Trains in Uzbekistan

Travelling to Uzbekistan next week and having some issues with finding availability for the fast Afrosiyob train tickets.

• Tashkent to Bukhara (Wed, 4th June)
• Bukhara to Samarkand (Thurs, 5th June)
• Samarkand to Tashkent (Fri, 6th June)

Can someone help me find the fast train tickets, or point me to the right websites? I have looked on 12GO, tickets.kz, and eticket.railway.uz but cannot find any fast trains. All the options are slow trains taking 6-7 hours! Would be eternally grateful for some help. Thanks a lot!