Topology design and routing: +Grid, motifs, ground relays and the latency arguments拓樸設計與路由：+Grid、motif、地面中繼與延遲論證
This chapter traces the “LEO beats fiber” claim to its simulations and their scope. You will calculate +Grid hop count and stretch between cities, explain Earth-fixed routing, and identify the assumptions behind topology results.本章會追溯「LEO 勝過光纖」的模擬依據與適用範圍，並計算兩座城市之間 +Grid 的跳數與伸長比。你也會理解路由為何採用固定於地球的地理座標，以及各篇拓樸論文採用了哪些固定假設。
This chapter builds on Chapters 1, 2 and 3. It uses orbital-plane geometry, the +Grid, laser acquisition time, and bent-pipe paths through a PoP. Each term links to its definition.
本章延續第 1、2、3 章，使用軌道面與 +Grid 的幾何、雷射終端的擷取時間，以及經過 PoP 的彎管路徑。各個名詞的連結可帶你回到定義。
New terms in this chapter (7)本章新名詞（7）
Each link opens the term’s first definition.
每個名詞都在它第一次出現的段落中定義，點連結可跳過去。
- Stretch伸長比 Path latency or length divided by the great-circle value between the same endpoints. 路徑延遲或長度除以同一對端點之間的大圓值。
- Hop count跳數 The inter-satellite links a packet crosses, used to estimate consumed capacity. 封包穿越的星間鏈路數，是所消耗容量的代理指標。
- Bisection capacity對分容量 The summed link capacity across the cut that splits a network into two halves. 把網路切成兩半的割集上所有鏈路容量之和。
- Ground relay地面中繼 A ground station that receives from one satellite and retransmits to another, replacing an ISL hop. 從一顆衛星接收再轉發給另一顆衛星的地面站，用來取代一跳星間鏈路。
- Geographic routing地理路由 Routing on Earth-fixed cell identifiers rather than satellite identities.以固定於地球的格元識別碼作為路由依據。
- Traffic engineering流量工程 Allocating each demand across candidate paths within link-capacity limits.決定每項需求在候選路徑上的分配量，使各鏈路的負載維持在容量範圍內。
- Topology holding time拓樸維持時間 How long the link graph stays unchanged before some link appears or disappears.鏈路圖維持原狀，直到某條鏈路出現或消失的時間。
5.1The founding argument: beating fibre beyond 3,000 km奠基的論證：在 3,000 km 外勝過光纖
Handley’s model showed how a vacuum path can offset the extra distance of a satellite route. Its result depends on the filed constellation, wiring and fiber baseline.
Handley 的模型顯示，真空路徑可補償衛星路由增加的距離，結果取決於申報布局、接線方式與光纖基準。
| # | Reported values and conditions |
|---|---|
| 1 | Mark Handley’s HotNets paper used SpaceX’s 2016 Starlink filing: 1,600 satellites in 32 planes of 50, at about 1,150 km and 53° inclination. |
| 2 | He interpreted its five “communication components” as five laser terminals per satellite. |
| 3 | Two links ran fore and aft, two reached same-index satellites in adjacent planes, and a fifth joined the north-east-bound and south-east-bound meshes [3, §2–3]. |
| 4 | The fifth link frequently went down for realignment. |
| 5 | Dijkstra calculated latency-based source routes for the topology 200 ms ahead, and stations reached satellites within 40° of vertical (Sec. 4). |
| 6 | Over three minutes, New York–London RTT ranged from roughly 57 to 66 ms. |
| 7 | The comparison was 55 ms for great-circle fiber and a measured 76 ms for the contemporary Internet path (Fig. 7). |
| 8 | London–Johannesburg approached half the best existing Internet path’s 182 ms (Fig. 9). |
| 9 | Of twenty link-disjoint New York–London paths, five beat the fiber bound and all twenty beat 76 ms (Fig. 11). |
| 10 | The abstract concluded that such a network could beat any terrestrial fiber path beyond about 3,000 km, a figure often repeated in talks. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 衛星拓樸的研究文獻始於一篇工作坊論文與一個論斷。 |
| 2 | Mark Handley 採用 SpaceX 在 2016 年申報的 Starlink 星座，即第一期 1,600 顆衛星、32 個軌道面各 50 顆、高度約 1,150 km、傾角 53°，從申報文件裡的五個「通訊元件」推論每顆衛星會帶五具雷射終端，並把它們接成同一軌道面內前後各一條鏈路、鄰接軌道面同編號衛星各一條，以及第五條橋接朝東北與朝東南兩張網格而在重新對準時常常中斷的鏈路[3, §2–3]。 |
| 3 | 他在這張圖上以延遲為度量執行 Dijkstra，針對 200 ms 之後的拓樸重新計算路徑並以來源路由送出封包，地面站可以看見天頂 40° 之內的任何衛星（Sec. 4）。 |
| 4 | 這個領域記得的結果是：紐約–倫敦經此星座的往返時間在三分鐘的視窗內大致落在 57 到 66 ms 之間，相較於大圓光纖的 55 ms 下限與當時實測的 76 ms 網際網路路徑（Fig. 7），倫敦–約翰尼斯堡幾乎只有現有最佳網際網路路徑 182 ms 的一半（Fig. 9），而在二十條鏈路不相交的紐約–倫敦路徑中，有五條勝過光纖下限、二十條全部勝過 76 ms（Fig. 11）。 |
| 5 | 摘要把這一切壓縮成一句話：這樣的網路在距離超過約 3,000 km 的通訊上可以勝過任何地面光纖路徑，而這個數字從此在演講裡被反覆引用。 |
Two quantities define this comparison. A path’s stretch is its latency or length divided by the great-circle value between the same endpoints. A stretch of 1.25 therefore means a path one quarter longer than the geodesic. Hop count records the inter-satellite links a packet crosses and commonly estimates the link capacity a flow consumes. LEO wins when the 47% speed advantage exceeds the grid detour and the ground legs to the first and last satellites. The crossover consequently depends on altitude, elevation mask and grid geometry.
伸長比與跳數是比較路徑的兩個量。伸長比等於路徑延遲或長度除以同一對端點的大圓值，1.25 代表比測地線多走四分之一。跳數記錄封包穿越的星間鏈路數，常用來估計一條流消耗的鏈路容量。當每公里 47% 的速度優勢足以補償網格繞路及地面到首尾衛星的上下行距離，LEO 路徑便能取得延遲優勢。交叉距離因此取決於高度、仰角遮罩與網格形狀。
Bhattacherjee and colleagues paired the latency comparison with aggregate capacity and cost estimates. Both comparisons describe their historical filing and economic assumptions.
Bhattacherjee 與同事把延遲比較連結到總容量與成本估計，兩種比較都描述當時的申報與經濟假設。
| # | Reported values and conditions |
|---|---|
| 1 | Bhattacherjee and colleagues’ second HotNets paper considered both latency and economics. |
| 2 | They modeled the 4,425-satellite filing at 1,160 km using uniformly spaced polar orbits and four ISLs per satellite. |
| 3 | Two links stayed within each orbit, and two crossed orbits with polar shutdowns. |
| 4 | Frankfurt–Washington took 46.4 ms over the Internet, 35.8 ms over Hibernia, 32.6 ms over best-case fiber, and 21.7 ms in vacuum. |
| 5 | Their dense LEO model reduced latency roughly 35% against the Internet and 16% against Hibernia [68, §3.3]. |
| 6 | They estimated 240 Tbps from about 12,000 satellites with 20 Gbps downlinks, against roughly 295 Tbps of fiber capacity. |
| 7 | Estimated cost was $0.06 per gigabyte, against $0.003–0.03 for transit (§2). |
| 8 | These historical estimates share the paper’s polar-orbit simplification. |
| 9 | This primer computes a 6,530 km great-circle distance and 21.8 ms vacuum delay, consistent with the paper’s 21.7 ms after rounding. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 同一場次的第二篇 HotNets 論文為這個領域設定了議程，也附上了相應的經濟比較。 |
| 2 | Bhattacherjee 與同事以均勻分布的極軌道模擬 1,160 km 高度、4,425 顆衛星的申報版本，每顆衛星四條 ISL，兩條在軌道內、兩條跨軌道並在極區附近關閉，並以一對跨大西洋城市來框定延遲增益：法蘭克福–華盛頓在網際網路上要 46.4 ms，經 Hibernia 海纜 35.8 ms，最佳光纖 32.6 ms，而真空光速只需 21.7 ms，因此稠密的 LEO 星座大致比網際網路低 35%、比 Hibernia 低 16%[68, §3.3]。 |
| 3 | 同一篇論文估計約 12,000 顆衛星、每顆 20 Gbps 下行可提供約 240 Tbps 的總容量，相對於約 295 Tbps 的光纖，成本約每 GB $0.06、對比轉送費 $0.003–0.03（§2），這些數字和它的極軌道簡化一樣清楚標示了論文的年代。 |
| 4 | 本教材為這兩座城市計算的大圓距離是 6,530 km，真空中需 21.8 ms，與論文的 21.7 ms 在四捨五入內一致，算是對教材常數與論文常數的一次小小核對。 |
Giuliari and colleagues examined satellite transit as a BGP-facing service. Their fiber baseline, ground-station placement and rain response jointly shape the result.
Giuliari 與同事檢視面向 BGP 的衛星轉送服務，光纖基準、地面站配置與雨衰處理共同影響結果。
| # | Reported values and conditions |
|---|---|
| 1 | Giuliari and colleagues’ CCR paper asked how changing ground connectivity affects a constellation that sells transit as a BGP-facing autonomous system. |
| 2 | Their claim that satellite paths “could cut long-range latency by more than half” used a specific fiber baseline (CCR 50(1) 2020, §9). |
| 3 | Its speed was two-thirds of vacuum light speed, and its route length was 2.3 times the great circle (App. |
| 4 | A.2). |
| 5 | This baseline gives satellites a larger advantage than Handley’s great-circle bound. |
| 6 | The paper also quantified operational costs. |
| 7 | At 40° latitude, a station saw about 20 daily connection changes after a six-minute filter that discarded 15–45% of connectivity (§2.4, Fig. 1). |
| 8 | Placement at 353 IXP sites added about 10 ms over city placement (§6.1, Fig. 2). |
| 9 | Rain rerouting reduced performance a few percent on average, over 30% in the average worst case, and over 80% in the worst case. |
| 10 | These results appear in §6.2 and Fig. 3. |
| 11 | The estimated 1,833-station ground segment cost $27–30 billion, against roughly $10 billion for the constellation (§3, Table 1). |
| 12 | The early literature thus treated latency gains and the cost of sustaining them as separate questions. |
| # | 數值、條件與證據 |
|---|---|
| 1 | Giuliari 與同事在 CCR 研究星座如何在地面連接持續變化時，以面向 BGP 的自治系統販售轉送服務。 |
| 2 | 他們「衛星路徑可以把長距離延遲砍掉一半以上」的結論，採用了特定的光纖基準（CCR 50(1) 2020，§9）。 |
| 3 | 光纖速度為真空光速的三分之二，路徑長度為大圓的 2.3 倍（App. A.2），給衛星的優勢空間比 Handley 的大圓下限更大。 |
| 4 | 研究也量化營運成本：緯度 40° 的地面站經過六分鐘過濾後，每天仍約有 20 次連線變化，而過濾會捨棄 15–45% 的連通性（§2.4，Fig. 1）。 |
| 5 | 站點只設在 353 個 IXP 時，平均延遲比設在城市多約 10 ms（§6.1，Fig. 2）。 |
| 6 | 雨衰重路由的損失平均為幾個百分點，平均最壞情況超過 30%，最壞情況超過 80%（§6.2，Fig. 3）。 |
| 7 | 1,833 座地面站的地面段估價為 270–300 億美元，星座本身則約 100 億美元（§3，Table 1）。 |
| 8 | 早期文獻因此分開處理延遲增益與維持服務所需的營運成本。 |
Propagation models describe path geometry, while measured RTT includes queues, scheduling and the PoP. Individual ISL cases show how gateway reach and PoP location affect the outcome.
傳播模型描述路徑幾何，實測 RTT 則包含佇列、排程與 PoP。ISL 個案顯示閘道涵蓋與 PoP 位置如何影響結果。
| # | Reported values and conditions |
|---|---|
| 1 | All three studies calculate propagation delay. |
| 2 | Their models set queueing, satellite switching and laser acquisition costs to zero, and omit the fifteen-second beam scheduler. |
| 3 | Dijkstra chooses a path, and delay is distance divided by light speed. |
| 4 | Measured Starlink idle RTT medians were 40–50 ms across most countries in 2022–2023. |
| 5 | Bent-pipe paths ranged from 36 to 48 ms, with a median near 40 ms [49, Figs. 5–7, 12]. |
| 6 | Long ISL chains reached 100–181 ms when traffic ended at a distant PoP. |
| 7 | A Seychelles yacht routed through Nigeria had a minimum RTT of 181 ms, against about 40 ms for a direct ISL path. |
| 8 | This example appears in Izhikevich et al., Proc. |
| 9 | ACM MACS 8(1) 2024, §7.2. |
| 10 | Evidence for the ISL advantage comes from individual cases. |
| 11 | A Réunion terminal reached Frankfurt about 60 ms faster than the submarine cable [49, §6.1, Fig. 14]. |
| 12 | A Nigerian customer fell below the two-satellite ISL bound over 70% of the time [35, §7.2]. |
| 14 | Figure 5.1 places propagation estimates alongside the measured end-to-end floor to show their separate meanings. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 這三項研究都只計算傳播延遲，將佇列、衛星內交換與雷射擷取的成本設為零，並省略每十五秒重配波束的排程器。 |
| 2 | Dijkstra 選定路徑後，延遲便是距離除以光速。 |
| 3 | 2022–2023 年間，Starlink 在多數國家的閒置往返時間中位數為 40–50 ms，彎管路徑為 36–48 ms，中位數接近 40 ms [49, Figs. 5–7, 12]。 |
| 4 | 長 ISL 鏈若在遙遠的 PoP 結束，使用者會看到 100–181 ms。 |
| 5 | 塞席爾遊艇經奈及利亞 PoP 的最小往返時間為 181 ms，直接 ISL 路徑的估計值則約 40 ms [35, §7.2]。 |
| 6 | ISL 優勢的實證來自個案：留尼旺終端經法蘭克福 PoP 比海纜快約 60 ms [49, §6.1, Fig. 14]，一位奈及利亞用戶則有超過 70% 的時間低於兩顆衛星 ISL 的往返下限 [35, §7.2]。 |
| 7 | 圖 5.1 並列傳播估計與實測端到端下限，說明兩者各自衡量的範圍。 |
Original figure note原始圖說出處
Drawn for this primer from Handley, HotNets 2018, Fig. 7 and Abstract, Giuliari et al., CCR 2020, App. A.2, Kassing et al., IMC 2020, Fig. 3, Mohan et al., WWW 2024, Fig. 12, constants from Chapter 2.| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| One-way LEO latency over distance \(d\) with stretch \(s\) and two 25° legs距離 \(d\)、伸長比 \(s\)、兩段 25° 腿的 LEO 單向延遲 | \(t_{\mathrm{LEO}} = 2\times 3.75\,\text{ms} + 3.336\,s\,d\) | 7.5 ms + 4.17 µs/km × dcomputed, s = 1.25 [1, §4.3], leg = 1,123 km slant at 25° from 550 km (Chapter 1)計算值，s = 1.25[1, §4.3]，腿長為 550 km、25° 的 1,123 km 斜距（第 1 章） |
| Crossover against the great-circle fibre bound對大圓光纖下限的交叉距離 | \(d = \dfrac{7.5\,\text{ms}}{4.895 - 3.336\times1.25}\) | ≈ 10,300 kmcomputed, the +Grid path only beats a straight fibre on very long routes計算值，+Grid 路徑只在很長的路線上才勝過筆直的光纖 |
| Crossover against a fibre path 2.3× the great circle對 2.3 倍大圓光纖路徑的交叉距離 | \(d = \dfrac{7.5\,\text{ms}}{2.3\times4.895 - 3.336\times1.25}\) | ≈ 1,060 kmcomputed, stretch 2.3 from Giuliari et al., CCR 2020, App. A.2計算值，伸長比 2.3 來自 Giuliari et al.，CCR 2020，App. A.2 |
| Great-circle fibre round trip New York–London紐約–倫敦大圓光纖往返 | \(2\times 5{,}570\,\text{km}\times 4.895\,\text{µs/km}\) | 54.5 mscomputed, distance by haversine with R = 6,371 km, Handley's bound is 55 ms [3, Fig. 7]計算值，距離以 haversine、R = 6,371 km 計，Handley 的下限為 55 ms[3, Fig. 7] |
5.2Wiring the constellation: +Grid, motifs and stable links把星座接起來：+Grid、motif 與穩定鏈路
Motifs repeat a local wiring pattern among co-moving satellites, keeping established links useful as the constellation moves. Their advantage depends on permitted range and the balance between stretch and hop count.
Motif 在同向衛星間重複局部接線樣式，使既有鏈路隨星座移動持續可用。優勢取決於允許射程，以及伸長比與跳數的取捨。
| # | Reported values and conditions |
|---|---|
| 1 | Bhattacherjee and Singla’s CoNEXT 2019 paper treated constellation wiring as a design problem. |
| 2 | Satellite pairs continually enter and leave laser range, so a topology optimized for one snapshot soon becomes obsolete. |
| 3 | Integer-programming topologies one minute apart shared only 9% of links, and 19% of random-graph links became infeasible within five minutes [1, §3.1–3.2]. |
| 4 | A motif repeats the same local choice of two in-range partners at every satellite. |
| 5 | Restriction to co-moving satellites lets established links last for the constellation’s lifetime [1, §4.1–4.2]. |
| 6 | The +Grid is the simplest motif. |
| 7 | The paper searched alternatives using population-product demands among the 1,000 most populous cities. |
| 8 | M1 adds each pair’s stretch and ISL hop count, while Φ1 sums M1 with traffic weights across pairs [1, §3.1]. |
| 9 | A 40×40 reference +Grid averaged stretch 1.25 and 10.57 hops [1, §4.3]. |
| 10 | A three-zone multi-motif changed partners about every 12 minutes. |
| 11 | With the 5,014 km visibility limit, it improved Starlink’s median M1 by 52% and Φ1 by 54%. |
| 12 | Capping range at the +Grid’s required 2,006 km reduced these gains to 37% and 40%. |
| 13 | Kuiper gains were 38% and 45% at 5,440 km, then 1% and 4% at 1,761 km [1, §5.4, §6, Tab. 1]. |
| 14 | The abstract’s “nearly 2× the throughput” expresses a hop-count gain as capacity, using hops to estimate the capacity consumed per connection [1, §2.4]. |
| # | 數值、條件與證據 |
|---|---|
| 1 | Bhattacherjee 與 Singla 在 CoNEXT 2019 把星座接線視為設計問題。 |
| 2 | 雷射射程內的衛星對持續變化，使針對單一快照最佳化的拓樸很快過時。 |
| 3 | 相隔一分鐘求得的兩個整數規劃拓樸只共用 9% 鏈路，隨機圖在五分鐘內則有 19% 鏈路超出可行範圍 [1, §3.1–3.2]。 |
| 4 | Motif 讓每顆衛星重複相同的局部接線樣式，選擇兩個射程內、同向運行的夥伴，使建立後的鏈路能維持整個星座壽命 [1, §4.1–4.2]。 |
| 5 | +Grid 是最簡單的 motif。 |
| 6 | 論文以 1,000 個人口最多城市的人口乘積流量矩陣搜尋替代方案，以 M1 加總各城市對的伸長比與 ISL 跳數，再以 Φ1 計算所有城市對的流量加權總和 [1, §3.1]。 |
| 7 | 40×40 參考星座上的 +Grid 平均伸長比為 1.25，跳數為 10.57 [1, §4.3]。 |
| 8 | 三區多 motif 讓衛星約每 12 分鐘換一次鏈路，在允許 5,014 km 可見極限時，把 Starlink 的中位 M1 與 Φ1 依序改善 52% 與 54%。 |
| 9 | 射程限為 +Grid 所需的 2,006 km 時，增益降為 37% 與 40%。 |
| 10 | Kuiper 在 5,440 km 下為 38% 與 45%，在 1,761 km 下則為 1% 與 4% [1, §5.4, §6, Tab. 1]。 |
| 11 | 摘要的「將近 2 倍吞吐量」把跳數增益表達為容量，依據是以 ISL 跳數估計每條連線消耗的容量 [1, §2.4]。 |
Hop count estimates the link resources each flow consumes. For equal-rate links, bisection capacity is the sum of link rates across a cut that divides the network into two halves. Each crossing flow consumes capacity on the links it traverses. Under a fixed traffic matrix, aggregate throughput therefore scales approximately inversely with average hop count.
Halving the hops at equal link rate can roughly double delivered traffic. CoNEXT’s hop-focused multi-motif reduced hops 53% while adding 9% stretch [1, §2.4, §5.5]. Chapter 10 uses hop count and cut width to compare torus and Clos fabrics for orbital clusters.
跳數可估計每條流使用的鏈路資源。在等速率鏈路組成的圖中，對分容量等於跨越網路兩半之間割集的鏈路速率總和。每條流都會消耗所經鏈路的容量，因此在固定流量矩陣下，總吞吐量大致與平均跳數成反比。鏈路速率相同時，把跳數減半可讓交付流量約增為兩倍。CoNEXT 偏重跳數的多 motif 以增加 9% 伸長比換得 53% 跳數減少 [1, §2.4, §5.5]。第 10 章會以跳數與割集寬度比較軌道叢集的 torus 與 Clos 架構。
Stable-link design selects partners that remain in range for an orbit. Real deployment gaps make this selection more flexible than same-index grid wiring.
穩定鏈路設計選擇整圈維持射程內的夥伴，對實際部署缺口的適應性比同編號網格接線更高。
| # | Reported values and conditions |
|---|---|
| 1 | Ali and Zhang revisited the question with 90 days of real Shell-1 Space-Track TLEs from October to December 2024. |
| 2 | The filed 72×22 layout remained partially populated after the 2019 launch, and the plan changed in early 2022. |
| 3 | Their stable links stay within sight for a whole orbit, with an 80 km atmospheric exclusion setting range [34, §1–4] preprint. |
| 4 | Four-ISL +Grid delay averaged 89.0 ms over 23.4 hops. |
| 5 | The stable-link design, LSL, averaged 52.9 ms over 8.2 hops, and simulated annealing achieved 49.3 ms over 12.0 hops. |
| 6 | At 100 Gbps per ISL direction, max-min-fair capacity rose from +Grid’s 7.5 Tbps to LSL’s 17.5 Tbps (Sec. 5.5, Tables 2–3). |
| 7 | The 2019 motif method requires complete, symmetric deployment, which places the partially populated shell outside its scope. |
| 8 | On a synthetic full constellation, it achieved 48.9 ms and 21.5 hops, against +Grid’s 60.6 ms and 23.5 hops (Table 2). |
| 9 | Starlink’s V2 Mini technology page specifies three terminals. |
| 10 | With that budget, the real-data grid split into disconnected components, while SA maintained about 60 ms and LSL 77–80 ms (Secs. 5.2, 5.6). |
| 11 | The +Grid therefore describes an idealized constellation layout. |
| # | 數值、條件與證據 |
|---|---|
| 1 | Ali 與 Zhang 取用 Shell 1 在 2024 年 10 至 12 月的 90 天 Space-Track TLE，重新檢驗拓樸設計。 |
| 2 | 自 2019 年發射以來，申報的 72×22 布局始終只部署部分衛星，計畫也在 2022 年初調整。 |
| 3 | 他們保留整個軌道週期都在視線內的穩定鏈路，並以 80 km 大氣排除層設定射程 [34, §1–4] 預印本。 |
| 4 | 四 ISL +Grid 的平均延遲為 89.0 ms、23.4 跳，穩定鏈路設計 LSL 為 52.9 ms、8.2 跳，模擬退火設計為 49.3 ms、12.0 跳。 |
| 5 | 每個方向 100 Gbps 時，最大最小公平容量從 +Grid 的 7.5 Tbps 升至 LSL 的 17.5 Tbps（Sec. 5.5，Tables 2–3）。 |
| 6 | 2019 年 motif 方法的適用前提是完整且對稱的部署。 |
| 7 | 在合成完整星座上，它得到 48.9 ms、21.5 跳，+Grid 則為 60.6 ms、23.5 跳（Table 2）。 |
| 8 | Starlink 的 V2 Mini 技術頁面列出三具終端，採用這項預算時，真實資料上的三 ISL 網格分裂成多個連通分量，SA 維持約 60 ms，LSL 為 77–80 ms（Secs. 5.2、5.6）。 |
| 9 | +Grid 因此描述的是理想化的星座布局。 |
TinyLEO combines company-sourced link rates with a baseline topology. Terminal counts have changed across filings, so each result needs its configuration.
| # | Evidence record |
|---|---|
| 1 | TinyLEO specifies a Starlink-like budget of three 200 Gbps ISLs per satellite and one 96 Gbps radio access link. |
| 2 | These figures come from public Starlink statements. |
| 3 | Because the deployed topology remains undisclosed, its baseline is a standard three-ISL grid [39, §2.1, §6.1]. |
| 4 | Terminal counts changed from Handley’s inferred five in 2016, to four in the 2018 filing, to three on current satellites. |
| 5 | The +Grid consequently provides a design-space baseline. |
| 6 | Figure 5.2 compares wiring ideas, and Panel 5.1 calculates +Grid torus stretch and hop count for published city pairs. |
TinyLEO 以公司公開速率搭配基準拓樸。終端數量隨申報版本變化，引用結果時須保留相應配置。
| # | 條件與結果 |
|---|---|
| 1 | TinyLEO 採用每顆衛星三條各 200 Gbps 的 ISL，加上一條 96 Gbps 無線存取鏈路，數字取自 Starlink 的公開聲明。 |
| 2 | 實際拓樸仍待公開，因此它採標準三 ISL 網格作基準 [39, §2.1, §6.1]。 |
| 3 | 終端數量從 Handley 解讀 2016 年申報的五具，變成 2018 年申報的四具，再到目前衛星的三具。 |
| 4 | +Grid 因此適合作為設計空間的比較基準。 |
| 5 | 圖 5.2 並列三種接線方式，面板 5.1 則在 +Grid 環面上計算論文城市對的跳數與伸長比。 |
Original figure note原始圖說出處
Drawn for this primer from Handley, HotNets 2018, Sec. 3, Bhattacherjee & Singla, CoNEXT 2019, §4.1 and Fig. 6, Ali & Zhang, arXiv 2602.07756, Secs. 4–5 and Fig. 4a.Select Sydney–São Paulo, then change 72 planes of 22 satellites to 24 planes of 66 at the same altitude. Path length stays nearly constant, while hop count falls by more than half. Change node delay from 0 to 10 ms. Which layout receives the larger penalty from Chaudhry and Yanikomeroglu’s assumption? Explain how node delay can determine a topology ranking.
選擇雪梨–聖保羅，再於相同高度下把 72 面各 22 顆改成 24 面各 66 顆。路徑長度大致維持原值，跳數卻減少一半以上。接著將節點延遲從 0 切到 10 ms。Chaudhry 與 Yanikomeroglu 的假設對哪種布局帶來較大代價？請說明節點延遲如何影響拓樸排名。
| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Capacity gain of stable links over +Grid, as reported穩定鏈路相對 +Grid 的容量增益（依論文所報） | \(17.5\,\text{Tbps} / 7.5\,\text{Tbps}\) | 2.33×computed from Ali & Zhang, arXiv 2602.07756, Table 3, at 100 Gbps per ISL direction由 Ali & Zhang，arXiv 2602.07756，Table 3 計算，每個 ISL 方向 100 Gbps |
| Hop and delay reduction of LSL over +GridLSL 相對 +Grid 的跳數與延遲減少 | \(1 - 8.2/23.4;\quad 1 - 52.9/89.0\) | −65% hops, −41% delaycomputed from Sec. 5.5, Table 2 of the same preprint由同一預印本 Sec. 5.5，Table 2 計算 |
| Why static links: acquisitions per laser per day (recall from Chapter 2)為什麼鏈路靜態：每具雷射每天的擷取次數（回顧第 2 章） | \(266{,}141 / 9{,}000\) | ≈ 30 per laser per day, one every ≈ 49 mincomputed, inputs are SpaceX's SPIE 2024 figures as reported by TechSpot company計算值，輸入為 TechSpot 轉述的 SpaceX SPIE 2024 數字 公司 |
| Great-circle distances of the four panel pairs面板四個城市對的大圓距離 | \(d = 2R_E\arcsin\sqrt{\sin^2\tfrac{\Delta\phi}{2}+\cos\phi_1\cos\phi_2\sin^2\tfrac{\Delta\lambda}{2}}\) | 5,570 / 9,070 / 13,360 / 2,700 kmcomputed with R_E = 6,371 km for NY–London, London–Johannesburg, Sydney–São Paulo, Manila–Dalian以 R_E = 6,371 km 計算，依序為紐約–倫敦、倫敦–約翰尼斯堡、雪梨–聖保羅、馬尼拉–大連 |
5.3Ground relays and the laser-free phase地面中繼與純地面鏈路階段
Ground relays turn a long route into connected bent pipes. Low-elevation visibility preserves much of the vacuum speed advantage, while relay density determines the usable path choices.
地面中繼把長路徑串成多段彎管，低仰角可見性保留多數真空速度優勢，中繼密度則決定可選路徑。
| # | Reported values and conditions |
|---|---|
| 1 | SpaceX’s November 2018 filing moved the first phase to 550 km in 24 planes of 66, initially with ground-only links. |
| 2 | Handley then studied how much latency advantage could survive through ground relays. |
| 3 | A ground relay receives from one satellite and retransmits to another, producing a chain of bent pipes. |
| 4 | One satellite bridging stations 1,880 km apart gives 7.5 ms one way, against 9.2 ms over fiber of refractive index 1.468. |
| 5 | The slant legs add little distance, while the vacuum speed advantage is 47% [7, §2, Fig. 1]. |
| 6 | Lowering minimum elevation from 40° to 25° enables this span. |
| 7 | With 1,250 candidate relays on a one-degree US–Canada grid, New York–Seattle RTT was roughly 35–40 ms. |
| 8 | Best fiber took 38 ms and the Internet 76 ms (Fig. 6). |
| 9 | Relay densities above about one per degree, roughly every 95 km, brought little further benefit (Fig. 8). |
| # | 數值、條件與證據 |
|---|---|
| 1 | 2018 年 11 月，SpaceX 把第一期重新申報為 550 km、24 面各 66 顆，初期採純地面鏈路。 |
| 2 | Handley 因而研究：衛星間全靠地面轉接時，能保留多少延遲優勢？地面中繼從一顆衛星接收，再傳給另一顆，使長路徑成為一串彎管。 |
| 3 | 一顆衛星橋接相距 1,880 km 的站點時，單向需 7.5 ms，折射率 1.468 的光纖則需 9.2 ms。 |
| 4 | 兩段斜距只增加少量距離，而真空速度優勢為 47% [7, §2, Fig. 1]。 |
| 5 | 最低仰角由 40° 降為 25°，使單段彎管能跨越這段距離。 |
| 6 | 在美加一度網格上放置 1,250 個候選中繼後，紐約–西雅圖 RTT 約為 35–40 ms，最佳光纖為 38 ms，網際網路為 76 ms（Fig. 6）。 |
| 7 | 密度超過約每度一個，也就是每 95 km 一個時，額外收益很小（Fig. 8）。 |
Ocean paths require mobile relays and depend more strongly on constellation coverage. Hybrid routes and graph partitioning address separate questions: path quality and computational cost.
跨海路徑需要移動中繼，也更依賴星座涵蓋。混合路由改善路徑品質，圖分塊則降低求路成本。
| # | Reported values and conditions |
|---|---|
| 1 | Ocean crossings require ship relays. |
| 2 | With two ships and six planes, London–New York RTT ranged from 55 to 70 ms, below the 75 ms Internet path. |
| 3 | With all 24 planes, the relay route averaged about 48 ms, against about 43 ms for hypothetical ISLs (Fig. 9). |
| 4 | Chicago–Tokyo required at least 12 planes. |
| 5 | With 24, it beat the Internet by about 50 ms, while its comparison with optimal fiber varied (Fig. 10). |
| 6 | Hybrid ISL–relay paths consistently won for Toronto–Miami and London–Johannesburg (Figs. 12–13). |
| 7 | For 1,584 satellites and 5,000 relays, Dijkstra took 1.55 s on a 2.7 GHz Core i7. |
| 8 | Graph tiling reduced this to 61 ms. |
| 9 | Each additional relay cost about 12.5 µs, and route changes averaged 2.5 s apart (Sec. 3). |
| 10 | Hypatia later found relay RTT typically about 5 ms above ISL RTT for the same pairs [6, App. A]. |
| 14 | Handley also proposed idle user terminals as relays, citing SpaceX’s one-million-terminal US filing. |
| 15 | Public operator adoption remains to be established. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 跨海路徑需要船舶中繼。 |
| 2 | 兩艘船、六個軌道面時，倫敦–紐約 RTT 為 55–70 ms，低於網際網路的 75 ms。 |
| 3 | 全部 24 面運行時，中繼路徑平均約 48 ms，假想 ISL 路徑約 43 ms（Fig. 9）。 |
| 4 | 芝加哥–東京至少需 12 面才能運作，24 面時比網際網路快約 50 ms，與最佳光纖的優劣則隨情況改變（Fig. 10）。 |
| 5 | 多倫多–邁阿密與倫敦–約翰尼斯堡都以 ISL、中繼混合路徑最佳（Figs. 12–13）。 |
| 6 | 在 2.7 GHz Core i7 上，Dijkstra 為 1,584 顆衛星與 5,000 個中繼求路需 1.55 s，圖分塊後降為 61 ms。 |
| 7 | 每加一個中繼約需 12.5 µs，路徑變更平均相隔 2.5 s（Sec. 3）。 |
| 8 | Hypatia 後來發現，同一城市對的地面中繼 RTT 通常比 ISL 高約 5 ms [6, App. A]。 |
| 9 | Handley 也引用 SpaceX 的美國一百萬終端申請，提議讓閒置用戶終端作中繼，公開採用案例仍待建立。 |
Handley’s relay model resembles several features of the deployed system. Current satellites carry lasers, while most traffic still takes a bent pipe to a nearby gateway. Terminals remain within about 1,200 km of a ground station, with roughly 5 ms from gateway to PoP [49, App. D]. Long ISL chains chiefly serve locations beyond gateway reach. A Starlink gateway–PoP pair resembles a relay whose second leg uses the terrestrial Internet. Figure 5.3 shows the chain and its delay calculation.
Handley 的中繼模型與現行系統有幾項相近之處。目前衛星帶有雷射，但多數流量仍經彎管送往附近閘道。終端通常位於地面站約 1,200 km 內，閘道到 PoP 約需 5 ms [49, App. D]。長 ISL 鏈主要服務超出閘道涵蓋的地點。依此觀點，Starlink 閘道與 PoP 就像第二段接入地面網際網路的中繼。圖 5.3 說明這條鏈與延遲計算。
Original figure note原始圖說出處
Drawn for this primer from Handley, HotNets 2019, Secs. 2–3, Figs. 1, 6, 8–9.5.4Routing with a moving namespace: Hypatia churn, SHORT and TinyLEO在移動的命名空間上路由：Hypatia 的路徑變動、SHORT 與 TinyLEO
Moving satellites change the shortest route even on a fixed grid. Hypatia quantifies the resulting RTT variation, extra hops and routing-update requirements.
即使網格接線固定，衛星移動仍會改變最短路徑。Hypatia 量化了 RTT 變化、額外跳數與更新頻率需求。
| # | Reported values and conditions |
|---|---|
| 1 | A fixed +Grid still has changing shortest paths because different satellites pass over the endpoints every few minutes. |
| 2 | ETH’s ns-3 simulator Hypatia quantified this effect on a 72×22 shell at 550 km, recomputing Floyd–Warshall forwarding state every 100 ms [6, §3]. |
| 3 | On Kuiper’s first shell, Manila–Dalian RTT varied from 25 to 48 ms within 200 seconds, and Istanbul–Nairobi from 47 to 70 ms. |
| 4 | At 32.9 s, a Rio–St Petersburg path change raised RTT from 96 to 111 ms. |
| 5 | The pair later lost connectivity around 155–165 s (§4.1, Fig. 3). |
| 6 | Over 80% of city pairs kept maximum RTT below twice the geodesic value. |
| 7 | The median pair saw four changes per 200 s on Starlink and Kuiper, and two on Telesat. |
| 8 | Over one third of Starlink pairs took at least two hops beyond their minimum. |
| 9 | Updating every 1,000 ms missed changes for 6% of pairs, against 0.4% at 100 ms (§5, Figs. 6–9). |
| 10 | Handley measured a 2.5 s mean route-change interval for his relay graph [7, §3]. |
| 11 | Chapter 6 explains how a 16 ms path shortening reordered delivered packets and halved NewReno’s window at zero packet loss. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 固定的 +Grid 仍有隨時間變化的最短路徑，因為端點上空的衛星每隔幾分鐘就會更換。 |
| 2 | ETH 團隊的 ns-3 模擬器 Hypatia 對 550 km、72×22 殼層量化這種變動，每 100 ms 用 Floyd–Warshall 重算轉送狀態 [6, §3]。 |
| 3 | 在 Kuiper 第一殼層中，馬尼拉–大連 RTT 於 200 秒內在 25–48 ms 間變化，伊斯坦堡–奈洛比則為 47–70 ms。 |
| 4 | 里約–聖彼得堡在 32.9 s 換路後，RTT 從 96 升至 111 ms，並於約 155–165 s 失去連通（§4.1，Fig. 3）。 |
| 5 | 超過 80% 城市對的最大 RTT 維持在測地線值兩倍以下。 |
| 6 | 中位城市對在 Starlink 與 Kuiper 每 200 s 換路四次，Telesat 為兩次。 |
| 7 | 超過三分之一 Starlink 城市對比最小值多走至少兩跳。 |
| 8 | 路由每 1,000 ms 更新會漏掉 6% 城市對的變化，每 100 ms 更新則為 0.4%（§5，Figs. 6–9）。 |
| 9 | Handley 的中繼圖平均每 2.5 s 換路一次 [7, §3]。 |
| 10 | 第 6 章將說明 16 ms 路徑縮短如何在封包全數送達時，透過重排讓 NewReno 視窗減半。 |
SHORT assigns stable identifiers to Earth-fixed cells and handles satellite replacement locally. This keeps the logical forwarding graph stable, with the cited results sourced from the authors’ slides.
SHORT 以固定地球格元作穩定識別碼，在局部處理服務衛星交替，讓邏輯轉送圖維持穩定。此處結果以作者投影片為依據。
| # | Reported values and conditions |
|---|---|
| 1 | A constellation’s satellites move while the ground beneath them provides stable geographic reference points. |
| 2 | Tsinghua’s 2024–2025 geographic routing geographic routing geographic routing geographic routing geographic routing work uses Earth-anchored cells as destination and forwarding identifiers. |
| 3 | Satellite replacement then preserves the logical forwarding graph. |
| 4 | SHORT organizes a three-tier hierarchy: terrestrial network, orbital shells and individual orbits [69, slide 22]. |
| 5 | Its orbit-aligned (α, γ) coordinates give linearly moving sub-points and time-invariant coordinate distances, unlike latitude–longitude, H3 or S2 grids [69, slides 27–32]. |
| 6 | Local shell routing handles ISL changes. |
| 7 | Inter-shell routing serves endpoints beyond one shell’s joint coverage, chiefly at high latitudes according to the authors [69, slides 33–36]. |
| 8 | Each terrestrial IPv6 address contains a network prefix, shell identifier, cell column α and row γ, and a cell-unique node identifier [69, slide 38]. |
| 9 | Against OLSR, TS-SDN, AODV and LBP on Starlink, Iridium and Telesat, reported table updates fell 81–1,489 times. |
| 10 | The slides describe near-optimal latency [69, slide 39] and connectivity through ISL failures [69, slide 40]. |
| 11 | This primer’s source is the authors’ slides. |
| 12 | Absolute update rates, convergence times and constellation parameters require the full paper. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 星座中的衛星持續移動，地面區域則提供穩定的地理參考。 |
| 2 | 清華團隊在 2024–2025 年的地理路由研究，以錨定地球的格元作為目的地與轉送識別碼，使服務衛星交替時邏輯轉送圖保持穩定。 |
| 3 | SHORT 分為地面網路、軌道殼層與各軌道三層 [69, slide 22]。 |
| 4 | 它採用對齊軌道的 (α, γ) 座標，讓星下點線性移動、座標距離維持固定，取代經緯度、H3 與 S2 格網 [69, slides 27–32]。 |
| 5 | 殼層內的局部路由處理 ISL 變動。 |
| 6 | 兩端點超出單一殼層共同涵蓋範圍時才啟用跨殼層路由，作者預期主要發生於高緯度地點 [69, slides 33–36]。 |
| 7 | IPv6 位址含網路前綴、殼層識別碼、格元欄 α 與列 γ，以及格元內唯一的地面節點識別碼 [69, slide 38]。 |
| 8 | 在 Starlink、Iridium、Telesat 上與 OLSR、TS-SDN、AODV、LBP 比較，作者報告每秒表更新減少 81–1,489 倍，延遲接近最佳 [69, slide 39]，ISL 失效時也維持連通 [69, slide 40]。 |
| 9 | 本教材的依據為作者投影片，絕對更新速率、收斂時間與星座參數需查閱完整論文。 |
TinyLEO combines geographic forwarding with demand-aware topology control. Long-lived matching reduces link churn, and local repair handles failures within the modeled constellation.
TinyLEO 結合地理轉送與感知需求的拓樸控制，以長壽配對降低換鏈，並在模型星座內局部修復故障。
| # | Reported values and conditions |
|---|---|
| 1 | TinyLEO couples geographic routing with topology control. |
| 2 | Its demand model places over 70% of users on about 5% of land. |
| 3 | Sparse Earth-repeat orbits satisfy the Starlink customer distribution with 1,763 satellites, against 6,793 Starlink satellites in January 2025, a 3.9-fold reduction. |
| 4 | International backbone demand requires 3,344 satellites, and Latin America 1,066 [39, §6.1]. |
| 5 | An orbital model-predictive controller translates operator intents into changing ISL topologies. |
| 6 | Gale–Shapley stable matching favors long-lived links, reflecting Chapter 2’s acquisition constraint. |
| 7 | SRv6 geographic segment anycast lets any satellite covering a cell forward toward the next cell in a segment list (§4.2–4.3). |
| 8 | Routing stretch reaches 1.29 at the 90th percentile and 1.63 at worst. |
| 9 | Local failover takes 13.6–44.3 ms after an ISL loss, and repair after 1,000 random link failures averages 83.8 ms. |
| 10 | Control signaling falls one to three orders of magnitude below TS-SDN (§6, Figs. 17, 19). |
| 11 | These results come from packet-level emulation of 1,741 satellites on a StarryNet-derived cluster. |
| 12 | MOSAIC’s direct-to-cell design in Chapter 3 also uses Earth-fixed cells. |
| 13 | Together these systems indicate growing use of geography to separate stable identifiers from moving satellite locations. |
| # | 數值、條件與證據 |
|---|---|
| 1 | TinyLEO 把地理路由與拓樸控制結合。 |
| 2 | 其需求模型中，超過 70% 使用者集中在約 5% 陸地。 |
| 3 | 稀疏且分布各異的地面軌跡重複軌道，以 1,763 顆衛星滿足 Starlink 用戶分布，相較於 2025 年 1 月的 6,793 顆，數量減為約 1/3.9。 |
| 4 | 國際骨幹與拉丁美洲需求則各需 3,344 與 1,066 顆 [39, §6.1]。 |
| 5 | 軌道模型預測控制器把營運商意圖轉成隨時間變化的 ISL 拓樸，Gale–Shapley 穩定配對偏好長壽鏈路，反映第 2 章的擷取限制。 |
| 6 | 資料平面用 SRv6 地理區段任播，讓涵蓋格元的衛星朝區段清單下一格轉送（§4.2–4.3）。 |
| 7 | 路由伸長比的第 90 百分位為 1.29，最差為 1.63。 |
| 8 | ISL 失效後局部切換需 13.6–44.3 ms，1,000 次隨機鏈路故障後的修復平均 83.8 ms，控制訊令比 TS-SDN 低一至三個數量級（§6，Figs. 17、19）。 |
| 9 | 這些結果都來自 StarryNet 衍生叢集對 1,741 顆衛星的封包層級模擬。 |
| 10 | 第 3 章的 MOSAIC 也採固定地球格元，兩者顯示研究逐漸以地理座標分離穩定識別碼與移動的衛星位置。 |
Original figure note原始圖說出處
Drawn for this primer from Li et al., MobiCom 2024 (SHORT), authors' slides 22, 33 and 38, data-plane idea shared with Li et al., SIGCOMM 2025 (TinyLEO), §4.3.| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Mean interval between shortest-path changes for the median Hypatia pairHypatia 中位數城市對最短路徑變更的平均間隔 | \(200\,\text{s} / 4\) | 50 scomputed from [6, Fig. 8] (Starlink and Kuiper), Telesat 100 s由 [6, Fig. 8]（Starlink 與 Kuiper）計算，Telesat 為 100 s |
| Scheduler reconfigurations in the same 200 s window on the real network真實網路在同樣 200 s 視窗內的排程器重組次數 | \(200\,\text{s} / 15\,\text{s}\) | ≈ 13computed, 15 s period from [13] Companion, Fig. 2, the simulated path churn is the rarer event計算值，15 s 週期來自 [13] Companion，Fig. 2，模擬的路徑變動反而是較少見的事件 |
| Path changes missed by a 1,000 ms versus a 100 ms routing step1,000 ms 與 100 ms 路由步長漏掉的路徑變更 | \(6\% / 0.4\%\) | 15× more pairs affectedcomputed from [6, Fig. 9] (Kuiper K1)由 [6, Fig. 9]（Kuiper K1）計算 |
5.5Traffic engineering in 70 ms: SaTE70 ms 內的流量工程：SaTE
Shortest-path routing optimizes distance while leaving load outside its objective. Continental demand can therefore concentrate on a few inter-plane links. Traffic engineering allocates each source–destination demand across candidate paths, subject to link capacities, to satisfy as much demand as possible. Stable terrestrial WANs solve this linear program every few minutes. A constellation’s topology holding time ends whenever a ground link or ISL appears or disappears.
SaTE estimates an average holding time near 70 ms at Starlink scale, while Gurobi needs about 46 s for the corresponding problem [70, §2.3–2.4]. The graph changes roughly 650 times during that solve. SaTE therefore targets solutions fast enough for the current topology.
最短路徑路由以距離為目標，負載則在其目標範圍之外，因此大陸的長途需求可能集中於少數跨面鏈路。流量工程把各來源–目的地需求分配至候選路徑，在各鏈路容量限制內滿足盡可能多的需求。拓樸穩定的地面廣域網路可每隔幾分鐘求解一次線性規劃。星座的拓樸維持時間則在任何地面鏈路或 ISL 出現、消失時結束。SaTE 估計 Starlink 規模的平均維持時間約 70 ms，Gurobi 求解對應問題卻需約 46 s [70, §2.3–2.4]。求解期間圖已改變約 650 次，因此 SaTE 的目標是在當前拓樸仍適用時完成求解。
SaTE learns a traffic allocator that can finish within a short topology holding interval. Graph pruning and variable-size attention make the problem tractable, while experimental rate scaling defines its throughput scope.
SaTE 學習能在短拓樸維持區間內完成的流量配置器。圖修剪與可變規模注意力降低計算負擔，速率縮放則界定吞吐量範圍。
| # | Reported values and conditions |
|---|---|
| 1 | SaTE uses a learned solver over a heterogeneous graph of satellites, demands, paths and links. |
| 2 | Graph-attention layers support variable graph sizes. |
| 3 | Pruning zero-demand pairs and idle paths reduces one Starlink data point from 335 GB to 15 MB. |
| 4 | Graph2Vec and determinantal point process sampling select 512 training topologies. |
| 5 | Gurobi solutions provide supervision, with penalties for capacity violations (§3, Table 1). |
| 6 | On 4,236 satellites in completed 540, 550, 560 and 570 km shells, mean solve time is 17 ms with 87 µs standard deviation. |
| 7 | This is 2,738 times faster than Gurobi, 1,462 times faster than POP, and 28 times faster than Teal. |
| 8 | With per-second TE, satisfied demand exceeds the best baseline by 23.5% for cross-shell lasers and 46.6% for RF relays at 222 sites. |
| 9 | These results appear in §5.1 and §5.4, Figs. 8 and 10. |
| 10 | Section 5.7 records four intra-shell ISLs, polar shutdowns above 75°, and cross-shell lasers limited to 2,000 km. |
| 11 | Capacity scales to 200 Mbps with reduced flow count, so absolute throughput describes the experimental model. |
| 12 | Laser setup cost is zero (§4, footnote 5). |
| 13 | Section 7 notes that Starlink’s fifteen-second schedule exposes 10–20% of ISLs to instability, explicitly connecting scheduling to topology limitations. |
| # | 數值、條件與證據 |
|---|---|
| 1 | SaTE 以衛星、需求、候選路徑與鏈路組成異質圖，用圖注意力層處理各種大小的圖。 |
| 2 | 修剪零需求城市對與閒置路徑後，一筆 Starlink 資料從 335 GB 降至 15 MB。 |
| 3 | Graph2Vec 與行列式點過程取樣選出 512 個訓練拓樸，以 Gurobi 的解作監督，並對超出容量的分配施加懲罰（§3，Table 1）。 |
| 4 | 在 540、550、560、570 km 四個完整殼層共 4,236 顆衛星上，平均求解為 17 ms，標準差為 87 µs，比 Gurobi 快 2,738 倍、POP 快 1,462 倍、Teal 快 28 倍。 |
| 5 | 每秒重算 TE 時，跨殼層雷射比最佳基準多滿足 23.5% 需求，222 個站點的 RF 中繼則多 46.6%（§5.1、§5.4，Figs. 8、10）。 |
| 6 | 第 5.7 節記錄其假設：每顆四條殼層內 ISL，75° 以上關閉跨軌道鏈路，跨殼層雷射限於 2,000 km。 |
| 7 | 容量依流量規模縮為 200 Mbps，絕對吞吐量因此描述實驗模型，雷射建立成本設為零（§4，註腳 5）。 |
| 8 | §7 另指出十五秒排程會使 10–20% ISL 面臨穩定性變化，將排程與拓樸限制直接連結。 |
| SaTE quantitySaTE 的量 | Value數值 | Where出處 |
|---|---|---|
| Average topology holding time, Starlink scaleStarlink 規模的平均拓樸維持時間 | ≈ 70 ms | [70, §2.3.1][70, §2.3.1] |
| Gurobi solve time for the TE problemGurobi 求解 TE 問題的時間 | ≈ 46 s | §2.4§2.4 |
| SaTE solve time on 4,236 satellitesSaTE 在 4,236 顆衛星上的求解時間 | 17 ms (σ = 87 µs), 2,738× faster | §5.1, Fig. 8§5.1，Fig. 8 |
| Satisfied demand vs best baseline, lasers / RF relays相對最佳基準的滿足需求，雷射 / RF 中繼 | +23.5% / +46.6% | §5.4, Fig. 10§5.4，Fig. 10 |
| Training set and data pruning訓練集與資料修剪 | 512 topologies, 335 GB → 15 MB per data point | §3, Table 1§3，Table 1 |
| ISLs, ISL capacity, TE periodISL 數、ISL 容量、TE 週期 | 4 intra-shell (off > 75°), 200 Mbps scaled, 1 s | §4, footnote 5§4，註腳 5 |
| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Topology changes during one Gurobi solve一次 Gurobi 求解期間的拓樸變化次數 | \(46\,\text{s} / 70\,\text{ms}\) | ≈ 657computed from [70, §2.3–2.4]由 [70, §2.3–2.4] 計算 |
| Fraction of a holding time consumed by a SaTE solve一次 SaTE 求解佔一個維持時間的比例 | \(17\,\text{ms} / 70\,\text{ms}\) | ≈ 0.24computed, the solve fits inside the interval it is solving for計算值，求解能在它所針對的區間內完成 |
5.6Operations break links: manoeuvres and conjunctions營運操作會打斷鏈路：機動與交會
Collision avoidance and maintenance create correlated link outages in addition to geometric changes. Cascades near orbital intersections concentrate disruption where cross-plane traffic is busy.
避碰與維持機動會在幾何變化之外造成相關斷鏈，軌道交點附近的連鎖則把中斷集中於忙碌的跨面區域。
| # | Reported values and conditions |
|---|---|
| 1 | These topology models keep selected links active until geometry removes them, while satellites also perform orbital maintenance and collision avoidance. |
| 2 | Li and colleagues studied Starlink conjunctions from April to August 2022. |
| 3 | Close approaches involved two Starlink satellites in 52% of cases, debris in 23%, and other operators’ satellites in 18%. |
| 4 | In 98% of cooperative cases, the satellite with sparser surroundings maneuvered. |
| 5 | Maintenance changed mean ISL delay within the plotted 5–9 ms range, and four-ISL neighbor updates reached about 60 per day [71]. |
| 6 | A follow-up preprint found that one external avoidance maneuver could trigger up to 41 internal maneuvers. |
| 7 | Of cascaded maneuvers, 97% involved satellites in separate orbits near intersections. |
| 8 | A TROPICS-triggered cascade spanned 22 hops, and COSMOS-1408 debris avoidance added 27 maneuvers. |
| 9 | The lifetime budget was roughly 350 maneuvers per satellite [72, Fig. 6] preprint. |
| 10 | Ali and colleagues’ TLE census estimated about 264 fleet-wide maneuvers per day, with 74.6% for collision avoidance. |
| 11 | Mean daily failure probability was 0.0128% over the first thousand days, and survival near 0.83 at 1,395 days. |
| 12 | The nominal design life was five years [16, §3.3–3.4, Figs. 16, 21] preprint. |
| # | 數值、條件與證據 |
|---|---|
| 1 | 上面的每一種拓樸都假設鏈路一旦選定就會維持到幾何把它移除。 |
| 2 | 衛星本身卻另有義務。 |
| 3 | Li 與同事把 Starlink 當成一個自駕星座來研究，從 2022 年 4 到 8 月的交會資料顯示 52% 的近距離接近發生在兩顆 Starlink 衛星之間、23% 涉及碎片、18% 涉及其他營運商的衛星，在 98% 的合作案例中由周圍較稀疏的那顆衛星進行機動，軌道維持對 ISL 長度的擾動足以讓他們圖中的平均 ISL 延遲在 5–9 ms 區間內移動，而四 ISL 拓樸每天的鄰居更新達約 60 次[71]。 |
| 4 | 後續的預印本追蹤了連鎖反應：一次外部避碰機動可觸發多達 41 次內部機動，97% 的連鎖機動發生在各異軌道的衛星於交點附近，一次由 TROPICS 觸發的連鎖長達 22 跳，一次對 COSMOS-1408 碎片的避讓造成 27 次額外機動，而每顆衛星一生的預算約為 350 次機動[72, Fig. 6]預印本。 |
| 5 | Ali 與同事的 TLE 普查把全艦隊的速率估為每天約 264 次機動、其中 74.6% 為避碰，並給出前一千天平均每日故障機率 0.0128%、1,395 天的存活率接近 0.83，相對於名目五年的設計壽命[16, §3.3–3.4, Figs. 16, 21]預印本。 |
Each maneuver shifts a satellite from the geometry to which its lasers point. A broken link then requires 2–30 s to reacquire on current terminals. A 41-maneuver cascade near a plane intersection concentrates outages where inter-plane links are shortest and most heavily used. Recent systems consequently emphasize repair.
TinyLEO reports 83.8 ms topology repair and 13.6–44.3 ms local failover, SHORT contains changes within shells, and Ali and Zhang select orbit-stable links. The panel’s node-delay control illustrates the importance of costs beyond propagation. Reestablishment can take seconds while a laser locks, a wait outside the Chapter 7 simulators’ models.
每次機動都會改變衛星與雷射指向的幾何關係，而斷鏈後的重新擷取在現有終端上需要 2–30 s。軌道面交點附近的 41 次連鎖機動，會把中斷集中在跨面鏈路最短、使用最密集的區域。近期系統因此重視修復：TinyLEO 的拓樸修復為 83.8 ms、局部切換為 13.6–44.3 ms，SHORT 在殼層內處理變動，Ali 與 Zhang 則挑選整個軌道週期都穩定的鏈路。本章面板的節點延遲控制項說明傳播以外成本的重要性。重新建立鏈路時，等待雷射鎖定可能花數秒，這段等待在第 7 章模擬器的建模範圍之外。
5.7What the topology papers assume and what has changed拓樸論文假設了什麼，又有什麼已經改變
The table records each paper’s constellation filing, terminal count, ISL rate, and treatment of setup, node delay and the fifteen-second scheduler. Work from 2018–2020 commonly used four or five ISLs, filings at 1,150–550 km, and instantaneous link changes. Work from 2022–2026 still mostly uses four ISLs and instant setup. Deployed satellites instead carry three terminals, an undisclosed topology, a fifteen-second schedule and a fleet with 264 daily maneuvers. Each result applies to its stated assumptions, which define its value as evidence about Starlink.
下表記錄各篇論文的星座申報、終端數、ISL 速率，以及建立延遲、節點延遲與十五秒排程的處理方式。2018–2020 年研究多採四或五條 ISL、1,150–550 km 間的申報布局與瞬時換鏈。2022–2026 年研究仍多採四條 ISL 與即時建立。實際部署則有三具終端、待公開的拓樸、十五秒排程及每天機動 264 次的艦隊。各項結果適用於各自的假設，這些條件也界定了它們作為 Starlink 證據的範圍。
| Paper論文 | Filing / geometry frozen凍結的申報 / 幾何 | ISLs per satellite每顆衛星 ISL 數 | ISL rateISL 速率 | Setup delay建立延遲 | Node delay節點延遲 | 15-s schedule15 秒排程 |
|---|---|---|---|---|---|---|
| [3][3] | 2016 filing: 1,150 km, 32×50, 53°2016 年申報：1,150 km，32×50，53° | 5 | outside the model (≥100 Gb/s speculated)在模型範圍之外（推測 ≥100 Gb/s） | setup omitted, fifth link “often down”省略建立成本，第五鏈路「常中斷」 | zero省略 | predates早於發現 |
| [68][68] | 4,425 at 1,160 km, polar simplification1,160 km 的 4,425 顆，極軌道簡化 | 4 | 20 Gbps downlink per satellite for aggregate only僅以每顆 20 Gbps 下行估總量 | omitted省略 | zero省略 | predates早於發現 |
| [1, §2.4, §6][1, §2.4, §6] | Nov 2018 filing: 550 km, 24×662018 年 11 月申報：550 km，24×66 | 4 | outside the model, hop count as proxy在模型範圍之外，以跳數代理 | omitted省略 | zero省略 | predates早於發現 |
| [7][7] | Nov 2018 filing: 550 km, 24×66, 25° mask2018 年 11 月申報：550 km，24×66，25° 遮罩 | 0 (phase 1), 4 later0（第一期），之後 4 | qualitative定性 | n/a適用範圍外 | zero省略 | predates早於發現 |
| [73][73] | "Phase 2" with ISLs, 40° mask, ±56° latitude帶 ISL 的「第二期」，40° 遮罩，±56° 緯度 | 4 | value unspecified資料待補 | omitted省略 | none, fibre 2c/3 × 2.3零節點延遲，光纖 2c/3 × 2.3 | predates早於發現 |
| [6] (Hypatia)[6] （Hypatia） | Aug 2019 filing: 550 km, 72×222019 年 8 月申報：550 km，72×22 | 4 | 10 Mbit/s in experiments (sweep to 10 Gbit/s)實驗用 10 Mbit/s（掃到 10 Gbit/s） | omitted省略 | none, 100-packet queues零節點延遲，100 封包佇列 | predates早於發現 |
| [33][33] | 550 km, 24×66550 km，24×66 | 4 permanent + temporary4 條永久 + 暫時 | outside the model在模型範圍之外 | tabulated 2–30 s, assumed ms (future)列表 2–30 s，假設毫秒級（往後） | 10 ms | omitted省略 |
| [32] preprint[32] 預印本 | 550 km, 24×66550 km，24×66 | range-limited links射程限制的鏈路 | outside the model在模型範圍之外 | yes: 100 ms–1 s swept有：掃 100 ms–1 s | 1 ms | omitted省略 |
| [71][71] | real TLEs 20222022 年真實 TLE | 4-ISL topologies4 ISL 拓樸 | outside the model在模型範圍之外 | omitted省略 | ISL delay 5–9 ms plotted圖示 ISL 延遲 5–9 ms | omitted省略 |
| [69, slide 39] (SHORT)[69, slide 39] （SHORT） | Starlink, Iridium, Telesat (slide 39), parameters outside the slides’ scopeStarlink、Iridium、Telesat（投影片第 39 頁），投影片參數待補 | outside the slides’ scope投影片資料待補 | outside the slides’ scope投影片資料待補 | outside the slides’ scope投影片資料待補 | outside the slides’ scope投影片資料待補 | omitted省略 |
| [39] (TinyLEO)[39] （TinyLEO） | synthesised Earth-repeat orbits vs Starlink 6,793 (Jan 2025)合成的地面軌跡重複軌道對比 Starlink 6,793 顆（2025 年 1 月） | 3 | 200 Gbps each + 96 Gbps access company每條 200 Gbps + 96 Gbps 存取 公司 | named as challenge, quantification pending列為挑戰，數量待補 | bounded by cell size以格元大小為界 | outside the stated scope在敘述範圍之外 |
| [70] (SaTE)[70] （SaTE） | 4,236 in four shells 540–570 km540–570 km 四個殼層共 4,236 顆 | 4 intra-shell, off > 75°4 條殼層內，>75° 關閉 | 200 Mbps scaled縮放後 200 Mbps | omitted省略 | zero省略 | §7 only: 10–20% of ISLs exposed僅 §7：10–20% ISL 受影響 |
| [34] preprint[34] 預印本 | real Shell-1 TLEs Oct–Dec 20242024 年 10–12 月真實 Shell-1 TLE | 4 and 34 與 3 | 100 Gbps per direction company每方向 100 Gbps 公司 | avoided by using only stable links以只用穩定鏈路迴避 | zero省略 | omitted省略 |
Four changes guide interpretation of these results. Terminal count fell from Handley’s inferred five in 2016, to four in the 2018 filing, and three in current SpaceX descriptions. Four-ISL results therefore assume extra connectivity, while a three-ISL grid splits into disconnected components on real ephemerides. Laser setup takes 2–30 s.
Setup delay and endpoint definitions determine how these modeled latencies relate to measured network delay.
| # | Evidence record |
|---|---|
| 1 | Chaudhry and Yanikomeroglu tabulate that range and assume shorter setup, while Bhattacharjee and colleagues model its effect. |
| 2 | Their 1 s setup raises mean New York–Istanbul latency from 25.9 to 123.9 ms, making frequent-link-change results upper bounds. |
| 3 | The fifteen-second scheduler appears only in SaTE’s limitations. |
| 4 | Propagation estimates from 2018–2020 measure a separate quantity from the measured 40 ms floor and SpaceX’s reported 25–35 ms end-to-end values. |
Those end-to-end values include PoPs, queues and scheduling. Finally, the chapter’s simulators use 10 Mbit/s–200 Mbps links. Their throughput results illustrate modeled dynamics, while predictions for 100–200 Gbps lasers require measurements or models at those rates.
終端數、鏈路建立、排程及速率假設，決定各結果的適用範圍。表中保留各研究的條件與量測端點。
| # | 條件與結果 |
|---|---|
| 1 | 四項變化決定這些結果的解讀。 |
| 2 | 終端數從 Handley 於 2016 年推論的五具，降至 2018 年申報的四具，再到目前 SpaceX 描述的三具。 |
| 3 | 因此四 ISL 結果假定較多連通性，三 ISL 網格在真實星曆上則分裂為多個連通分量。 |
| 4 | 雷射建立需 2–30 s，Chaudhry 與 Yanikomeroglu 列出這個範圍後採更短假設，Bhattacharjee 與同事則模擬其影響。 |
| 5 | 後者的 1 s 建立延遲使紐約–伊斯坦堡平均延遲從 25.9 升至 123.9 ms，頻繁換鏈結果因此屬上界。 |
| 6 | 十五秒排程只出現在 SaTE 的限制討論。 |
| 7 | 2018–2020 年的傳播估計與實測 40 ms 下限、SpaceX 報告的 25–35 ms 端到端數字，各有其量測範圍，後者包含 PoP、佇列與排程。 |
| 8 | 最後，本章模擬器採 10 Mbit/s–200 Mbps 鏈路，吞吐量結果說明模型動態，100–200 Gbps 雷射的預測則需要相應速率的量測或模型。 |
Propagation simulations explain when orbital routes gain a distance advantage. Measured endpoints and newer topology results supply separate evidence.
| # | Evidence record |
|---|---|
| 1 | The “LEO beats fiber” claim comes from three propagation simulations published in 2018–2020. |
| 2 | Their vacuum paths use +Grid stretch near 1.25 and compare against great-circle or stretched fiber. |
| 3 | Altitude, elevation mask and fiber model move the crossover from about 1,000 to 10,000 km. |
| 4 | Measured end-to-end delay has a roughly 40 ms floor shaped by PoPs and scheduling. |
| 5 | Topology research progressed from motifs with a 54% gain on a four-terminal 24×66 filing to ground relays and stable links on real ephemerides. |
The stable-link results cut hops 65%, more than double capacity, and reveal disconnected three-ISL grids. Earth-fixed routing cells reduce updates by two to three orders of magnitude. SaTE solves in 17 ms against a 70 ms holding time, while 264 daily maneuvers make repair time an operational metric. Section 5.7 records the filing, terminal and setup assumptions that accompany these results.
傳播模擬說明軌道路徑何時取得距離優勢，實測端點與新拓樸結果則補上其他證據。表中整理本章的比較條件與結果。
| # | 條件與結果 |
|---|---|
| 1 | 「LEO 勝過光纖」源自 2018–2020 年三項傳播模擬，以伸長比約 1.25 的 +Grid 真空路徑，對照大圓或拉長的光纖路徑。 |
| 2 | 高度、仰角遮罩與光纖模型使交叉距離落在約 1,000–10,000 km，實測端到端延遲則有受 PoP 與排程影響的約 40 ms 下限。 |
| 3 | 拓樸設計從四終端、24×66 申報上改善 54% 的 motif，發展至地面中繼與真實星曆上的穩定鏈路。 |
| 4 | 後者減少 65% 跳數、使容量超過兩倍，也揭示三 ISL 網格會分裂。 |
| 5 | 固定地球格元讓路由表更新減少兩至三個數量級，SaTE 在 70 ms 維持時間內以 17 ms 求解，每日 264 次機動則使修復時間成為營運指標。 |
| 6 | 引用結果時，第 5.7 節提供相應申報、終端與建立時間假設。 |
Chapter 6 follows path changes into the congestion window. Hypatia’s 16 ms path shortening halves NewReno’s window at zero loss, and the fifteen-second schedule misleads delay- and loss-based controllers. Chapter 7 examines the assumptions built into Hypatia, StarryNet and other emulators. Chapter 10 uses bisection capacity to compare torus and Clos fabrics for orbital training clusters.
第 6 章追蹤路徑變化對壅塞視窗的影響。Hypatia 的 16 ms 路徑縮短，在封包全數送達時讓 NewReno 視窗減半，十五秒排程則誤導延遲與遺失式控制器。第 7 章檢查 Hypatia、StarryNet 與其他模擬平台的內建假設。第 10 章以對分容量比較軌道訓練叢集的 torus 與 Clos 架構。