The best way to accelerate the process is to revise a paper quickly and be responsive to advice given by the editor and the referee. Typically, an accepted paper will have undergone two or three revisions. I resubmitted my paper and received a report from a different referee. The editor wants the opinion of a referee with different knowledge from the first referee to make the paper converge faster. For instance, the first referee might have been a theorist and now the editor wants advice from an empiricist.
Every effort is made to assign to each paper the most appropriate referee.
Authors can help the editor who assigns a referee by having an abstract, an introduction and a conclusion that are clear, precise, and reflect the contribution of the paper accurately. Omitting an author from the references hoping that, as a result, the editor will not think of asking him or her to referee the paper is generally noticed by the editor. Typically, the first referee asked to offer advice on a paper will respond with a referee's report. However, referees are busy and successful colleagues. If, when reading the paper, they find it difficult or impossible to understand because of poor and careless exposition, they may choose to return the paper without a report.