What is the significance of queue depth in the MRI exercise in P4 tutorial and where exactly is inband network telemetry used ?
Hi akshara, welcome to the community.
Consider that my answer is just a personal opinion about the exercise and its significance. I did not make it so this is just my understanding about it.
The exercise you point seem to be this one. Answering your questions, let me first go with the second question:
and where exactly is inband network telemetry used
In-band Network Telemetry (INT), as defined in the specification, includes multiple headers like the INT shim, INT meta (in INt-MD mode) and possibly the INT metadata stack (if any has been appended). Different INT modes will require different configurations, but as a general view, you can see that it requires a deeper approach than the one followed in the exercise. In fact, if you check the first sentence from the exercise:
The objective of this tutorial is to extend basic L3 forwarding with a scaled-down version of In-Band Network Telemetry (INT), which we call Multi-Hop Route Inspection (MRI).
So there is no real INT used, but instead, a custom “protocol” named MRI which follows the same (or almost the same) principles as INT. I believe that the developers mention INT in the exercise because MRI follows those principles (like carrying in-band telemetry data). In general terms it is the same as using INT but a scaled down protocol and exercise, much more suitable for a tutorial than actual INT implementations  (there are more examples around, easy to Google ).
So checking your first question:
What is the significance of queue depth in the MRI exercise in P4 tutorial
I believe that the whole “spirit” of the exercise is to learn how to integrate a custom protocol that can track the path (multi route hop inspection), and additionally, include some metadata in the packet. I have checked the exercise and I do not see any particular use of the
qdepth apart from verification purposes at the destination.