Is it possible to change the emission rate of particles over time? Is it possible to change the emission rate of particles over time?

E.g. Start off with an initial burst of particles, then emit at a steady rate.

Here is a (poor) example of what I mean by the emission rate:



Is this possible to do using only one particle system? (This is necessary because the particles are being used to emit smoke) 



The gif above was made by manually sliding the End value, but it gives strange and unpredictable results (as can be seen in the gif) as well as not being keyframeable.
In short, there's no ready solution. Lukas Tönne was responsible for a feature known as "Paged Buffers for Particles" but at some point he stopped working on it and the feature never made it to trunk. Here's a timeline of what happened:


March 11 2011: This video shows that variable particle emission was working.
March 17 2011: Paged Buffers for Particles research was published on Blender's developer blog.
July 22 2011: A crowd-funding campaign launched through Lukas's blog.
Dec 6 2011: Lukas spoke about his progress at the 2011 Blender Conference.
May 4 2012: Last blog post on the subject.
August 4 2013: Lukas was hired to do general bug fixing with the Blender Foundation. His work would be "especially for nodes and [the] compositor. When time allows, he then can also pick up work on new particle system."
August 26 2013: In episode 26 of the Blender Podcast, Lukas stated "I started working on the particles, but there are a few basic issues that need to be fixed on a more general level before I can go into the details of node-ifying particles and things like that."
2014–Present: His tweets about node development continue to mention relevant subject matter including duplis which will eventually feed into particle nodes.
Nov 1, 2015: B2.8 project developer kickoff meeting notes mentions that "The particle system and constraints may need a complete overhaul."