A CONSTELLATION-WIDE VIEW

We use the first planned deployments for Starlink and Kuiper, and the first shell for Telesat to examine constellation-scale behavior. Starlink and Kuiper plan to deploy their shells S1 and K1 in Table 1 first. Telesat’s deployment plan is more complex [72]; we simply use its first shell, T1. We use the world’s 100 most populous cities as GSes, and examine connections between all pairs of GSes.

我们使用Starlink和Kuiper的首次计划部署，以及Telesat的第一个壳层（T1）来检查星座规模的行为。Starlink和Kuiper计划首先部署其壳层S1和K1（见表1）。Telesat的部署计划更为复杂[72]；我们仅使用其第一个壳层T1。我们选择世界上100个人口最多的城市作为地面站（GSes），并检查所有地面站对之间的连接。

RTTs and variations therein

We measure the minimum and maximum RTT for each connection over the simulation duration. We also compute the “geodesic RTT” i.e., the time it would take to travel back and forth between a connection’s end-points at the speed of light in vacuum, 𝑐. This is thus the minimum achievable RTT.

我们测量了每个连接在仿真持续时间内的最小和最大RTT。我们还计算了“测地RTT”，即以真空中的光速 \(c\) 来回穿越连接端点所需的时间。因此，这就是可实现的最小RTT。

For each connection, we compute the ratio of its maximum RTT over time to the geodesic RTT between its end-points. Fig. 6 shows this ratio as a CDF across connections. For all three constellations, more than 80% of connections see a maximum RTT less than 2× the geodesic. Given that terrestrial fiber paths are often longwinded, and the speed of light in fiber is roughly 2𝑐/3 [9], this implies that for most connections in our simulation, LEO networks will have substantially lower latencies than today’s Internet. The long tail of latency inflation compared to the geodesic arises from connections between relatively nearby end-points, for which the overheads of the up-down connectivity to satellites are significant. For this reason, we already exclude end-point pairs that are within 500 km of each other from this plot and other results in this section.

对于每个连接，我们计算其最大RTT与连接端点之间测地RTT的比值。图6展示了这个比值在所有连接中的累积分布函数（CDF）。对于所有三个星座，超过80%的连接的最大RTT都小于测地RTT的2倍。考虑到地面光纤路径通常很长，而且光纤中的光速大约是真空中光速的 \(2c/3\) [9]，这意味着在我们的仿真中，大多数连接的LEO网络延迟将显著低于今天互联网的延迟。与测地RTT相比，延迟膨胀的长尾来自于相对较近的端点之间的连接，对于这些连接，上下行连接到卫星的开销是显著的。因此，我们在该图和本节中的其他结果中，已经排除了距离小于500公里的端点对。

Similar observations about latency in LEO networks have already been made in other work [5, 6, 29, 44]. However, a new and surprising finding here is about the comparison of the constellations. Telesat has the fewest satellites, with less than a third of Kuiper’s and less than a fourth of Starlink’s, and yet it achieves the lowest latencies for most connections. Starlink’s latencies are also higher than Kuiper’s.

关于LEO网络延迟的类似观察已经在其他工作中提出[5, 6, 29, 44]。然而，本文中的一个新的且令人惊讶的发现是关于不同星座之间的比较。Telesat的卫星最少，只有Kuiper的不到三分之一，Starlink的不到四分之一，但它仍然在大多数连接中实现了最低的延迟。Starlink的延迟也高于Kuiper的。

The explanations for these results lie in the connectivity parameters and the orbital structure of the constellations. Telesat claims that it will use a much lower minimum angle of elevation, 10°, compared to Starlink (25°) and Kuiper (30°). This allows GSes to see more of Telesat’s satellites at any time, providing more options for end-end paths. Additionally, as these low elevation paths are closer to the horizon, the overhead of the up-down link is often smaller.

这些结果的解释在于星座的连接参数和轨道结构。Telesat声称，其最低仰角将远低于Starlink（25°）和Kuiper（30°），为10°。这使得地面站（GSes）在任何时刻都能看到更多的Telesat卫星，从而提供更多的端到端路径选择。此外，由于这些低仰角路径更接近地平线，上下行链路的开销通常较小。

The Starlink-Kuiper differences are not due to the angle of elevation, which is similar, but the orbital structure. Both constellations use a minimum angle of elevation that is much higher than Telesat’s. This means that typically, GSes can see fewer satellites. This restricts the GS-satellite connectivity, and increases the impact of satellite-satellite connectivity. Kuiper’s orbital design, with 34 orbits of 34 satellites each, is more uniform than Starlink’s, with 72 orbits of 22 satellites each. In particular, satellites within an orbit are much farther apart in Starlink, and paths often require zig-zagging through multiple orbits to reach the destination.

Starlink和Kuiper之间的差异并非由于仰角（两者相似），而是由于轨道结构。两个星座都使用了比Telesat更高的最低仰角，这意味着通常地面站可以看到的卫星较少。这限制了地面站与卫星之间的连接，并增加了卫星间连接的影响。Kuiper的轨道设计比Starlink更均匀，采用34个轨道，每个轨道上有34颗卫星，而Starlink则采用72个轨道，每个轨道上有22颗卫星。特别是，在Starlink中，同一轨道内的卫星相距较远，路径通常需要穿越多个轨道并进行折返，才能到达目的地。

We also evaluate how much the RTT fluctuates over time across different connections. Fig. 7 shows the distribution across connections of: (a) the absolute value of the maximum RTT within a connection; (b) the difference between the maximum and minimum within a connection; and (c) the ratio between the maximum and minimum within a connection. The results show that while Starlink sees the largest latency changes (∼10 ms in the median), the other constellations also feature significant latency variation at the tail. Telesat’s variations are the smallest again because of its low inclination: the same satellites are reachable for longer, and result in more continuous and smaller latency changes. For Starlink, for more than 30% of connections, the maximum RTT is at least 20% larger than the minimum RTT.

我们评估了不同连接中往返时间（RTT）随时间的波动情况。图7展示了连接间的分布情况：（a）连接中最大RTT的绝对值；（b）连接中最大与最小RTT之间的差异；（c）连接中最大与最小RTT之间的比率。结果显示，虽然Starlink的延迟变化最大（中位数约为10毫秒），但其他星座在尾部也表现出显著的延迟变化。Telesat的变化最小，这再次归因于其低倾角：同一颗卫星可被更长时间访问，从而导致更连续且较小的延迟变化。对于Starlink，超过30%的连接中，最大RTT至少比最小RTT大20%。

For two reasons, we caution readers against concluding that ‘Telesat is a better design’: (a) There are downsides to using a lower minimum angle of elevation, as discussed in §2.1; and (b) We are evaluating constellations strictly from their filings, and it is unclear to us if some operators are more optimistic than others about the plausible design parameters; it is worth remembering that the filings are meant to secure radio spectrum for an operator by showing the potential utility of its network. The larger point, as far as the Hypatia framework is concerned, is that given the right input parameters, we can compare different designs along metrics like RTTs and RTT variability.

我们提醒读者不要轻易得出“Telesat设计更优”的结论，原因有二：（a）使用较低的最低仰角会有缺点，如第2.1节所讨论；（b）我们仅根据各自的申请文件评估星座，尚不清楚某些运营商是否对可行设计参数过于乐观；值得注意的是，这些申请文件旨在为运营商争取无线电频谱，通过展示其网络的潜在效用来实现。就Hypatia框架而言，关键在于，在正确的输入参数下，我们可以沿着RTT及其变异性等指标比较不同设计。

Path structure evolution

Besides RTTs, we also examine the structure of the underlying paths. For each connection, we measure the number of times its path changes over the simulation. If the forwarding state computed in two successive time-steps shows any different satellites composing the path, we count this as one path change. Across connections, we compute the CDF of these path changes. For each connection, we also calculate the maximum and minimum number of satellite hops in the path across the simulation.

在这项研究中，我们除了考察往返时间（RTT）外，还分析了底层路径的结构。对于每个连接，我们测量其路径在模拟过程中变化的次数。如果在两个连续的时间步中计算出的转发状态显示路径中组成卫星有任何不同，我们就将其视为一次路径变化。我们计算这些路径变化的累积分布函数（CDF）。对于每个连接，我们还计算了在整个模拟过程中路径中卫星跳数的最大值和最小值。

Fig. 8(a) shows that in the median, over the 200 s simulation, Starlink and Kuiper connections see 4 path changes, while Telesat connections see 2 changes. These results are in line with our explanation of RTT variations: Telesat’s use of a lower minimum angle of elevation allows remaining connected to a satellite for longer, and reduces path changes. The tail of path changes is long as well: for Kuiper and Starlink, 10% of connections see 7 or more path changes.

图8(a)显示，在200秒的模拟中，Starlink和Kuiper连接的中位数路径变化次数为4次，而Telesat连接则为2次。这些结果与我们对RTT变化的解释一致：Telesat使用较低的最低仰角使得与卫星保持连接的时间更长，从而减少了路径变化。路径变化的尾部也很长：对于Kuiper和Starlink，10%的连接看到7次或更多的路径变化。

Fig. 8(b) shows how these different paths differ in terms of their hop count. For Telesat, paths do not typically change in terms of hop count. This is explained by Telesat being sparser: there are simply fewer options for end-end paths, and with farther-apart satellites, one hop of change would already be substantial. For Starlink, with its large number of satellites, there are many more options for paths, and more than a third of connections see paths with at least 2 more hops than the minimum number.

图8(b)展示了这些不同路径在跳数上的差异。对于Telesat，路径在跳数上通常不会发生变化。这是因为Telesat网络较稀疏：可供选择的端到端路径较少，并且由于卫星之间距离较远，一次跳数的变化已经相当显著。相比之下，Starlink拥有大量卫星，因此有更多路径选择，超过三分之一的连接看到路径跳数比最小值多出至少2次。

Fig. 8(c) shows the same hop-count data in terms of relative change in hop-count. For Starlink, more than 10% of connections see more than 50% change in hop-count.

图8(c)以相对跳数变化的形式展示了相同的跳数数据。对于Starlink，超过10%的连接看到跳数变化超过50%。

Unlike today’s Internet, LEO network paths evolve rapidly, especially for the denser networks, with paths changing multiple times per minute, and often by a substantial number and fraction of hops. Routing within LEO networks thus features high churn. Nevertheless, given the tens of seconds between typical changes, we do not expect the setting up of desired routing state itself to be a major bottleneck.

与今天的互联网不同，低地球轨道（LEO）网络的路径迅速演变，尤其是在更密集的网络中，路径每分钟可能发生多次变化，并且通常涉及大量和比例显著的跳数。因此，在LEO网络中的路由特征表现出高频率的变动。然而，考虑到典型变化之间通常有几十秒的间隔，我们不认为设定所需路由状态本身会成为主要瓶颈。

Granularity of time-step updates

Hypatia converts a continuous process of satellite movement and the resulting path changes into a discrete one. While latencies along paths are continuously updated, the forwarding state is only recomputed at fixed time-steps. We thus test how this affects our observations on path changes.

Hypatia将卫星运动的连续过程及其导致的路径变化转化为离散过程。在此过程中，路径上的延迟是持续更新的，而转发状态则仅在固定的时间步长内重新计算。因此，我们将测试这种方法对路径变化观察结果的影响。

We compute the network’s forwarding state at different timesteps of 50, 100, and 1000 ms. For each configuration, we calculate: (a) how many path changes per second occur in a time-step; (b) how many path changes are missed at coarser time-steps compared to 50 ms.

我们在不同的时间步长（50毫秒、100毫秒和1000毫秒）下计算网络的转发状态。对于每种配置，我们计算： (a) 每秒发生的路径变化次数；(b) 与50毫秒相比，较粗时间步长下错过的路径变化次数。

We only include results for Kuiper K1, but the conclusions hold broadly. Fig. 9(a) shows the distribution of the number of path changes network-wide across time-steps. Ideally, the 100 ms timestep would have 2× the number of changes compared to the 50 ms one, and 1000 ms would have 20×. This is almost always the case for 100 ms, but for 1000 ms a significant fraction of path changes are simply missed because multiple changes happened entirely within that interval. Fig. 9(b) shows the distribution of these missed changes for both the 100 ms and 1000 ms time-steps compared to the 50 ms one. The 100 ms time-step misses for a negligible fraction (0.4%) of pairs one or more path changes, while 1000 ms misses for 6% of pairs one or more path changes.

我们仅包括Kuiper K1的结果，但结论具有广泛适用性。图9(a)显示了网络范围内在不同时间步长下路径变化次数的分布。理想情况下，100毫秒的时间步长应有2倍于50毫秒的变化次数，而1000毫秒应有20倍。对于100毫秒，这几乎总是成立，但对于1000毫秒，由于在该时间段内发生了多次变化，因此会错过相当一部分路径变化。图9(b)显示了与50毫秒时间步长相比，100毫秒和1000毫秒时间步长下错过的变化分布。100毫秒的时间步长错过的路径变化对比为0.4%的微不足道的比例，而1000毫秒则错过了6%的路径变化。

Note that finer granularity of time-steps requires expensive shortest-path computations for the entire large network. Based on our results, 100 ms is a good compromise. Further, given that path changes occur over tens of seconds, the 100 ms time-step can only be inaccurate and not provide the actual shortest paths for at most 1% of the time.

需要注意的是，较细粒度的时间步长需要对整个大型网络进行昂贵的最短路径计算。根据我们的结果，100毫秒是一个良好的折中。此外，考虑到路径变化发生在几十秒内，100毫秒的时间步长最多只在1%的时间内不准确，和无法提供实际的最短路径（说明它的效果非常牛）。

Bandwidth fluctuations

Beside the structure and latency of paths, and the response of individual TCP connections, we would also like to understand the result of interactions between traffic flows in such networks. Towards this goal, we conduct a simple experiment, sending long running TCP flows between pairs of GSes over their shortest paths.

我们希望理解在这样的网络中，流量流之间的相互作用结果，除了路径的结构和延迟以及单个TCP连接的响应。为此，我们进行了一项简单的实验，在其最短路径上在一对地面站（GS）之间发送长时间运行的TCP流。

We use the same LEO network as in §4, i.e., Kuiper’s K1 shell, with each link in the network set to 10 Mbps capacity to allow us to scale the experiment. Instead of just pings, we now send long running TCP NewReno flows between these GS pairs, which are still the same random permutation of the world’s 100 most populous cities. From the random permutation matrix, we remove the pairs which have the same source or destination satellite as Rio de Janeiro or St. Petersburg at any point through the simulation; this prevents the first and last hops from being the bottleneck, allowing us to focus on the ISL network’s behavior. We do not put this forth as a representative traffic matrix; rather, it is simply one way of sending substantial traffic through the network, and as we show next, reveals interesting network behavior. Hypatia can support arbitrary input traffic matrices.

我们使用与第4节中相同的低地球轨道（LEO）网络，即Kuiper的K1壳层，网络中每个链路设置为10 Mbps的容量，以便我们能够扩展实验。我们不再仅仅发送ping，而是在这些GS对之间发送长时间运行的TCP NewReno流，这些GS对仍然是世界上100个最人口稠密城市的随机排列。从随机排列矩阵中，我们去除了在模拟过程中任何时刻与里约热内卢或圣彼得堡有相同源或目的卫星的对，这样可以防止第一跳和最后一跳成为瓶颈，从而使我们能够专注于星间链路（ISL）网络的行为。我们并不将此视为一个代表性的流量矩阵；相反，这只是通过网络发送大量流量的一种方式，正如我们接下来所展示的，这揭示了有趣的网络行为。Hypatia可以支持任意输入流量矩阵。

We find that despite the traffic matrix being fixed throughout our 200 s experiment, and the routing policy consistently being shortest path routing, the motion of satellites makes the path-level behavior highly dynamic.

我们发现，尽管流量矩阵在200秒的实验过程中是固定的，并且路由策略始终是最短路径路由，但卫星的运动使得路径级别的行为高度动态。

Monitoring link utilization at one link is not a particularly useful way of demonstrating this in LEO networks — a particular ISL will traverse the globe in ∼100 min, seeing conditions corresponding to its location over time. We thus measure the “unused bandwidth” for each GS-pair, i.e., how much unused capacity is there on the endend path for that GS-pair over time. This is simply the path’s link capacity (10 Mbps in our running scenario) minus the utilization of the most congested on-path link at any time. In a static network with fixed routing, and a fixed set of long-running TCP flows, we should expect this unused bandwidth to be small. This static-network TCP behavior is shown as the the gray line in Fig. 10 for the topology frozen at its 𝑡 = 0 position.

在低地球轨道（LEO）网络中，仅监测单个链路的利用率并不是一个特别有效的方法来展示网络性能 —— 一个特定的星间链路（ISL）大约需要100分钟才能环绕地球一周，因此在这段时间内，它会经历与其位置相关的各种条件。因此，我们测量每对地面站（GS）之间的“未使用带宽”，即在该GS对的端到端路径上随时间变化的未使用容量。这简单地定义为路径的链路容量（在我们的实验场景中为10 Mbps）减去在任何时刻最拥挤的链路的利用率。在一个具有固定路由和固定长时间运行TCP流量的静态网络中，我们应该期望未使用带宽较小。图10中的灰线显示了这种静态网络TCP行为，数据基于在 \(t = 0\) 时刻冻结的拓扑结构。

However, we find that in an LEO network with cross-traffic, the amount of unused bandwidth is larger than that in the static case. Fig. 10 shows the unused bandwidth, measured at a 1 s granularity, for the same connection we examined in §4, from Rio de Janeiro to St. Petersburg. While there are short periods, such as around 20 s, where the full capacity of the path is used (together, by this connection and other cross-traffic), for a lot of the time, there is substantial unused capacity: 31% of the time, more than a third of the capacity is unused (excluding the unreachable period between 155-165 s), compared to 11% of the time if the satellite network were kept static at its 𝑡 = 0 state.

在低地球轨道（LEO）网络中，我们发现，与静态情况相比，未使用带宽的量更大。图10显示了我们在第4节中检查的从里约热内卢到圣彼得堡的相同连接的未使用带宽，测量粒度为1秒。尽管在约20秒的短时间内，路径的全部容量被使用（由该连接和其他交叉流量共同使用），但在大部分时间内，存在大量未使用的容量：31%的时间内，超过三分之一的容量未被使用（不包括155到165秒之间无法到达的时间段），而如果卫星网络保持在其 \(t = 0\) 状态下，仅有11%的时间未使用带宽。

The reason for this difference is the shifts in cross traffic resulting from the path changes: links constituting a GS-pair’s shortest path change over time, and for each link, the set of GS-pairs it is used for changes as well. This implies that the traffic mix at any link is highly dynamic, making it difficult for transport to adapt – the goal of TCPlike transport is, after all, to fairly share bandwidth across the flows traversing a bottleneck. In LEO networks the bottlenecks and which flows constitute the traffic mix change substantially over time. Note that this finding is not at odds with the results on infrequent path structure changes in Fig. 8. Although the median GS-pair’s path changes only a few times over our 200-second simulation period, each end-end path has many links, and some of these links carry traffic from many GS-pairs. This results in a cumulative effect of changes in the cross-traffic traversing (the relatively stable) links of an individual GS-pair’s path.

这种差异的原因在于由于路径变化导致的交叉流量的变化：构成GS对最短路径的链路随时间变化，而对于每条链路，它所用于的GS对集合也会变化。这意味着任何链路上的流量组合是高度动态的，使得传输适应变得困难——毕竟，TCP类传输的目标是公平地共享穿越瓶颈的流量带宽。在LEO网络中，瓶颈和构成流量组合的流量会随着时间显著变化。需要注意的是，这一发现与图8中关于路径结构变化不频繁的结果并不矛盾。尽管在我们的200秒模拟期间，中位数GS对的路径仅变化几次，但每条端到端路径有许多链路，其中一些链路承载来自多个GS对的流量。这导致了穿越（相对稳定）链路的交叉流量变化所产生的累积效应。

These observations have consequences for both traffic engineering and transport. Routing and traffic engineering could be planned ahead, such that knowing the upcoming changes in paths, traffic can be shifted a priori from links that will become new bottlenecks. This is a network-layer operation within the LEO network, and thus in the operator’s control. A likely more difficult remedy is to attempt to make transport more responsive in adapting to changes: it is not clear that this can be done without causing more instability, as aggressive transport ramps up and down faster.

这些观察结果对流量工程和传输都有重要影响。路由和流量工程可以提前进行规划，这样在知道即将发生的路径变化时，可以将流量从将成为新瓶颈的链路上提前转移。这是在低地球轨道（LEO）网络中的网络层操作，因此在运营商的控制之下。一个可能更困难的解决方案是尝试使传输更具响应性，以适应变化：尚不清楚这是否可以在不导致更多不稳定的条件下做到，因为激进的传输会更快地上下波动。

Takeaway for routing / TE 路由/流量工程小结

LEO networks present uncharted territory for routing and TE, and their interactions with transport. Traffic could potentially be moved away from links that will otherwise soon become bottlenecks due to changes in the set of end-end paths they serve.

低地球轨道（LEO）网络为路由和流量工程（TE）以及它们与传输的相互作用提供了未知领域。

由于路径集的变化，流量可能会被转移离开那些即将成为瓶颈的链路:

为routing和TE带来了更多的可能：由于链路的高速移动，hotpoint可能被“消散” -> 值得探索