In this work, we investigate resource allocation strategy for real time communication (RTC) over satellite networks with virtual network functions. Enhanced by inter-satellite links (ISLs), in-orbit computing and network virtualization technologies, large-scale satellite networks promise global coverage at low-latency and high-bandwidth for RTC applications with diversified functions. However, realizing RTC with specific function requirements using intermittent ISLs, requires efficient routing methods with fast response times. We identify that such a routing problem over time-varying graph can be formulated as an integer linear programming problem. The branch and bound method incurs
O(∣Lτ∣⋅(3∣Vτ∣+∣Lτ∣)∣Lτ∣) time complexity, where
∣Vτ∣ is the number of nodes, and
∣Lτ∣ is the number of links during time interval
τ. By adopting a k-shortest path-based algorithm, the theoretical worst case complexity becomes
O(∣Vτ∣!⋅∣Vτ∣3). Although it runs fast in most cases, its solution can be sub-optimal and may not be found, resulting in compromised acceptance ratio in practice. To overcome this, we further design a graph-based algorithm by exploiting the special structure of the solution space, which can obtain the optimal solution in polynomial time with a computational complexity of
O(3∣Lτ∣+(2log∣Vτ∣+1)∣Vτ∣). Simulations conducted on starlink constellation with thousands of satellites corroborate the effectiveness of the proposed algorithm.