随机呼叫的均衡路由
Balanced routing of random calls
摘要：
我们考虑一个在线网络路由问题在连续时间内，呼叫泊松到达和指数持续时间。首先适合的动态备选路由选择算法顺序地选择呼叫的两个端点之间经由中间节点的多达$d$的随机双链路路由，并且如果存在这样的路由，则将呼叫分配给每个链路上具有空闲容量的第一路由。平衡动态备选路由算法同时选择$d$随机双链路路由，并且在使其两个链路上的负载的最大值最小化的路由上接受呼叫，只要这两个链路都不饱和。我们确定这些算法成功地路由呼叫所需的容量，并发现平衡算法需要更小的容量。为了处理网络上的这种相互作用的随机过程，我们开发了适当的工具，如有偏随机游动引理。
英文摘要：
We consider an online network routing problem in continuous time, where calls have Poisson arrivals and exponential durations. The first-fit dynamic alternative routing algorithm sequentially selects up to $d$ random two-link routes between the two endpoints of a call, via an intermediate node, and assigns the call to the first route with spare capacity on each link, if there is such a route. The balanced dynamic alternative routing algorithm simultaneously selects $d$ random two-link routes, and the call is accepted on a route minimising the maximum of the loads on its two links, provided neither of these two links is saturated. We determine the capacities needed for these algorithms to route calls successfully and find that the balanced algorithm requires a much smaller capacity. In order to handle such interacting random processes on networks, we develop appropriate tools such as lemmas on biased random walks.
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