Probability distribution for sms response responses

Question

I am writing an application using sms as a connection. I decided to subscribe to the sms gateway, which provides me with an API for this.

The API has functions for sending, as well as for drawing new messages. However, it does not have any push functions.

To make my queries more efficient, I am looking for data on how long people wait before they reply to a text message as a function of probability.

Additional Information:

• The application is interactive (as it may be), so I believe that time will be very similar to real human-human communication.
• I don’t think that differences in personal style will have a big impact on the correct times and frequencies for the request, so the average data should be accurate.

Update

I was impressed and provoked by many great answers. I came to the conclusion that my best hit would be some adaptable heuristics, including exponential (or possibly polynomial) digression.

Everywhere I will collect statistics for further analysis. Maybe something will appear. I think that I will deceive the launch of the algorithm for generating poll-frankenies from the probability distribution. It will be fun.

Thanks again.

Answer 1

In the absence of any real data, the best solution would be to write code so that the application adjusts the latency based on the current response time history.

Main idea:

Step 1: Set the initial stretch frequency once every x seconds.

Step 2: Pull messages at the above frequency for duration y.

Step 3: If you find that messages are always waiting for you to reduce the decrease in x, otherwise increase x.

A few design considerations:

• Forever adjust or stop

  You can repeat steps 2 and 3 forever, in which case the application is dynamically configured according to sms templates. In addition, you can stop after a while to reduce application overhead.

• Setting criteria: for the client or for all clients

  You can configure in step 3 based on the client or for all clients.

I believe that the GMAIL smtp service runs on the same lines.

Answer 2

Well, I would suggest finding some statistics about the daily use of SMS / text messages by geographic location and age groups and make an average daily value, but this will not be an accurate measurement for everyone.

Answer 3

Good question.

Keep in mind that people can have multiple tasks and that responding to a text message can be one of these tasks. If each of these tasks takes a period of time that is exponentially distributed, the time required to respond to the text message is the sum of these tasks. The sum of n iid random variables has a Gamma distribution.

The number of tasks before returning the text also has a distributed distribution of, say, Poisson. I don’t have time to get the resulting distribution, but imitating it with @Risk, I get either a Weibull or Gamma distribution.

Answer 4

SMS is an instant messaging service, so you need to add a delay that can be added by various SMSC (Short Message Service Centers) along the way. If you are connecting to one of the large aggregation houses (Sybase, TNS, mBlox, etc.), Commercial bulk SMS providers (Clickatel, etc.), then you need to allow the message to transfer your network, as well as the network of operators. If you use a small store, then most likely they use a GSM modem (or modems), and there is a limit to the bandwidth of the message, which can receive and process (as well as push)

All that said if you use a direct connection or one of the large MO messages (mobile messages) arriving to you as a CP (content provider) takes less than 5 seconds. Add to this the time that Mobile subscribers respond to.

I would say that anonymous evidence constitutes the services that I worked on earlier, when the Mobile Subscriber should provide a simple answer, usually within 10 seconds or not be performed at all.

If you are responsible for specific answers, I would interrogate after 5 and 10 seconds, and then apply exponential indentation.

All this from a North American point of view. Europe will be pretty close, but places like Africa and Asia will be a little slower as networks are a little slower. (if you are not connected directly to the operator, and even then some of them are slow).