Short of sleep,... como se traduciria al español?

Question

Tengo este parrafo y no se como podria traducir la ultima oracion. Si alguien pudiera ayudarme estaria bueno! Gracias!

History tells us, however, that cities have always been in crisis. Ancient Rome had terrible traffic problems. One solution tried was to allow wheeled vehicles into the city only at night. But that left the city's population ill-tempered and short of sleep.

Answer 1

But that left the city's population ill-tempered and short of sleep.

Pero eso dejo a la población [de la ciudad] malhumorada y falta de sueño.

Here we usually say Estoy falto de sueño to express we have not slept enough.

(Note: it´s not the same as falta de sueños, which would be like ´ a lack of dreams´)

Answer 2

...falta de sueño

...privada de sueño (this is more extreme)