Network slicing across multiple administrative domains raises two coupled challenges: enforcing slice-specific trust constraints while enabling fast online admission and placement decisions. This paper considers a multi-domain infrastructure where each slice request specifies a VNF chain, resource demands, and a set of (un)trusted operators, and formulates the problem as a Node-Link (NL) integer program to obtain an optimal benchmark, before proposing a Path-Link (PL) formulation that pre-generates trust and order-compliant candidate paths to enable real-time operation. To mitigate congestion, resource prices are made dynamic using a Kleinrock congestion function, which inflates marginal costs as utilization approaches capacity, steering traffic away from hotspots. Extensive simulations across different congestion levels and slice types show that: (i) PL closely tracks NL with negligible gaps at low load and moderate gaps otherwise, (ii) dynamic pricing significantly reduces blocking under scarce resources, and (iii) PL reduces computation time by about 3x-6x compared to NL, remaining within a few seconds even at high load. These results demonstrate that the proposed PL and dynamic pricing framework achieves near-optimal performance with practical runtime for online multi-domain slicing under trust constraints.

翻译：跨管理域的网络切片带来两个相互耦合的挑战：在实现快速在线接纳与部署决策的同时，需强制执行切片特定的信任约束。本文考虑一个多域基础设施，其中每个切片请求指定一条VNF链、资源需求以及一组（非）可信运营商，并将该问题建模为节点链路（NL）整数规划以获取最优基准，随后提出一种路径链路（PL）公式，该公式预先生成符合信任与顺序要求的候选路径以实现实时操作。为缓解拥塞，采用Kleinrock拥塞函数使资源价格动态化：当资源利用率接近容量时，该函数会提高边际成本，从而将流量从热点区域转移。跨不同拥塞水平与切片类型的大量仿真表明：（i）PL与NL紧密贴合，在低负载下差距可忽略，高负载下差距适中；（ii）动态定价显著降低资源稀缺时的阻塞；（iii）PL相比NL将计算时间缩减约3-6倍，即使在高负载下也保持在数秒内。上述结果证明，所提出的PL与动态定价框架能在信任约束下实现接近最优的性能与实用化的在线多域切片运行时。