PGPS servers with time-varying capacities

We consider a server with a time-varying capacity, We show that the virtual time implementation of the packetized generalized processor sharing (PGPS) scheme in Parekh and Gallager (1993) does not yield the right approximation of the generalized processor sharing (GPS) scheme in such an environment. Via the concept of change of time, we observe that a server with a time-varying capacity can be viewed as a server with a constant capacity under an appropriate change of clock. This leads to a modified version of the virtual time implementation and various bounds of the PGPS server with a time-varying capacity.