Answer by Professional Japanese Teacher
To tell the guest that you can’t get through the line, you can say
Omataseshite, mooshiwakearimasen. Resutoran ni nakanaka denwa ga tsuujimasen. Moosukoshi omachiitadakemasu ka.
I’m sorry to keep you waiting. I cannot get through the restaurant. Would you please wait for a while?
To tell the guest that you’ve gotten through the line, you can say
Omataseshimashita. Yatto denwa ga tsuujimashita.
I’m sorry to keep you waiting. I’ve finally gotten through the line.
This expression is often used when you have kept someone waiting. There is no direct translation in Japanese. It would sound more Japanese if you use an expression to show apology rather than one that shows gratitude.
For other expressions of showing thanks and gratitude in a business context, see”23 Ways Of Saying Thank You In Business Japanese”.