具有不同服务员的超市模型的报酬过程及性能仿真
Reward Processes and Performance Simulation in Supermarket Models with Different Servers
摘要：
具有不同服务器的超市模型成为随机网络资源管理建模的关键，如计算机网络、制造系统和运输网络。虽然这些不同的服务器总是使分析这样一个超市模型更有趣，更困难和更具挑战性。本文通过多维连续时间马尔可夫报酬过程为分析具有不同服务员的超市模型提供了一种新的方法。首先，构造效用函数来表示依赖于队列长度、服务率和个人偏好的某些概率的例程选择机制。然后，应用连续时间马尔可夫报酬过程，通过事件驱动技术建立了随机报酬函数的分段随机积分。在此基础上，利用马尔可夫报酬过程的状态跳变点，有效地计算了有限时间段内随机报酬函数的均值，并通过同样的事件驱动技术计算了无限时间段内折现随机报酬函数的均值.最后，通过仿真实验说明了超市模型中各服务员的期望队长与模型中主要参数的关系。
英文摘要：
Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis of such a supermarket model more interesting, difficult and challenging. This paper provides a new novel method for analyzing the supermarket model with different servers through a multi-dimensional continuous-time Markov reward processes. Firstly, the utility functions are constructed for expressing a routine selection mechanism that depends on queue lengths, on service rates, and on some probabilities of individual preference. Then applying the continuous-time Markov reward processes, 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 period is effectively computed by means of the state jump points of the Markov reward process, and also the mean of the discounted random reward function in an infinite time period can be calculated through the same event-driven technique. Finally, some simulation experiments are given to indicate how the expected queue length of each server depends on the main parameters of this supermarket model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
