Reward processes and performance simulation in supermarket models with different servers

Supermarket models with different servers have become a key in modelling resource management of stochastic networks, such as computer networks, manufacturing systems, transportation networks, and healthcare systems. However, the different servers always make analysis of such a supermarket model more interesting, difficult and challenging. This paper provides a novel method for analysing the supermarket models with different servers through a multi‐dimensional continuous‐time Markov reward process. Firstly, some utility functions are constructed for designing the routine selection mechanism according to the queue lengths, the service rates, and the probability of individual preference. Secondly, using the state jump points of the continuous‐time Markov reward process, 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 interval is computed, and the mean of the discounted random reward function in an infinite time interval can also be calculated. Finally, some simulation experiments are given to indicate how the expected queue length of each server depends on some key parameters of this supermarket model.