Disponibilidad de reserva de MySQL, rangos de fechas superpuestas

Cree una lista de todos los límites de la reserva (es decir, fechas de inicio y finalización) que ocurren en el período deseado:

  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

Agregue a eso el límite que ocurre inmediatamente antes del período deseado:

-- [ 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

Haga una combinación externa entre este resultado y las bookings tabla, manteniendo todos los límites pero solo incluyendo una reserva si contribuye al número de personas simultáneas después el límite:
```
FROM bookings RIGHT JOIN (
  -- [ from part 2 above ]
) t ON date_start <= boundary AND boundary < date_end
```

Sume el número de personas en cada límite:

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

Encuentra el máximo y el mínimo:

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

Poniendo todo junto:

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

Véalo en sqlfiddle .