Retiring rooms are available in New Delhi on a first come first serve basis. My personal experience is that they issue you rooms/dormitories (AC/Non-AC) for 12 hours 8am-8pm or 8pm-8am. So, if you contact the Retiring Room Matron/Attendant at New Delhi by 7:30am, he should let you know the availability. My suggestion would be to go to New Delhi as soon as you get down from Rajdhani. That's because Nizamuddin has only 2 retiring rooms while NDLS has 10 room and many beds in dormitory too. So, your chances are good there. As a backup plan, you can get very cheap hotels (although very dirty) in Paharganj Market very near to NDLS railway station (Rs 300-350). Amritsar Shatabdi will depart from platform 1, which is also at Paharganj side. I would recommend reserving tickets in 12013 Shatabdi, instead of Paschim Express. All the best!