Numerical Studies on Braess-Like Paradoxes for Non-Cooperative Load Balancing in Distributed Computer Systems
Numerical Studies on Braess-Like Paradoxes for Non-Cooperative Load Balancing in Distributed Computer Systems
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通讯作者：
Said Fathy;Hisao El-Zoghdy;Kameda Jie;Li
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作者：
Said Fathy;Hisao El-Zoghdy;Kameda Jie;Li
分布式计算机系统由节点(主机、计算机)和连接节点的通信装置组成。作业到达每个节点，并且可以通过通信装置转发到其他节点以进行远程处理。已经报道了类Braess悖论的数值例子，在该悖论中，向分布式计算机系统增加容量可能会降低系统中所有用户的性能。与原始的Braess悖论不同，在所研究的模型中，只有在fi个用户有限多的情况下才会发生这种行为，而在fi个用户不多的情况下不会发生这种行为，并且性能下降的程度可以不受限制地增加。这项研究考察了一些围绕类布雷斯悖论的数字例子。从数值算例中可以看出，在类最优的情况下，在完全对称的情况下，悖论中的最坏性能降低率最大(即获得最差的性能)，到达速率最接近于处理速率。并且，随着系统参数设置逐渐偏离上述对称情况而不保持任何类型的对称性，性能恶化的最坏比率迅速降低。如果系统参数设置偏离完全对称，同时保持单个(整体)对称属性，则其减小速度较慢(更慢)。事实上，还观察到，在完全对称的情况下，如果使用类型(C)的通信手段，则随着到达速率变得非常接近处理速率，性能降级的最坏比率可能不受限制地增加。
Distributed computer systems consists of nodes (hosts, computers) and a communication means that connects nodes. Jobs arrive at each node and can be forwarded through the communication means to the other nodes for remote processing. Numerical examples of a Braess-like paradox in which adding capacity to a distributed computer system may degrade the performance of all users in the system have been reported. Unlike the original Braess paradox, in the models examined, this behavior occurs only in the case of finitely many users and not in the case of infinite number of users, and the degree of performance degradation can increase without bound. This study examines numerically, some examples around the Braess-like paradox. From the numerical examples, it is observed that, in the class optimum, the worst ratio of performance degradation in the paradox is largest ( i.e. , the worst performance is obtained) in the complete symmetry case with the arrival rate is closest to the processing rate. And, as the system parameter setting gradually departs the above-mentioned symmetric case without keeping any kind of symmetries, the worst ratio of performance degradation decreases rapidly. It decreases slowly (more slowly) if the system parameter setting departs the complete symmetry while keeping the individual (overall) symmetry property. Indeed, it is also observed that in complete symmetry, if the communication means of type (C) is used, the worst ratio of performance degradation may increase without bound as the arrival rate gets very close to the processing rate.