Disponibilidade de reserva do MySQL, intervalos de datas sobrepostos

1. 
   Construa uma lista de todos os limites de reserva (ou seja, datas de início e término) que ocorrem no período desejado:
   

     SELECT date_start AS boundary
     FROM   bookings
     WHERE  date_start BETWEEN @start AND @end
   UNION
     SELECT date_end
     FROM   bookings
     WHERE  date_end BETWEEN @start AND @end
   

2. 
   Adicione a isso o limite que ocorre imediatamente antes do período desejado:
   

   -- [ from part 1 above ]
   UNION
     SELECT MAX(boundary)
     FROM (
       SELECT MAX(date_start) AS boundary
       FROM   bookings
       WHERE  date_start <= @start
     UNION ALL
       SELECT MAX(date_end)
       FROM   bookings
       WHERE  date_end <= @end
     ) t
   

3. 
   Faça uma junção externa entre este resultado e as bookings mesa, mantendo todos os limites, mas apenas incluindo uma reserva se contribuir para o número de pessoas simultâneas depois o limite:
   

   FROM bookings RIGHT JOIN (
     -- [ from part 2 above ]
   ) t ON date_start <= boundary AND boundary < date_end
   

4. 
   Some o número de pessoas em cada fronteira:
   

   SELECT IFNULL(SUM(quantity),0) AS simultaneous_people
   -- [ from part 3 above ]
   GROUP BY boundary
   

5. 
   Encontre o máximo e o mínimo:
   

   SELECT MIN(simultaneous_people),
          MAX(simultaneous_people)
   FROM (
     -- [ from part 4 above ]
   ) t
   

SELECT MIN(simultaneous_people),
       MAX(simultaneous_people)
FROM (
  SELECT IFNULL(SUM(quantity),0) AS simultaneous_people
  FROM   bookings RIGHT JOIN (
    SELECT date_start AS boundary
    FROM   bookings
    WHERE  date_start BETWEEN @start AND @end
  UNION
    SELECT date_end
    FROM   bookings
    WHERE  date_end BETWEEN @start AND @end
  UNION
    SELECT MAX(boundary)
    FROM (
      SELECT MAX(date_start) AS boundary
      FROM   bookings
      WHERE  date_start <= @start
    UNION ALL
      SELECT MAX(date_end)
      FROM   bookings
      WHERE  date_end <= @end
    ) t
  ) t ON date_start <= boundary AND boundary < date_end
  GROUP BY boundary
) t