# New Sufficient Conditions for a HT Limit Theorem

## Theorem (W ‘98) Assume standard

## heavy traffic assumptions and

## (i) multiplicative state space collapse

## (ii) the reflection matrix R is well defined and completely-S.

## where W* is a SRBM with pushing

## FIFO Kelly type and HLPPS networks

## (Example of Dai-Wang-Wang: FIFO Kelly type network with no continuous mapping construction of SRBM)