The Supermarket Model Research Based On Customer Behavior Choice And Environmental Risks

The supermarket model is a dynamic randomized load balancing scheme forreal-time dynamic control of large scale parallel queuing network. Its operation is simpleand practical, it can greatly improve the system performance and efficiency. And it hasmany important practical applications in, for example, computer networks, cloudcomputing, manufacturing systems and transportation networks. Based on this, this paperconsiders the following two types of supermarket models: supermarket model withimpatient customers and supermarket model with negative customers.Firstly, we analyze a supermarket model with impatient customers, which consists ofone server and N waiting lines under two classes of dynamic randomized load balancingschemes. If the customer can’t get service for a long time, he will become impatient andleave the queuing system. We use an infinite-dimensional Markov process to study thissupermarket model, and set up an infinite-dimensional system of differential equations.Furthermore, we provide an effectively iterative algorithm for computing the fixed pointof the infinite-dimensional system of differential limiting equations.Secondly, we analyze a supermarket model with negative customers. The differentremovel rules by the negative customers lead to three different supermarket models:remover all the positive customers in the shortest queue length, remover all the positivecustomers in the shortest queue length, remover all the positive customers in the choice ofthe queue. We set up an infinite-dimensional system of differential equations for each case.And we provide an effectively iterative algorithm for computing the fixed point.Thirdly, we abstract the call center model into supermodel model. Under the researchbackground of the call center, we give a performance analysis of the two type of model.This makes the article has more practical significance. And we give a performanceanalysis including the mean of stationary queue length in any server and the the expectedsojourn time of any arriving customer spending in this system. This makes the article morepractical significance.In a word, for large scale network of resources, task scheduling and resource allocation have become important means to improve the efficiency and effectiveness ofthe business. Dynamic randomized load balancing strategies is an important approach forthe organization and management of large scale network resources. Therefore, suchsupermarket models will have many applications to our real life.