Pyroclastic flows have been directly measured at up to 90-130 m/s (200-290 mph), though even more typical speeds of 10-100 m/s (22 - 220 mph) exceed the pace of a walking human in good shape, let alone the elderly, young, or infirm. I'm not aware of specific indicated speeds of the 79 CE Vesuvius flows.

Escape on foot would have been at ~5 kph (3 mph). The safest destination from Pompeii, we can say in 2020 with hindsight, would have been perpendicular to the wind flow, to the north-east, at least 10 km (3+ hours continuous walking), up-hill.

Keep in mind that modern vulcanology, meterology, risk analysis, and disaster mitigation were also in their infancies, as well as wide-area information broadcasting, making such information largely unavailable at the time. In particular, the likely "obvious" safety of water (south-west) lead not only toward the centre of the kill zone, but a dead end as well. Walking strictly away from Vesuvius would reduce risk, but involved a longer path to safety than the NE route.

https://en.wikipedia.org/wiki/Eruption_of_Mount_Vesuvius_in_...

Few people at the time had access to SUVs, high-speed watercraft, helicopters, motorcycles, or bicycles, to aid in escape.

The wind was blowing onshore, a factor substantially credited to the death of Pliny the Elder, who, with the words "Fortune favours the brave" had attempted a sea rescue with his naval fleet, but found itself trapped at the beach. Pliny died there.

Temperatures within the cloud were a minimum of 100C (212F), and reached as much as 360C (500F) or more, all deadly. Wood and human remains at Herculaneum show carbonisation -- effectively having been turned into charcoal. Temperatures were extreme.

The surges themselves occurred well into the eruption, after substantial damage to the city by both earthquakes and bombardment, lasting overnight.

Total volcanic deposits on Herculaneum, which was spared windblown ash and hence resulted only from pyroclastic flows, were 23 meters (75 feet). Digging your way out of 7 storeys of searing-hot rock is a challenge for many people.

Any remaining survivors at the time of the surge would likely have been in terror, sleep deprived, utterly confused by the transformation to their surroundings, and probably not most able to have escaped in the first place. The eruption occurred during a festival in which the local population would have been increased by tourists and visitors. In Pompeii, though the initial pyroclastic surge saw lower temperatures close to the ground, later surgers (by surviving evidence) saw consistent temperatures throughout the vertical column, even at or below ground level. Surviving in a basement or cellar was not an option.

Total population of Pompeii and Herculaneum is estimated at ~16-20k, with about 1,500 bodies having been identified to date. Total victims clearly lie somewhere between these two numbers, and there's little agreement as to the precise number, though a fair argument can be made that mortality was a minimum of 10-20%.

At some point, if you were within the kill zone of Vesuvious, regardless of your mental state or fitness, you were walking dead. You might not have been dead yet, but there was simply no way out or to survivable shelter. There was no survivable shelter within the zone.

Again: by midnight August 28, if you were anywhere but heading north-east of Pompeii, or north-west of Herculaneum, you were already dead.