Please wait for your mails. First written first comes.
Your patience is requested. First written first arrives.
Mails will come in shortly. First sent first delivered.
「早い者勝ち」First comes first served. をもじりましょう。
気軽な言い方です。
Please wait for your emails. First written first comes.
お詫びの気持ちを込めた丁寧な言い方になります。
Your patience is requested. First written first arrives.
人ではなく、ものを主体にした冷静な言い方です、
Mails will come in shortly. First sent first delivered.
日本 
