I have built a model using tesnorflow serving and also ran it on server using this command:-
bazel-bin/tensorflow_serving/model_servers/tensorflow_model_serv
For rudimentary HTTP request logging, you can set TF_CPP_VMODULE=http_server=1 to set the VLOG level just for the module http_server.cc — that will get you a very bare request log showing incoming requests and some basic error cases:
2020-08-26 10:42:47.225542: I tensorflow_serving/model_servers/http_server.cc:156] Processing HTTP request: POST /v1/models/mymodel:predict body: 761 bytes.
2020-08-26 10:44:32.472497: I tensorflow_serving/model_servers/http_server.cc:139] Ignoring HTTP request: GET /someboguspath
2020-08-26 10:51:36.540963: I tensorflow_serving/model_servers/http_server.cc:156] Processing HTTP request: GET /v1/someboguspath body: 0 bytes.
2020-08-26 10:51:36.541012: I tensorflow_serving/model_servers/http_server.cc:168] Error Processing HTTP/REST request: GET /v1/someboguspath Error: Invalid argument: Malformed request: GET /v1/someboguspath
2020-08-26 10:53:17.039291: I tensorflow_serving/model_servers/http_server.cc:156] Processing HTTP request: GET /v1/models/someboguspath body: 0 bytes.
2020-08-26 10:53:17.039456: I tensorflow_serving/model_servers/http_server.cc:168] Error Processing HTTP/REST request: GET /v1/models/someboguspath Error: Not found: Could not find any versions of model someboguspath
2020-08-26 11:01:43.466636: I tensorflow_serving/model_servers/http_server.cc:156] Processing HTTP request: POST /v1/models/mymodel:predict body: 755 bytes.
2020-08-26 11:01:43.473195: I tensorflow_serving/model_servers/http_server.cc:168] Error Processing HTTP/REST request: POST /v1/models/mymodel:predict Error: Invalid argument: Incompatible shapes: [1,38,768] vs. [1,40,768]
[[{{node model/transformer/embeddings/add}}]]
2020-08-26 11:02:56.435942: I tensorflow_serving/model_servers/http_server.cc:156] Processing HTTP request: POST /v1/models/mymodel:predict body: 754 bytes.
2020-08-26 11:02:56.436762: I tensorflow_serving/model_servers/http_server.cc:168] Error Processing HTTP/REST request: POST /v1/models/mymodel:predict Error: Invalid argument: JSON Parse error: Missing a comma or ']' after an array element. at offset: 61
... you can skim https://github.com/tensorflow/serving/blob/master/tensorflow_serving/model_servers/http_server.cc for occurrences of VLOG(1) << to see all logging statements in this module.
For gRPC probably there's some corresponding module that you can similarly enable VLOG for — I haven't gone looking for it.