Time Travel book from 70's where people were sent from 150 years in the future to our present time

Question

I read this book either in the late 70's or early 80's. It was set in a distant future, about 150 years in the future. Numerous people were being sent from that time to the present. This occurred for a period of 20 or 30 years. (I don't remember.) After that, no more people were sent. Fast forward to the future.

The time travel device could send to any time, the farther back you went the less accurate the arrival time. The person who made the device did a test where a pig was sent to the middle ages. He found it mentioned in some old history book. The person who made the device at the end sent himself to ancient Rome. The person who made the device sent large numbers of people back 150 years because that was fairly accurate and it would be easier for a traveler to arrive in a period where people were accustomed to time travelers arriving.

Most of the book was set in the future 150 years from now. After 150 years (when people stopped being sent) they were now at the time where people needed to be sent backwards.

The future was very dystopian. The world had a system where everyone had a level. So the ruler was the only "level 1" (or maybe it was rank.) High level leaders were rank 2 or 3. And just ordinary people were levels in the 20's or 30's. The amount of privilege's you received were based on the rank level. (I remember the protagonist able to get some water for a shower as his level was high enough. Otherwise it was just an ultrasound shower of some sort)

The level 1 ruler wanted to make sure people were sent back like they were supposed to, fearing disruption of the timeline if they were not. The level 1 ruler was basically immortal and would have surgery done while awake to keep the ability to run things. The level 1 ruler was also building a giant subway system to travel around Earth specifically mentioning he didn't need it it was just a whim.

The protagonist had somehow figured out a way to get some privileges of a level 3, far above what he should have.

Answer 1

The Time Hoppers by Robert Silverberg, published 1967.

According to an Amazon review:

In "The Time Hoppers," the year is 2490, and the Earth has become an overpopulated, overdeveloped mess. The bulk of humanity--at least, those with a Class 10 rating and below--lives in tiny, windowless, one-room apartments with their small nuclear families. The reader meets Joseph Quellen, a Class 7 by dint of his position as a "CrimeSec" in the Secretariat of Crime, who lives in the impossibly widespread city known as Appalachia.
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For the previous five years, some unknown person has enabled some 60,000 folks to flee backwards in time; the High Government wants the emigration ended, and the time travel device in its own hands.
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"The Time Hoppers" is also a trove of ideas that Silverberg would develop more fully in his later work: Peter Kloofman, the 132-year-old Class One governmental head, who has stayed alive only via multiple organ transplants, is but a warm-up for the Genghis II Mao IV Khan character in 1976's "Shadrach in the Furnace"