EDIT December 26, 2019:
I found the issue of the server problems: the culprit was the server GUI, I tested this by loading up my old world I had issues with and still had the spike problems. I edited my custom bat file that allocates 4GB of memory now and a few other stuff to let my out-of-country friends play latency free on my home hosted server. By changing the file to tell it to run the 'nogui' part, the server latency spikes stopped completely as my friends said their connections were no longer laggy by any means. Using the Tab key showed their icons all as 4 or 5 bars on my end (instead of the old 0 to 3 bars) so I believe the entire issue was just having the server GUI running when the modded server was running and had at least 1 player in.
TL;DR: use the 'nogui' command in your bat file for the server.
END OF EDIT;
When starting the server jar, and no one is logged into the server, the server runs at a constant ~20-30% memory usage. *see serverGraph1.png
When someone logs into the server, the memory steadily rises and then plummets only to repeat the cycle forever. The nature of this causes in-game lag/latency as the server reaches high memory usage. *see serverGraph2.png
The nature of the spikes cause server-client issues. Players sometimes look like they aren't moving but then teleport to where they were moving all along. Sometimes players are kicked for this as the server catches up and see the player movement and calls it flying. Entities are not properly translated from the client or server through normal means when the spikes are at their highest. Blocks are delayed when destroyed (still exist for a moment and then vanish and drop the item they drop).
Also, at the start of this, the server will throw 5 warnings of ambiguity between the various teleport commands. The memory usage here at the start also looks different from past versions. Not sure if this is expected or not but see serverOutput1.png
Summary:
Start of server throws teleport ambiguity warnings.
Server runs fine at a constant memory usage until someone logs on.
When 1+ people are logged on (via localhost, LAN, or outside connection), memory spikes begin to start.
Server spikes stop when all players leave the server.
Linked issues
is duplicated by 4
relates to 2
Attachments
Comments 12
I have the same issue on a 1.13.2 server.
Where the average tick for the server is 0.033 constantly, but when someone joins the server's average tick rate becomes in the 20ms and it immediately starts to build up memory usage then suddenly drop.
Is this just a problem with this version of Minecraft, 1.13.X?
Here is a picture of the Issue. with task manager in the background like in the other picture.
[media]I hope this can be fixed, I check my email regularly.
I am having the exact same issue on 1.13.2. Mine cycles between 600mb and 2200mb and keeps repeating. I have 8G allocated to the Windows Server and 6G allocated to the Minecraft Server.
Confirmed for 19w08a
Confirmed issue on a server in Windows 10 1809 build (latest) and snapshot 19w12b. Using flags -xms 10G -xmx 10G in 64-bit java. The 10 gigs of memory get filled quite fast while standing still, then garbage collection happens and goes back to 1G memory and starts filling again. When flying on creative mode or using elytra, the sawtooth pattern gets quite ridiculous: like a full spike every 1-2 seconds and countless "Can't keep up" messages show up despite CPU topping at 50% usage.
Guaranteed there's a memory leak somewhere in the code.

This ticket seems to be describing 2 different things.
First, there's the memory usage, which cycles as memory is allocated and then cleared by the garbage collector. This behaviour, while not entirely unusual for the java virtual machine, is not indicative of a memory leak, since that would suggest the memory is not being freed. It's also a lot more difficult to leak memory in a Java application compared to some other languages.
Second is the latency/high tick times on the server.
From what I can tell, there isn't any evidence being presented here to show that these two problems are related. Seeing as there are already many different reports about server lag, it is my recommendation that the scope of this ticket be reduced to uniquely cover the memory allocation issue.
Should anyone want to go further into discussion about this ticket, I recommend creating a post on the bug tracker subreddit so as to not flood the comments here with chatter.
I have the same issue on any version above 1.13 i dont know why i tested this on my friends computers and they have the same issue what can i do?
Been waiting for 1.15 and sadly it is still a thing... They didnt fixed it and 1.15 is a bug fix update so sad....
1.16 and still buggy. Nogui doesnt help either sad

There's no strong indication that something is wrong here. The only way in which it would be viable report if the long-term average slowly increased, ending with outofmemory exception, since that would suggest memory leak.
I am seeing the same thing. As soon as a server starts get the weird teleport messages. When a player joins it immediately starts throwing Can't keep up! messages and continues to do so entire time players are on server. Before 1.13.1 (1.12.2 and older) I might see these once in a great while due to map size growing or fast movement (i.e.. horse or boat) opening new chunks. Now I see it constantly – usually around 40 to 44 ticks behind however I get regular spikes to 100 and occasional spikes over 2000 ticks behind. Again, never saw this before 1.13.1. I didn't run 1.13, moved from 1.12.2 to 1.13.1 so can't speak to what would have happened there.
I run nogui so that doesn't figure in. I have tried numerous java parameters to adjust memory and memory allocation with no success.
I used to run 2 servers concurrently and FTP and TeamSpeak with no issues – now I have issues running just the 1 Minecraft 1.13.1 server with the others disabled.
Sever is dedicated Ubuntu Server 16.04 64bit Dual Core 2.8 GHz 4Gb Ram
I noticed that someone else mentioned this and the ticket was marked Invalid but I think there is a bug or something going on as there is a marked change in memory usage. I also notice my CPU usage spikes quite regularly much more than it used to.
As a note this happens while on land while not near an ocean so the new chunks don't seem to be the direct cause. I imagine there is another underlying reason.