Allow me to point out a rare example of a famine in a modern industrialised nation and it's consequences: the Netherlands during the winter of '44/'45.
http://en.wikipedia.org/wiki/Hongerwinter

A railwaystrike combined with an offensive that cut the country in half, Germans blocking food transports to the west of the Netherlands in retaliation for the railwaystrike, and an unusually harsh winter, lead to a famine that caused circa 18000 people to die (on a population of 9 million).

There was not a lot of violence; surprisingly little actually. Families trekked long and far to reach farmers, with whom they bartered for food. Most farmers were reasonable, some were shrewd, some were stolen from and some took advantage of the situation (it's been suggested the latter 2 categories overlapped). There were NO violent robberies. There were instances of German-controlled constables seizing food on the roads, and subsequently dumping it in a ditch, and there were examples of hungry people stealing collected food from other hungry people when they weren't looking.

Mostly timid victims, I'd say.

Regarding to how it would play out in a modern day situation, I think it would depend on local culture (vis a vis attitude), gun prevalence, and mainly: the suddenness. If oil *suddenly* stopped flowing, and food suddenly stopped being transported into populated areas, panic will set in, and violence will occur. If it happens slowly (i.e. food harder to get but not impossible), the population will sooner grow morose and discontent, a much more manageable combination.