To know how many tickets are active on a particular day, you need to know both when a ticket first became active and when it was closed. Your design already contains this data, so the count can be generated without adding any data. This can be done by calculating the number if days between the open and close and then joining that with a data set large enough to accommodate your longest open duration. Here is an example in Oracle doing something conceptually similar.
DROP TABLE Tickets;
CREATE TABLE Tickets (ID Number(10), CreateDate Date, CloseDate Date);
INSERT INTO Tickets VALUES (1, to_date('12/30/2012','MM/DD/YYYY')
, to_date('12/31/2012','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (2, to_date('12/30/2012','MM/DD/YYYY')
, to_date('01/05/2013','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (3, to_date('12/30/2012','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (4, to_date('12/31/2012','MM/DD/YYYY')
, to_date('01/01/2013','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (5, to_date('12/31/2012','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (6, to_date('12/31/2012','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (7, to_date('01/01/2013','MM/DD/YYYY')
, to_date('01/20/2013','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (8, to_date('01/01/2013','MM/DD/YYYY')
, to_date('01/02/2013','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (9, to_date('01/01/2013','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (10, to_date('01/01/2013','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (11, to_date('01/01/2013','MM/DD/YYYY')
, NULL);
INSERT INTO Tickets VALUES (12,to_date('01/01/2013','MM/DD/YYYY')
, to_date('01/04/2013','MM/DD/YYYY'));
INSERT INTO Tickets VALUES (13, to_date('01/02/2013','MM/DD/YYYY')
, to_date('01/20/2013','MM/DD/YYYY'));
COMMIT;
SELECT ActiveDate, count(*) FROM
(
SELECT ID, CreateDate, CreateDate-1+x ActiveDate, NVL(CloseDate,TRUNC(sysdate)) CloseDate
FROM Tickets
JOIN (SELECT Level x FROM dual CONNECT BY Level < 999)
ON x <= (NVL(CloseDate,TRUNC(sysdate)) - CreateDate)
)
GROUP BY ActiveDate ORDER BY ActiveDate;
SQL Fiddle