Yii2:no se puede actualizar el valor de la columna en + 1

Prueba esto:

 Yii::$app->db->createCommand("UPDATE room_types SET total_booked=total_booked+1 WHERE room_type = '$model->room_type' ")->execute();

O

public function actionCreate()
    {
        $model = new CreateBookings();
        if ($model->load(Yii::$app->request->post())) {

    $RoomType = new room_types(); // room type replace with model name
    $RoomType->updateCounters(['total_booked' => 1]);

      $model->save();
            return $this->redirect(['view', 'id' => $model->id]);
        } else {
            return $this->render('create', [
                'model' => $model,
            ]);
        }
    }

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