CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2015, 31(4) 411-431 DOI:      ISSN: 1001-4268 CN: 31-1256

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Reward Processes and Performance Optimization in Asymmetric Supermarket Models

Li Quanlin, Ding Yuanyuan, Yang Feifei

School of Economics and Management Sciences, Yanshan University

Abstract��

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.

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