  We study Batch Processor-Sharing (BPS) queuing model with hyper-exponential
service time distribution and Poisson batch arrival process. One of the main
goals to study BPS is the possibility of its application in size-based
scheduling, which is used in differentiation between Short and Long flows in
the Internet. In the case of hyper-exponential service time distribution we
find an analytical expression of the expected conditional response time for the
BPS queue. We show, that the expected conditional response time is a concave
function of the service time. We apply the received results to the Two Level
Processor-Sharing (TLPS) model with hyper-exponential service time distribution
and find the expression of the expected response time for the TLPS model. TLPS
scheduling discipline can be applied to size-based differentiation in TCP/IP
networks and Web server request handling.
