Research On Markov Reward Process In Asymmetric Supermarket Models

The supermarket model is a real-time controlled random load balancing strategy tothe large service network system. The different servers of the asymmetric supermarketmake the analysis of the parallel system become more difficult and challenging. At thesame time, the supermarket is a key and one of the most efficient mathematical tools tosolve the stochastic large-network resource management, for example, computer networksand transportation systems.Firstly, we studied the nature of the discrete-time asymmetric supermarket model indetail. In this paper, we establish the reward functions in the asymmetric supermarketmodel according to the nature of the Markov reward processes and the associated optimaltechnology, provide an iterative algorithm for computing the reward functions, and give acriterion of performance evaluation in the asymmetric supermarket through thedouble-direction optimization with respect to the reward functions.Secondly, due to the particularity of multi-dimensional continuous-time asymmetricMarkov reward process, we provide an expression of segmented integrals for a randomreward function by means of an event-driven technique. Based on this, the mean of therandom reward function in a finite time period is effectively computed by caring for thestate change points of the asymmetric Markov reward process. Also, the mean of thediscounted random reward function in an infinite time period is similarly calculatedthrough the event-driven technique. And we propose three optimal problems based on themean of the discounted random reward function.Thirdly, we use the hospital registration system as an instance to verify the results ofthe discrete-time and continuous-time asymmetric supermarket models from theperspectives of both patients and doctors. Quantitatively analyze to the changes of the twokinds of reward function, when the several important parameters in the model occurchange. We obtain the main way to improve the efficiency of management of hospitalregistration system is to improve the service efficiency of hospital registration system,perfect the online registration system and telephone registration system. Asymmetric supermarket model is a common application of random load balancingstrategy, provides the theoretical foundation in the fields of resource management, such ascomputer application, supply chain management, transportation and manufacturingservices. Therefore, asymmetric supermarket models will have many importantapplications to our real life.