Mucus plug

This has came out all day long, most of the time there’s blood in it too, there’s some in this picture but not a lot. I have an induction set for Saturday but I’d really love to go in on my own. How long after losing it did you go into labor? I’ve had mucus plug coming out since about 35 weeks but it has increased this week and now tinged with blood. I’m also 39 weeks & 3 days.