
11:01 STOP
11:45 STOP
Count(Event) Where Event='START'
Would return 2, I also need to count the missing START value, so the result should be 3. Any ideas on how this could be done? Thanks!

Answer 1

Two constraints must be met to enable event counting.
Two START-STOP periods cannot overlap.
Two consecutive and chronologically ordered START and STOP event cannot be possibly originated from two different events, namely START+(missing TOP) and (missing START)+STOP.
It the conditions are met, a simple state machine can be implemented to detect the "missing" events. Such a row-by-row logic could (almost always) be implemented using the cursor syntax.
N.B. To exemplify the generality of the cursor method you can also see other answers A (update columns), B (a tedious algo) I made. The code structures are highly similar.
Test Dataset
use [testdb];
if OBJECT_ID('testdb..test') is not null
drop table testdb..test;
create table test (
[time] varchar(50),
[event] varchar(50),
);
insert into test ([time], [event])
values ('10:50', 'START'),('10:52', 'STOP'),('10:59', 'START'),
('11:01', 'STOP'),('11:45', 'STOP'),('11:50', 'STOP'),('11:55', 'START');
select * from test;
Code
/* cursor variables */
-- storage for each row
declare #time varchar(50),
#event varchar(50),
#state int = 0, -- state variable
#count int = 0; -- event count
-- open a cursor ordered by [time]
declare cur CURSOR local
for select [time], [event]
from test
order by [time]
open cur;
/* main loop */
while 1=1 BEGIN
/* fetch next row and check termination condition */
fetch next from cur
into #time, #event;
-- termination condition
if ##FETCH_STATUS <> 0 begin
-- check unfinished START before exit
if #state = 1
set #count += 1;
-- exit loop
break;
end
/* program body */
-- case 1. state = 0 (clear state)
if #state = 0 begin
-- 1-1. normal case -> go to state 1
if #event = 'START'
set #state = 1;
-- 1-2. a STOP without START -> keep state 0 and count++
else if #event = 'STOP'
set #count += 1;
-- guard
else
print '[Error] Bad event name: ' + #event
end
-- case 2. start = 1 (start is found)
else if #state = 1 begin
-- 2-1. normal case -> go to state 0 and count++
if #event = 'STOP' begin
set #count += 1;
set #state = 0;
end
-- 2-2. a START without STOP -> keep state 1 and count++
else if #event = 'START'
set #count += 1;
-- guard
else
print '[Error] Bad event name: ' + #event
end
END
-- cleanup
close cur;
deallocate cur;
Result
print #count; -- correct answer: 5
Tested on SQL Server 2017 (linux docker image, latest version).

Answer 2

Well, you could count each start and then each "stop" where the preceding event is not a start:
select count(*)
from (select t.*,
lag(event) over (order by time) as prev_event
from t
) t
where event = 'start' or
(prev_event = 'stop' and event = 'stop');