Reward Processes and Performance Optimization in Asymmetric Supermarket Models

The supermarket model has been an important mathematical tool in the study of resource management in large-scale networks by means of some advantages, such as, simple operations, quick reaction, real-time management and control and so on. It is widely applied in internet of things, cloud computing, cloud manufacturing, big data, transportation, health care and other important practical fields. Up to now, analysis of the asymmetric supermarket models is an increasingly interesting topic in this area.
In this paper, we analyze an asymmetric supermarket model. Because the M servers are different from each other, the routine selection policies of each customer become to have a complex structure, where not only are the routine selection policies related to the different queue lengths and the different service speeds among the M servers, but they are also related to the customer's preference for the M servers. For this, we set up several useful routine selection policies in terms of the decision-making methods. Based on this, we provide the Markov reward processes of the asymmetric supermarket model and establish the associated functional reward equations, give a useful value iterative algorithm for solving the functional reward equations, obtain a criterion of performance evaluation in the asymmetric supermarket model through a double-direction optimization, and show that the sequence of iterative reward functions is monotone and the value iterative algorithm is convergent. This paper provides new and useful highlight on understanding how the asymmetric supermarket model is applied to resource management and control in large-scale networks both from the objective conditions and from the subjective behavior. At the same time, the methodology and main results of this paper give some basic theory and techniques in the study of asymmetric supermarket models for the first time.