We run Sharepoint 2013 (Upgraded from fresh install of SP2010) and one of our applications ("Intranet") is set as a publishing app for obvious reasons.
On Friday one of the Content authors logged a call to say she was unable to publish a page. Just took her round in circles and asked her to publish again. Also the emails were not sent for approval. A short while later we found that it had managed to publish. I noted that the servers were a little slow to respond and put it down toe the servers just being overloaded at the time. Unfortunately the same problem was again reported today and we have investigated this for several hours now and cannot find the issue.
We have found that the workflow tasks shows a message "Failed to start" and have already rebooted all servers in the farm and de-activated and re-activated workflow.
Another user using a team site application has now also logged a similar call for his site claiming workflow failed to start.
I have re-created trying to publish the item and checked ULS logs and found a message saying "Unable to write SPDistributedCache call usage entry. Would really appreciate some direction with this as it seems nobody is able to publish anything at the moment.