This isn't an easy question to answer because there are dozens of factors to take into consideration ... The simplest way to put it is that they release a new console when they think that their medium to long term strategy depends on new hardware to maintain or increase sales.
Quite often the market leader is "Forced" to release a new console because their competition releases a console and they can not let that console build support (for fear of losing their market position); and often the trailing consoles are forced to release a new console because of poor sales or manufacturing difficulty. Microsoft released the XBox 360 because they couldn't manufacture the XBox anymore which triggered Sony to release the PS3; Sega released the Dreamcast because the Saturn's poor sales prevented them from being a profitable company which triggered Sony to release the PS2; and Sony released the PSP to take over the handheld market and Nintendo responded with the Nintendo DS.
I can't think of any generation which was started by the market leading console manufacturer, but every time the successor to the market leading console has been given a head start they have dominated the generation.
