I had an issue recently and did a bunch of poking around and never really found a resolution. On my iPhone 6, callers were not hearing the distinctive "beep" that normally occurs at the end of each ring when I'm already on a call.
It seems that some people don't like this function, but I like it and I know most of my co-workers and customers know what the sound indicates.
I opened a chat session and the tech I worked with was very patient, but she wasn't able to determine why the beep wasn't present.
I took a look at my wife's iPhone 6, where the beep was working, and I only found one difference between mine and hers. It turned out to be the culprit.
Under Settings>Cellular>Enable LTE there are 3 options - Off, Voice & Data and Data Only.
It turns out that if Voice and Data is on, the "I'm on the phone" beep won't work. However, if you change the setting to Data Only, the beep returns.
This has something to do with the calls going over the LTE network, not the Verizon towers, so it overrides some of the Verizon specific features (according to the tech).
Anyways, I hope this helps someone along the way that also relies on this feature to let the boss know you're not ignoring them 
