We have also a job which is executed concurrent. In average approximately 12 are running at the same time. We also see problems with update of premalinks.
For us not working links for this job are no big issue but the "NoSuchFileException" is flooding Jenkins log.
This job is running ~1300 times a day and therefore the exception is adding ~1.5 MBytes to log.
Is there a way to reduce logs for such a case?

I don't think this has anything to do with parallel jobs execution ... except perhaps that it is easier to expose the race condition?

We see the same failures to update permalinks – both lastSuccessfulBuild and lastFailedBuild – on a small installation without parallel jobs (one node, with #executors set to 1) and with low execution rates. Also the server is Windows Server 2012 R2 Standard, so not a linux-only issue. Jenkins ver. 1.642.2.

Another difference is that instead of NoSuchFile, we see DirectoryNotEmptyException:

Mar 05, 2016 4:06:09 AM jenkins.model.PeepholePermalink updateCache
WARNING: Failed to update hudson.model.FreeStyleProject@320509[40018_mmiDotNetMath_main] lastSuccessfulBuild permalink for 40018_mmiDotNetMath_main #767
java.nio.file.DirectoryNotEmptyException: C:\Jenkins\jobs\40018_mmiDotNetMath_main\builds\lastSuccessfulBuild
at sun.nio.fs.WindowsFileSystemProvider.implDelete(Unknown Source)
at sun.nio.fs.AbstractFileSystemProvider.delete(Unknown Source)
at java.nio.file.Files.delete(Unknown Source)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at hudson.Util.deleteFile(Util.java:255)
at hudson.util.AtomicFileWriter.commit(AtomicFileWriter.java:113)
at jenkins.model.PeepholePermalink.writeSymlink(PeepholePermalink.java:200)
at jenkins.model.PeepholePermalink.updateCache(PeepholePermalink.java:150)
at jenkins.model.PeepholePermalink$RunListenerImpl.onCompleted(PeepholePermalink.java:237)
at hudson.model.listeners.RunListener.fireCompleted(RunListener.java:201)
at hudson.model.Run.execute(Run.java:1783)
at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:43)
at hudson.model.ResourceController.execute(ResourceController.java:98)
at hudson.model.Executor.run(Executor.java:410)

Hi all
We Have some problem with lasBuild on Jenkins ver. 1.651.3

WARNING: Failed to update hudson.model.FreeStyleProject@1c6fcad[CD-CFW_Selenium_Part1] lastSuccessfulBuild permalink for CD-CFW_Selenium_Part1 #5631
java.nio.file.DirectoryNotEmptyException: c:\Jenkins\jobs\CD-CFW_Selenium_Part1\builds\lastSuccessfulBuild
at sun.nio.fs.WindowsFileSystemProvider.implDelete(Unknown Source)
at sun.nio.fs.AbstractFileSystemProvider.delete(Unknown Source)
at java.nio.file.Files.delete(Unknown Source)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at hudson.Util.deleteFile(Util.java:257)
at hudson.util.AtomicFileWriter.commit(AtomicFileWriter.java:113)
at jenkins.model.PeepholePermalink.writeSymlink(PeepholePermalink.java:200)
at jenkins.model.PeepholePermalink.updateCache(PeepholePermalink.java:150)
at jenkins.model.PeepholePermalink.resolve(PeepholePermalink.java:122)
at hudson.model.Job.getLastSuccessfulBuild(Job.java:913)
at jenkins.tasks.SimpleBuildStep$LastBuildActionFactory.createFor(SimpleBuildStep.java:113)
at jenkins.tasks.SimpleBuildStep$LastBuildActionFactory.createFor(SimpleBuildStep.java:99)
at hudson.model.Actionable.createFor(Actionable.java:107)
at hudson.model.Actionable.getAllActions(Actionable.java:98)
at hudson.model.Actionable.getAction(Actionable.java:165)
at hudson.plugins.nunit.NUnitPublisher.getProjectAction(NUnitPublisher.java:94)
at hudson.tasks.BuildStepCompatibilityLayer.getProjectActions(BuildStepCompatibilityLayer.java:98)
at hudson.model.Project.createTransientActions(Project.java:252)
at hudson.model.AbstractProject.updateTransientActions(AbstractProject.java:755)
at hudson.model.AbstractProject.onLoad(AbstractProject.java:339)
at hudson.model.Project.onLoad(Project.java:98)
at hudson.model.Items.load(Items.java:327)
at jenkins.model.Jenkins$18.run(Jenkins.java:2720)
at org.jvnet.hudson.reactor.TaskGraphBuilder$TaskImpl.run(TaskGraphBuilder.java:169)
at org.jvnet.hudson.reactor.Reactor.runTask(Reactor.java:282)
at jenkins.model.Jenkins$8.runTask(Jenkins.java:926)
at org.jvnet.hudson.reactor.Reactor$2.run(Reactor.java:210)
at org.jvnet.hudson.reactor.Reactor$Node.run(Reactor.java:117)
at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)

My case: JENKINS-54863

I do not understand how much they are the same..