Kutaa Señor Vilhjalmur Stefansson. It’s time for me to get back to blogging as well.

I visited Liberty Island and Ellis Island last month, Ellis Island for the first time in my life, and had a good time. The immigrant experience has changed quite a bit since the immigration station at Ellis Island closed. Journeys of exploration are also not like they used to be in what seem like more heroic eras. The immigrant journey still involves waiting, but waiting for an immigrant visa interview rather than waiting on a vessel as it crosses the ocean. In this post, I want to present some data I collected about immigrant visa appointment schedules from the Consulate General of the United States in Mumbai. I’m hopeful that this post will attract some traffic from around the world, perhaps “tired”, “poor”, “huddled masses yearning to breathe free,” but probably not.

The Mumbai consulate lists interview dates for immigrant visas on their website by case number here. An example of an entry is this:

BMB2010568011 IR5 10/6/2010 7:30

where the first item is the case number, the second item is the type of immigrant visa, the third item is the interview date at which the applicant is supposed to show up at the consulate, and the fourth item is the interview time. For bureaucratic reasons, the case number is assigned by the State Department in an interesting way. The first three characters indicate the embassy or consulate, here BMB referring to Mumbai (Bombay). Other codes are things like LND for London, MNL for Manila, NWD for New Delhi, and OUG for Ouagadougou. The next four characters indicating a year, the three characters after that the day of the year plus 500, and the last three characters the sequential case number assigned that day. The most interesting of these is the day of the year plus 500. In the example above, 568 indicates the 68th day of 2010, which is March 10.

This date, 3/10/2010, is when the case is given a case number by the National Visa Center in Portsmouth, NH. After this assignment, the case is forwarded to the appropriate consulate or embassy, who then assign interview dates. Before the consulate or embassy assigns the interview date, the applicant may also have to fill out some other form at the consulate or embassy which comes in the so-called Packet 3. For example with the K1 visa, the applicant needs to submit a DS-230 Part I. This page has a nice flowchart describing the procedure for the K1 visa.

Thus based on the case number and interview date, one can determine the immigrant visa interview waiting time. I collected interview date listings and calculated waiting times for 26 months in Mumbai: 8/2007, 1/2008, 3/2008, 4/2008, 5/2008, 10/2008, 11/2008, 1/2009, 2/2009, 4/2009, 5/2009, 6/2009, 7/2009, 8/2009, 9/2009, 10/2009, 12/2009, 2/2010, 3/2010, 4/2010, 5/2010, 6/2010, 7/2010, 8/2010, 9/2010, 10/2010, and 11/2010. There were 543 K1 visa cases in the data. A histogram of waiting time is as follows:

This histogram looked to me like a gamma distribution with a 6 week delay. Gamma distributions are often used to model waiting time in queueing theory and other places, so it’s interesting that the data reveals the same form. I did a maximum likelihood estimate of the parameters of a gamma distribution with 6 week delay and obtained the following:

The blue line is the maximum likelihood fit, and the green and red dashed lines represent a 95% confidence interval.

The mean waiting time for a K1 visa interview at Mumbai from the date assigned by the National Visa Center is 114.6 days. The means of the 95% confidence interval boundaries are 99.4 days and 134.0 days.

The mode of the 543 data samples is 76 days. The mode of the maximum likelihood fit distribution is 78.6 days. The modes of the 95% confidence interval boundaries are 67.6 days and 93.1 days.

The bottom line is that one should expect a K1 visa interview 2-3 months after the National Visa Center assigns the case. It would be interesting to analyze whether or not there are seasonal trends in the waiting times. (For example, work on stochastic analysis and optimization of workforce evolution predicts hiring, termination, and job role transitions in December 2010 based on estimates of transition probabilities in previous Decembers.) What can be done to make the waiting time shorter for a specific case is another interesting question, but one beyond the scope of this analysis. Once the case number is known, contacting the State Department at (603)-334-0700 and visiting the embassy or consulate even before receipt of Packet 3 may be good ways to expedite the process.

If a reader would like the raw data used in this analysis, or would like this analysis performed for an immigrant visa type other than K1, e.g. CR1 visa, DV visa, E2 visa, E3 visa, F1 visa, F2B visa, F3 visa, F4 visa, FX visa, IR1 visa, IR5 visa, K3 visa, SB1 visa, and SD visa, please leave a comment. Once there is enough interest, I will make that happen.

Are you still bound for Antartica, Lav?