How can I find correlation between features? The problem

I want to figure out how routers correlate between each other. Like, if a specific error occurred in router A, and almost at the same time the error occurs in router B, they probably have some connection with each other (are at one line).  

The Data

Suppose I have a dataframe that looks like this:  

|Router|Error|Duration|Timestamp          |    
|DB-XX |GSM  |26.5374 |2019-05-01 00:20:14|     
|DT-XY |AUC  |15.5400 |2019-05-01 01:15:01|     
|DR-YY |AUC  |02.0333 |2019-05-01 01:17:13|     
|DP-YX |LOC  |45.2609 |2019-05-01 00:01:10|    


The question

What is the best way to deal with it? Regression (one vs the rest) for each router? The problem is, that there are hundreds of models and I also want to reduce computational costs...
Correlation is a metric that can be used when two features have the same number of total observations. Given your scenario, each router can fail for different number of times. So, we can't estimate correlation between two routers since they will be having different number of observations.

One thing you can do would be to convert every router into a time series signal, using the provided duration and start time. You can they compute the correlation then. But, it might not be really informative of the actual situation, as the signal will be predominantly sparse