Assuming the Imperium consists of 11,000 systems (the Imperium proper, plus the area of the illegal, secessionist ‘Solomani Confederation’), and a week to jump from system to system, nonstop, then you can visit the entire Imperium in 210 years: a pureblooded Vilani could pull it off, if given an early start.
“But it’s still a wanna-be compared to the original, 15,000-system Ziru Sirka!”
Eleven thousand star systems doesn’t even amount to a rounding error before the billion-plus stars within the Orion Arm of the Galaxy (which usually I treat as just a part of the Perseus Arm): and our Galaxy itself contains between 100 billion to 400 billion stars.
And behind every grain-sized part of the sky, is 10,000 galaxies.
“We’ll never conquer space,” said Arthur C. Clarke. He wasn’t kidding.