Using Ground Relays for Low-Latency Wide-Area Routing in Megaconstellations在巨型星座中使用地面中繼實現低延遲廣域路由

ACM HotNets 2019Mark Handley (University College London) · paper論文 peer-reviewed

This digest explains ground-relay paths on a 550 km shell, the relay-density saturation, and the benefits of combining relays with ISLs.本導讀說明 550 km 殼層的地面中繼路徑、中繼密度飽和，以及中繼與 ISL 混合的效益。

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Ground relays recover a geometric vacuum advantage by joining bent-pipe spans. Relay density saturates, while ocean paths benefit from combining relays and ISLs.

地面中繼串接彎管以取得幾何真空優勢，密度效益會飽和，跨海路徑則受益於中繼與 ISL 混合。

Filed configuration and propagation results
#	Reported values and conditions
1	SpaceX’s November 2018 filing moved 1,584 satellites to 550 km in 24×66, lowered minimum elevation from 40° to 25°, and removed first-phase lasers ^{[7, §2]}.
2	Handley shows that ground-relay chains retain much of the geometric latency advantage.
3	One 1,880 km bounce takes 7.5 ms one way, against 9.2 ms over fiber ^{[7, Fig. 1]}.
4	New York–Seattle through 1,250 relays on a one-degree grid gives about 35–40 ms RTT, against 38 ms best fiber and 76 ms Internet ^{[7, Fig. 6]}.
5	Density beyond roughly one relay per degree gives little additional latency benefit ^{[7, Fig. 8]}.
6	Ocean routes require ships or ISLs, and mixed experiments favor hybrids ^{[7, Figs. 12–13]}.
7	Results use propagation-only simulation of a filing replaced by 72×22 nine months later.

申報設定與傳播結果
#	數值、條件與證據
1	2018 年 11 月 SpaceX 申報改為 1,584 顆、550 km、24×66，把最低仰角從 40° 降至 25°，並移除第一階段雷射 ^{[7, §2]}。
2	Handley 顯示地面中繼鏈保留多數幾何延遲優勢，1,880 km 反彈單向需 7.5 ms，光纖需 9.2 ms（Fig. 1）。
3	紐約–西雅圖透過一度網格 1,250 中繼約為 35–40 ms RTT，最佳光纖為 38 ms、網際網路為 76 ms（Fig. 6）。
4	密度超過每度約一個時額外收益很小（Fig. 8），跨海需船或 ISL，混合實驗則以混合路徑最佳（Figs. 12–13）。
5	結果是純傳播模擬，該申報九個月後被 72×22 取代。

1. Where this paper sits1. 這篇論文的位置

Handley’s second HotNets paper studies the ground-only first phase that resembled 2019’s v1.0 launch. It introduces relays as topology elements, developed in Section 5.3 and later SaTE’s RF relays, which raise satisfied demand 46.6% ^{[70, §5]}. It also reduces Dijkstra cost for 1,584 satellites and 5,000 relays from 1.55 s to 61 ms through tiling and graph reuse ^{[7, §3]}. The shared 24×66 snapshot connects it with CoNEXT 2019, temporary-link studies and setup-delay work.

Handley 第二篇 HotNets 研究純地面第一階段，與 2019 v1.0 發射型態相近。地面中繼作為拓樸元件出現在第 5.3 節，後續 SaTE 的 RF 中繼則使滿足需求提高 46.6% ^{[70, §5]}。分塊、重用圖也讓 1,584 衛星加 5,000 中繼的 Dijkstra 從 1.55 s 降至 61 ms ^{[7, §3]}。相同 24×66 快照使它連結 CoNEXT 2019、暫時鏈路與建立延遲研究。

2. The problem, measured2. 問題，用量測說話

Low altitude and low elevation permit a long vacuum bounce with a modest distance penalty. Repeating useful bounces can preserve that propagation advantage.

低高度與低仰角允許長距真空反彈，距離代價較小，重複合適反彈可保留傳播優勢。

Single-bounce geometry and timing
#	Reported values and conditions
1	Lowering the shell from 1,150 km to 550 km shortens ground legs. A 25° mask permits longer station-to-station spans.
2	With ground-only communication, each satellite returns packets to Earth.
3	A 1,880 km bounce takes 7.5 ms versus 9.2 ms in fiber ^{[7, §2, Fig. 1]}.
4	At 550 km, each mask-angle slant leg is 1,123 km, giving 7.49 ms for two legs, while fiber takes 9.20 ms at 4.895 µs/km.
5	The vacuum path is about 20% longer, with a 47% propagation-speed advantage.
6	Relays repeat this benefit when useful landing points allow long bounces toward the destination.
7	The modeled 5,739 s orbit gives a new station pass every 87 s, setting a path-change timescale ^{[7, §2.3]}.

單次反彈幾何與時序
#	數值、條件與證據
1	殼層從 1,150 km 降至 550 km，縮短了地面路徑。25° 遮罩則允許更長站間跨度，純地面通訊使每顆衛星把封包送回地球。
2	1,880 km 反彈為 7.5 ms，光纖為 9.2 ms ^{[7, §2, Fig. 1]}。
3	550 km 的遮罩斜距為 1,123 km，兩腿合計 7.49 ms，光纖按 4.895 µs/km 得 9.20 ms。
4	真空路徑約長 20%，速度優勢則為 47%。
5	若落點允許朝目的地方向長反彈，中繼可重複這項效益。
6	模型 5,739 s 軌道使站點每 87 s 看到新過頂，界定路徑變化尺度 ^{[7, §2.3]}。

Question	問題	Formula
One-way delay of a single bounce with both legs at the 25° mask兩段路程都在 25° 遮罩上的單次反彈單向延遲	\( t=\tfrac{2\,d(25^\circ)}{c} \)	2 × 1,123.4 km → 7.49 mscomputed, d(25°) = 1,123.4 km at 550 km (fact base Ch. 1 table), c = 299,792,458 m/s, Handley's Fig. 1 gives 7.5 ms計算值，550 公里處 d(25°) = 1,123.4 km（事實庫第 1 章表），c = 299,792,458 m/s，Handley 圖 1 給 7.5 ms
One-way delay of 1,880 km of fibre1,880 公里光纖的單向延遲	\( t=\tfrac{n\,L}{c},\ n=1.468 \)	1,880 km × 4.895 µs/km → 9.20 mscomputed, n = 1.468 is the paper's value ^{[7, §2]}, Handley's Fig. 1 gives 9.2 ms計算值，n = 1.468 為論文採用值^{[7, §2]}，Handley 圖 1 給 9.2 ms
Relay grid spacing at one relay per degree每一度一個中繼時的網格間距	\( s=\tfrac{2\pi R_E}{360} \)	≈ 111 km of latitude, Handley quotes ≈ 95 km for his gridCalculated with R_E = 6,378.137 km. The paper gives ≈ 95 km for a 1° grid over 30–55° N, where longitude degrees are shorter ^{[7, §2.1]}以 R_E = 6,378.137 km 計算，≈ 95 km 是論文對北緯 30–55° 一度網格自己給的數字，該處經度一度較短^{[7, §2.1]}

3. The design3. 設計

The design combines candidate relays with geometry-predicted route changes. Tiling and graph reuse reduce computation while fine timing limits packet reordering.

設計結合候選中繼與幾何預測換路，分塊、圖重用降低計算，細緻時序則限制封包重排。

Relay layout and routing-computation benchmark
#	Reported values and conditions
1	A relay receives from one satellite and retransmits to another.
2	Handley places 1,250 candidates about 95 km apart on a one-degree grid over 75–122° W and 30–55° N ^{[7, §2.1]}.
3	He sweeps spacing from 2.5°, or 238 km, to 0.5°, or 48 km, and also tests ten population-center relays.
4	Atlantic experiments use two ships, while London–Johannesburg uses 25 African relays.
5	Idle user terminals are another proposal, supported by SpaceX’s one-million-terminal filing ^{[7, §2.2–2.3]}.
6	On a 2.7 GHz Core i7, Dijkstra for 1,584 satellites plus 5,000 relays takes 1.55 s.
7	Using 10° tiles with 100 km margins and incremental rebuilds reduces it to 61 ms.
8	Graph reuse lasts about 13.7 s, with under 4% of satellites rebuilt per 500 ms.
9	Each added relay costs about 12.5 µs, and 40,000 relays stay under 500 ms.
10	Routes change every 2.5 s on average.
11	Predictable geometry permits millisecond switchovers, while 300 versus 18 ms updates differ about 30 µs, enough to reorder fifty packets at 20 Gb/s ^{[7, Fig. 11]}.

中繼配置與求路基準
#	數值、條件與證據
1	中繼從一衛星接收，再轉給另一顆。
2	Handley 在 75–122° W、30–55° N 以一度網格放置 1,250 候選，間距約 95 km ^{[7, §2.1]}，掃描 2.5°／238 km 至 0.5°／48 km，也測試十個人口中心中繼。
3	大西洋用兩艘船，倫敦–約翰尼斯堡用 25 個非洲中繼，另依 SpaceX 百萬終端申請提議閒置用戶中繼 ^{[7, §2.2–2.3]}。
4	2.7 GHz Core i7 上，1,584 衛星加 5,000 中繼的 Dijkstra 需 1.55 s，10° 區塊、100 km 邊界與增量重建使它降為 61 ms。
5	圖可重用約 13.7 s，每 500 ms 重建少於 4% 衛星。
6	每加一中繼約 12.5 µs，40,000 中繼仍低於 500 ms。
7	路徑平均每 2.5 s 改變，幾何預測可支援毫秒切換，300 與 18 ms 更新造成約 30 µs 差距，足以讓 20 Gb/s 的五十封包重排（Fig. 11）。

Figure A. Left: a packet reaches a satellite near the 25° mask, returns to a ground relay, then climbs again. Each bounce covers about 1,880 km in 7.5 ms, compared with 9.2 ms through fibre. Right: two comparisons use 24 planes. New York–Seattle uses a relay grid, and London–New York uses two ships. Each compares relay paths with best fibre, the ISL alternative and measured Internet.圖 A。左：機制——封包爬到接近 25° 遮罩的衛星，降到地面中繼再爬一次，所以每次反彈以 7.5 ms 跨越約 1,880 公里，光纖則需 9.2 ms。右：24 個軌道面下的兩個主要比較，使用中繼網格的紐約–西雅圖與使用兩艘船的倫敦–紐約，對比最佳光纖、ISL 替代方案與實測網際網路。Sources來源: ^{[7, §2, Figs. 1, 6, 8, 9]}

Original figure note原始圖說出處

Drawn for this primer from Handley, HotNets 2019, §2, Figs. 1, 6, 8 and 9, slant range from the fact base Chapter 1 table.

4. Evaluation setup4. 實驗設定

The evaluation isolates propagation on a historical shell. Later filing geometry and actual relay processing require their own treatment.

評估分離歷史殼層的傳播，後續申報幾何與實際中繼處理則需另行處理。

Simulation configuration and later filing
#	Reported values and conditions
1	The custom simulation extends Handley’s 2018 tool.
2	Its November 2018 snapshot uses 1,584 satellites, 24×66, 550 km and 53°.
3	The first phase uses ground-only links, later phases assume four lasers, and partial deployments use six and twelve planes ^{[7, §2]}.
4	Minimum elevation is 25° and fiber index 1.468.
5	Relay forwarding, queue and node delay are zero, while capacity is discussed qualitatively.
6	The afterword acknowledges the August 2019 72×22 filing and estimates continuous US coverage with eighteen planes from Fig. 14.
7	Evaluation remains on the earlier snapshot.

模擬設定與後續申報
#	數值、條件與證據
1	專用模擬延伸 Handley 2018 工具，採 2018 年 11 月的 1,584 顆、24×66、550 km、53° 快照。
2	第一階段為純地面鏈路，後續假設四雷射，也測試六、十二軌道面部分部署 ^{[7, §2]}。
3	最低仰角 25°、光纖折射率 1.468，轉送、佇列與節點延遲皆設零，容量作定性討論。
4	後記引用 2019 年 8 月的 72×22 申報，並依 Fig. 14 估計十八面可連續涵蓋美國，評估則仍採早期快照。

5. What was measured5. 量到了什麼

Claim宣稱	Setup and caveat設定與附註
One satellite bounce over 1,880 km: 7.5 ms one way against 9.2 ms in fibre ^{[7, Fig. 1]}.跨越 1,880 公里的單次衛星反彈：單向 7.5 ms，光纖 9.2 ms（圖 1）。	Both stations sit at 25° elevation, with 1,123 km slant legs and zero relay-forwarding cost.兩站皆採 25° 仰角、1,123 km 斜距與零中繼轉送成本。
New York–Seattle RTT is ≈ 34–40 ms with 1,250 relays and ≈ 34–50 ms with 10 relays. The comparison values are 38 ms for best fibre and 76 ms for Internet ^{[7, Fig. 6]}. Mean RTT is ≈ 34.6–34.7 ms ^{[7, Fig. 8]}.紐約–西雅圖 RTT 在 1,250 個中繼下約 34–40 ms、只有 10 個中繼時約 34–50 ms，對比最佳光纖 38 ms 與網際網路 76 ms（圖 6），平均約 34.6–34.7 ms（圖 8）。	24 planes, relay-only path over land, values read from figures. The mean barely moves with density, which is the saturation result.24 軌道面、陸地純中繼路徑，數值由圖讀出。密度增加時平均值大致固定，顯示飽和。
"Very little latency benefit" from relays denser than one per degree, about 95 km ^{[7, Fig. 8]}.中繼比每度一個（約 95 公里）更密時「延遲改善極少」（圖 8）。	Sweep from one per 2.5° to one per 0.5°, the regular grid produces an aliasing ripple in the curves that the author flags.從每 2.5° 一個掃到每 0.5° 一個，規則網格在曲線上產生作者指出的混疊波紋。
Two ships give London–New York RTT of 55–70 ms at 6 planes. At 24 planes, RTT stays below the great-circle fibre bound. Internet takes 75 ms, while mean ISL and relay RTTs are ≈ 43 ms and ≈ 48 ms ^{[7, Fig. 9]}.倫敦–紐約配兩艘船：6 個軌道面時 55–70 ms，24 個軌道面時始終低於大圓光纖下限，網際網路 75 ms，ISL 平均約 43 ms，中繼平均約 48 ms（圖 9）。	The ISL case assumes four lasers per satellite in a later phase. The relay case uses two ships at author-selected positions.ISL 情境假設後期階段每顆衛星四個雷射，中繼情境依賴兩艘由作者選定位置的船。
Chicago–Tokyo requires twelve planes for continuous coverage. At twenty-four planes, mean RTT beats Internet by 50 ms. The comparison with optimal fiber varies ^{[7, Fig. 10]}. Toronto–Miami and London–Johannesburg hybrid paths beat both pure ISL and pure relay paths ^{[7, Figs. 12–13]}.芝加哥–東京至少十二面才有連續路徑，二十四面時平均比網際網路快 50 ms，與最佳光纖的優劣則隨時變動（Fig. 10）。多倫多–邁阿密、倫敦–約翰尼斯堡的混合路徑皆勝純 ISL、純中繼（Figs. 12–13）。	The Pacific path requires political availability of a Kamchatka relay. The hybrid result describes the two tested city pairs.太平洋路徑需要堪察加中繼的政治可用性，混合結果適用於受測的兩組城市。
Dijkstra uses 1,584 satellites and 5,000 relays. Runtime falls from 1.55 s to 61 ms with 10° tiles. Each extra relay costs ≈ 12.5 µs, and 40,000 relays require under 500 ms. Routes change every 2.5 s on average ^{[7, §3]}.1,584 顆衛星與 5,000 個中繼的 Dijkstra：樸素 1.55 秒，10° 區塊 61 ms，每多一個中繼約 12.5 µs，40,000 個中繼低於 500 ms，路徑平均每 2.5 秒改變^{[7, §3]}。	This is a single-source software benchmark on one 2.7 GHz core. A deployed routing protocol requires additional evaluation.這是單一來源、單顆 2.7 GHz 核心的軟體基準，部署路由協定仍需額外評估。

6. Limits and open questions6. 限制與待解的問題

Relays are zero-delay reflectors in the model. Receive, decode, scheduling, retransmission, queues and shared user-uplink capacity require additional treatment. Real relays also encounter 15-second reconfiguration (Part C, item 57). Measured bent-pipe floors near 40 ms and idle medians of 25–50 ms show the scale of end-to-end overhead beyond propagation (Part C, item 58).模型把中繼視為零延遲反射器，接收、解碼、排程、重傳、佇列與共享上行容量需要額外處理。實際中繼也面對15 秒重配（C 部第 57 項），實測約 40 ms 彎管下限與 25–50 ms 閒置中位數則顯示傳播之外的端到端成本尺度（C 部第 58 項）。
Fiber bounds and measured routes have separate meanings. The source labels 38 ms New York–Seattle and 75 ms London–New York as great-circle values at index 1.468. Comparisons with actual Internet paths retain the measured baseline’s routing and operational overhead.光纖下限與實測路線各有意義。來源把紐約–西雅圖 38 ms、倫敦–紐約 75 ms 標為折射率 1.468 的大圓值，實際網際網路比較則保留基線的路由與營運成本。
Relay availability is an assumption. The grid, ships and idle terminals are hypothetical, and regular grids cause aliasing ripples. Ocean crossings and politically blocked sites remain constraints. Public latency-relay deployment evidence remains open, while Starlink’s ISL shells provide another path option.中繼可用性屬假設，網格、船舶、閒置終端均為假想，規則網格也產生混疊波紋。跨海與政治封鎖站點仍是限制，延遲中繼的公開部署證據待建立，Starlink 的 ISL 殼層則提供另一種路徑。
The historical 24×66 layout changes to 72×22 in August 2019 (Part C, item 12). Intra-plane spacing grows from 659 to 1,969 km, altering pass cadence. Later terminal counts are three, with deployed topology undisclosed (Part C, items 13 and 55).24×66 歷史布局在 2019 年 8 月改為 72×22（C 部第 12 項），面內間距從 659 增至 1,969 km，並改變過頂節律。後續終端數為三具，部署拓樸仍待公開（C 部第 13、55 項）。
Both comparisons set setup cost to zero: persistent lasers on one side and instantaneous antenna repointing on the other. Modern acquisition takes 2–30 s (Part C, item 18). Later comparable-pair analysis shows 100 ms setup raising mean delay from 25.9 to 35.7 ms ^{[32, §IV-B]}.兩側比較都把建立成本設零，依序是假設持續雷射與瞬時天線重指。現代擷取需 2–30 s（C 部第 18 項），後續相近城市對分析中，100 ms 建立使平均延遲從 25.9 升至 35.7 ms ^{[32, §IV-B]}。
Most latency values come from figure readings. New York–Seattle means include 34.56 and 34.70 ms across the density sweep, and hybrid superiority is demonstrated for two city pairs.多數延遲由圖讀出，密度掃描中的紐約–西雅圖平均含 34.56、34.70 ms，混合優勢則展示於兩組城市。

7. How it connects7. 與其他內容的關聯

Section 5.3 is built on this paper's numbers for the laser-free phase and the hybrid result.第 5.3 節以本文純地面鏈路階段與混合路徑結果為基礎。
Section 5.1 places the single-bounce arithmetic beside the 2018 crossover argument and the measured 40 ms floor.第 5.1 節把單次反彈的算術放在 2018 年交叉論證與實測 40 ms 下限旁邊。
Section 5.7 lists the 24×66 snapshot and the four-laser later phase among the assumptions that have changed.第 5.7 節把 24×66 快照與後期階段的四雷射列入已改變的假設。
Section 2.5 explains the shared 24×66 shell in the motif and temporary-link papers. Section 3.3 describes operational bent-pipe service through gateways and points of presence.第 2.5 節說明為什麼同一個 24×66 殼層出現在 motif 與暫時鏈路論文中，第 3.3 節給出實際營運中的彎管，含閘道與 PoP。
Related pages: Handley 2018 supplies the laser-equipped predecessor. Gearing Up 2018 and CCR 2020 study capacity and transit with lasers. CoNEXT 2019 optimizes the four-laser lattice on the same 24×66 shell. Ali & Zhang 2026 and TinyLEO study three terminals on real orbits. SaTE incorporates RF ground relays into traffic engineering.相關導讀：Handley 2018 是配備雷射的前作，Gearing Up 2018 與 CCR 2020 保留雷射並討論容量與中轉，CoNEXT 2019 在同一個 24×66 殼層上最佳化四雷射格狀結構，Ali 與 Zhang 2026 和 TinyLEO 顯示三個終端在真實軌道上能做到什麼，SaTE 在流量工程求解器中重新啟用無線電地面中繼。

Key numbers關鍵數字

Number	數字	Meaning (setup)
24 × 66, 550 km, 53°	November 2018 filing, 1,584 satellites, ground-only routing in the first phase ^{[7, §2]}, replaced by 72 × 22 in August 2019.	2018 年 11 月申請文件，1,584 顆，第一階段純地面鏈路^{[7, §2]}，2019 年 8 月被 72×22 取代。
40° → 25°	Minimum elevation before and after the 2018 modification ^{[7, §2]}, the change that makes long single bounces possible.	2018 年修改前後的最低仰角^{[7, §2]}，讓長距離單次反彈成為可能的改變。
7.5 vs 9.2 ms	One-way delay over 1,880 km via one satellite versus fibre ^{[7, Fig. 1]}, reproduced from a 1,123 km slant range [computed].	經一顆衛星跨越 1,880 公里的單向延遲對比光纖（圖 1），由 1,123 公里斜距重現［計算值］。
1,250 / 1° / ≈ 95 km	Candidate relays, grid pitch and spacing over 75–122° W, 30–55° N ^{[7, §2.1]}.	候選中繼數、網格間距與 75–122° W、30–55° N 範圍內的距離^{[7, §2.1]}。
≈ 35–40 / 38 / 76 ms	NY–Seattle RTT via relays at 24 planes / best fibre / Internet ^{[7, Fig. 6]}.	24 個軌道面下經中繼的紐約–西雅圖 RTT／最佳光纖／網際網路（圖 6）。
≈ 48 / ≈ 43 / 75 ms	London–NY mean RTT via relays and two ships / via four-laser ISLs / Internet at 24 planes ^{[7, Fig. 9]}.	24 個軌道面下倫敦–紐約經中繼與兩艘船／經四雷射 ISL／網際網路的平均 RTT（圖 9）。
1.55 s → 61 ms	Single-source Dijkstra for 1,584 satellites + 5,000 relays, naive versus 10° tiling with 100 km margin ^{[7, §3]}.	1,584 顆衛星加 5,000 個中繼的單一來源 Dijkstra，樸素對比 10° 分塊加 100 公里邊界^{[7, §3]}。
87 s / 2.5 s	Interval between satellite passes at a station and mean time between route changes ^{[7, §2.3, §3]}.	地面站看到衛星通過的間隔與路徑改變的平均間隔^{[7, §2.3, §3]}。
~ 40 ms	Measured Starlink bent-pipe RTT floor, for contrast, external comparison (fact base Part C, item 58).	實測 Starlink 彎管 RTT 下限，作外部對照（事實庫 C 部第 58 項）。