The original 360 family was announced in 1964, and the lower midrange model 40 was the first to ship a year later. The most interesting version was model 67 (first shipped June 1966) which had hardware to support virtual memory. IBM had planned a special operating system for it (TSS/360), which they never managed to get to work well enough to be usable. Within IBM, model 67 was used with a system known as CP-67, which allowed a single 360/67 to simulate multiple machines of various models. This turned out to be very useful for developing operating systems.Indeed, I was temporarily assigned to help with the development of TSS/360 and did some of the modules. That OS got nowhere. The CP-67 OS, really a research project, became a very successful "un-planned" product. This was the first commercially used virtual machine OS (akin to VMWare of today). The CP-67 OS became the VM/370 OS with the next generation of CPUs.
And in the above, a reference to: [link|http://www.research.ibm.com/journal/rd/441/amdahl.pdf| Architecture of the IBM System/360] by Gene Amdahl, Fred Brooks and G A Blaauw. (16 pages, PDF).