This paper studies an important rate allocation problem that arises in many networked and distributed systems: steady-state traffic rate allocation from multiple sources to multiple service nodes when both (i) the access-path delay on each source-node route is rate-dependent (capacity-constrained) and convex, and (ii) each service node (also capacity-constrained) experiences a load-dependent queueing delay driven by aggregate load from all sources. We show that the resulting flow-weighted end-to-end delay minimization is a convex program, yielding a global system-optimal solution characterized by KKT conditions that equalize total marginal costs (a path marginal access term plus a node congestion price) across all utilized routes. This condition admits a Wardrop-type interpretation: for each source, all utilized options equalize total marginal cost, while any option with strictly larger total marginal cost receives no flow. Building on this structure, we develop a lightweight distributed pricing-based algorithm in which each service node locally computes and broadcasts a scalar congestion price from its observed aggregate load, while each source updates its traffic split by solving a small separable convex allocation problem under the advertised prices. Numerical illustrations demonstrate convergence of the distributed iteration to the centralized optimum and highlight the trade-offs induced by jointly modeling access and service congestion.

翻译：本文研究一个在众多网络与分布式系统中出现的重要速率分配问题：当(i)每条源节点路由上的接入路径延迟具有速率依赖性（容量约束）且为凸函数，同时(ii)每个服务节点（同样受容量约束）承受来自所有源的聚合负载所产生的负载依赖性排队延迟时，从多源到多服务节点的稳态流量速率分配问题。我们证明由此产生的流加权端到端延迟最小化问题是一个凸规划，其全局系统最优解可由KKT条件刻画，该条件要求所有被使用路由的总边际成本（路径边际接入项与节点拥塞价格之和）相等。这一条件可解释为Wardrop型原理：对每个源节点，所有被选用的路径具有相等的总边际成本，而任何总边际成本严格更大的路径将不获得流量。基于此结构，我们提出一种轻量级的分布式定价算法：每个服务节点根据观测到的聚合负载本地计算并广播一个标量拥塞价格，而每个源节点则在公布的价格下通过求解一个小规模可分离凸分配问题来更新其流量分配方案。数值算例表明该分布式迭代能收敛至集中式最优解，并突显了联合建模接入与服务拥塞所引发的权衡关系。