  Supermarket models with different servers become a key in modeling resource
management of stochastic networks, such as, computer networks, manufacturing
systems and transportation networks. While these different servers always make
analysis of such a supermarket model more interesting, difficult and
challenging. This paper provides a new novel method for analyzing the
supermarket model with different servers through a multi-dimensional
continuous-time Markov reward processes. Firstly, the utility functions are
constructed for expressing a routine selection mechanism that depends on queue
lengths, on service rates, and on some probabilities of individual preference.
Then applying the continuous-time Markov reward processes, some segmented
stochastic integrals of the random reward function are established by means of
an event-driven technique. Based on this, the mean of the random reward
function in a finite time period is effectively computed by means of the state
jump points of the Markov reward process, and also the mean of the discounted
random reward function in an infinite time period can be calculated through the
same event-driven technique. Finally, some simulation experiments are given to
indicate how the expected queue length of each server depends on the main
parameters of this supermarket model.
