I have submitted a paper on applied probability in one of SIAM journals. The paper is under review for 9 months. I asked the editor 1 month ago about it, I was told that one review report has come and they are waiting for the other. Will it be ok if I politely inquire about it now (I have inquired 3 times till now after submission). How frequently I should inquire from now on so that it is not rude. Another question is that, is it the usual time taken for review in SIAM journals?
My experience is in Pure Mathematics, not in Applied Probability. In my area, at least, it is unusual to have a full report recommending acceptance (pending revisions) in under a year, although it can happen much faster. It has happened to me within a few weeks, but that is the exception rather than the rule. My first paper was three pages long and took about 10 months from submission to acceptance. At the time, this seemed quite long to me, but by now I realise it was actually rather reasonable.
It is certainly "fine to inquire about a paper that's been under review for around 9 months". However, if you have already inquired 3 times, and most recently one month ago, then I suggest that you should wait. Editors are busy people, and it can be hard to find willing referees, and even the ones you find are busy people too, so it may take a while to get a report. You don't want to make the editor cranky by inquiring too often. My rule of thumb (again, in Pure Mathematics) is that it is OK to inquire after about 3 months or so, just to make sure the paper has not fallen through the cracks (it happens), and perhaps give a gentle reminder. But usually it would be about 6 months before I inquire, and not more than every three months after that.
It may be that there is an important reason, such as upcoming job applications / interviews etc, that some (even informal/partial) feedback on the status of the paper would be useful. In that case, it is OK to mention this. As long as it is done respectfully, and without appearing impatient, the editor is likely to be sympathetic. However, they are still unlikely to be able to do very much about it, unless you just happen to write at a time where reports have arrived but the editor hasn't yet been able to deal with them.
TL;DR: Be patient and wait another couple of months. It sounds as though your paper is progressing normally.
You have access to the journal through your institution, yes?
I suggest that you randomly selection some papers, from recent years.
Look at the date submitted. Also do consider how many times these were revised. This is a good proxy for how thoroughly the reviewers tend to scrutinize papers. It takes much longer to write a review, with improvements, for a paper longer than a few pages, rather than just clicking as reviewer, Accept As Is, or Reject, and 5 or 2 out of 1 to 5 in two or three menus.
Compare this with the date accepted.
Most often the time between dates is correlated for all the articles you picked. Randomly.
If so, before submitting to a journal, one can anticipate from this on average how long you will wait before you get feedback.
Some journals it is a year interval. Some it is rejected by the editor in days, or sent out for reviews, which come back in a few weeks.
If the intervals are not correlated, but some articles take two months, others a dozen, to be accepted, that typically is the case for journals which are interdisciplinary. Difficult to get reviewers who accept, except if this is a very widely read journal in science or a broad field in general. If the journal is too specialized, same problem; it takes long, relatively long to find reviewers willing to referee.