Population of medieval central asian cities

I heard that several medieval muslim cities in central asia, persia(like Herat, Samarkand, Bukhara, Urgench, Merv) had more than 100,000 residents.

https://en.wikipedia.org/wiki/Historical_urban_community_sizes
https://en.wikipedia.org/wiki/Herat
https://en.wikipedia.org/wiki/History_of_Bukhara

In wikipedia, it says

Merv: 500,000 at height
Nishapur: 125,000 at height
Herat: had more than 440,000 houses(which indicates that the city's population was more than a million)
Bukhara: more than 300,000

Also, some medieval muslim documents point that during the fall of Herat, Nishapur, Merv, Urgench by the mongols, hundreds of thousands or even millions of people were killed(which indicates that these cities had hundreds of thousands of population).




But can this be really true? I personally think the population of medieval central asian, persian cities is grossly exaggerated. In fact, back in medieval times persia and central asia's productivity(especially agriculture) was not large enough to support these cities. Also, I've heard that even during 19th century central asia(including Uzbekistan, Turkmenistan, Tajikistan, Kyrgyzstan) had population less than 6 million, Iran had population close to 10 million and Afghanistan had 3 million. So the total population of central asia and persia was less than 20 million even in 19th century. In medieval times, however(let's say 12th century) population of this region must have been much lower than 20 million, maybe around 10 to 15 million.

So the question is: could a region with population of 10~15 million support several cities with population more than 100,000? I would definiely say "NO". To support these large cities, the population of Persia and Central Asia should have been more than 30 million or 40 million. Even the Byzantine Empire which had population close to persia+central asia (at AD 10th century)had only two cities with population more than 100,000 residents: Constantinople with 400,000 and Thessaloniki with 150,000. Although central asia and persia was very large(as large as the realm of Roman Empire) its productivity was very low because much of the land was made up of barren desert and mountains. So its agricultural productivity was definitely not high enough to feed hundreds of thousands of city residents. I personally believe that medieval central asia and persia(of about 12th century)had one or two cities with more than 100,000 residents. Maybe Merv, which was the capital of Seljuk Empire, and Isfahan, which was also the capital of Seljuk Empire and the biggest city in persia, were the ones.