Because Docker replaces the default /sbin/init with its own, there's no way to run the Upstart init inside a Docker container. However this causes some problems: some Debian packages try to communicate with Upstart, and will fail to install if this fails. For example the "at" package.

$ sudo apt-get install at
Reading package lists... Done
Building dependency tree
Reading state information... Done
Suggested packages:
  default-mta mail-transport-agent
The following NEW packages will be installed:
  at
0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded.
Need to get 37.4 kB of archives.
After this operation, 188 kB of additional disk space will be used.
Get:1 http://archive.ubuntu.com/ubuntu/ quantal/main at amd64 3.1.13-2ubuntu1 [37.4 kB]
Fetched 37.4 kB in 0s (75.2 kB/s)
Selecting previously unselected package at.
(Reading database ... 23544 files and directories currently installed.)
Unpacking at (from .../at_3.1.13-2ubuntu1_amd64.deb) ...
Processing triggers for ureadahead ...
Setting up at (3.1.13-2ubuntu1) ...
initctl: Unable to connect to Upstart: Failed to connect to socket /com/ubuntu/upstart: Connection refused
start: Unable to connect to Upstart: Failed to connect to socket /com/ubuntu/upstart: Connection refused
invoke-rc.d: initscript atd, action "start" failed.
dpkg: error processing at (--configure):
 subprocess installed post-installation script returned error exit status 1
Processing triggers for ureadahead ...
Errors were encountered while processing:
 at
E: Sub-process /usr/bin/dpkg returned an error code (1)