"Flux", a novelette by Barrington J. Bayley and Michael Moorcock, also the answer to these old questions; first published in New Worlds Science Fiction #132, July 1963, available at the Internet Archive.
In the Balkans, people are assigned times when they may be awake and times when they must be asleep in cryogenic vaults. But the relatively sparse awake people become nervous and demand to see their frozen relatives; they break into the vaults, killing the occupants.
— Briefly, as is generally known, the European Council gave permission for the Population Phasing Group to conduct an experiment in Greece. This Group, using the principles of suspended animation discovered a few years earlier by Batchovski, instituted total birth-control and placed three-quarters of the population of Greece into suspended animation, the other quarter being thought sufficient to run public and social services and so on, reasoning, quite rationally it seemed, that in this way further population explosion would be averted, less overcrowding would result and the pace of our society could be relaxed. After a given time, the first quarter would go into suspended animation and be replaced by the next quarter and so on. This phasing process did seem to be the most reasonable solution to the Problem of Europe, as it was called.
— However, in ridding the population of claustrophobia, the system produced an effect of extreme agoraphobia. The people, being used to living close together, became restless, and the tension which had preceded the introduction of the PPG Experiment, was turned into new channels. Mobs, exhibiting signs of extreme neurosis, completely insensate and deaf to all reason, attacked what were called the S.A. Vaults and demanded the release of their relatives and friends. The authorities attempted to argue with them but, in the turmoil which followed, were either killed or forced to flee. Unable to
operate the machines keeping the rest of the population in suspended animation, the mobs destroyed them, killing the people they had intended to re-awaken.
In another experiment (unless perchance I am conflating two stories), men and women are placed in the vaults alternately and become bitter enemies of one another.
—Unable to wait any longer, the Council reluctantly agreed, and a large part of Bavaria was set aside so that the plan of the Untermeyer faction could be implemented. The plan necessitated sexual segregation. Men and women were separated and each given an intensive psychoconditioning to hate the opposite sex. Next, acts were passed making contact with the opposite sex punishable by death. This act had to be enforced frequently, although not as frequently as originally had been thought. Ironically, Untermeyer was one of the first to be punished under the act.
—It is difficult these days, to make a clear assessment of the results of this experiment (which so quickly got out of hand and resulted in the literal war between the sexes, which now exists with cannibalism so prevalent, each sex regarding it as lawful to eat a member of the other) but it is obvious that measures for reassimilation have so far met with little success and that, since this creed has now spread through Germany, Scandinavia and elsewhere, an incredible depletion of life in Northern Europe is likely. In the long run, of course, repopulation will result as the roving hordes from France and Spain press northward. Europe, having collapsed is ready for conquest, and when the squabblings of America and the United East are ended, either by bloodshed or peaceful negotiation, Europe's only salvation may be in coming under the sway of one of those powers. However, as we know, both these powers have similar problems to those of Europe in its last days of sanity.
All this is viewed through the eyes of a protagonist who, if memory serves, is sent ahead in time to see the results of the experiments.
"Our only hope lies in discovering how events are organized in time—this might sound highly speculative for such a serious and practical matter, but this is what things have come to. In order to take effective action in the present, we must first know the future. This is the mission we have in mind for you. The Research Complex at Geneva has found a way to deposit a man some years in the future and bring him back. You will be sent ten years forward to find out what will happen and how it will come about. You will then return, report your findings to us, and we will use this information to guide our actions, and also—scientifically—to analyze the laws governing the sequence of time. This is how we hope to formulate a method of human government for use by future ages, and, perhaps, remove the random element from human affairs."