Pith. sign in

REVIEW 3 major objections 5 minor 54 references

Stochastic Geometry-Based Performance Evaluation for LEO Satellite-Assisted Space Caching

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper provides the first tractable stochastic-geometry framework for a LEO satellite-assisted space caching MEC network, with closed-form coverage probabilities and average delay.

desk verdict Useful first framework for LEO space-caching MEC, but the central coverage derivations are approximations presented as exact closed forms and need correction before the paper should be accepted. read the letter →

arxiv 2505.21259 v1 pith:UUDY6SH7 submitted 2025-05-27 eess.SY cs.SY

Chunyi Ma , Jiajie Xu , Jianhua Yang , Mustafa A. Kishk This is my paper
classification eess.SYcs.SY
keywords stochasticgeometryLEOsatellitespacecachingmobileedgecomputingcoverageprobabilityaveragedelayqueuingtheorybinomialpointprocess
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the delay performance of a mobile edge computing network can be evaluated with closed-form formulas when low-Earth-orbit satellites carrying cached services assist terrestrial servers. The authors model satellite positions as points on a sphere, terrestrial base stations and users as random point processes, and derive expressions for uplink and downlink coverage plus average task delay. The value of the claim is that network designers can directly see how delay responds to satellite altitude, satellite count, and user density without running simulations. If correct, the framework offers the first tractable stochastic-geometry tool for space-caching MEC networks.

What carries the argument

The central objects are the binomial point process on a sphere for satellite locations and independent Poisson point processes for ground servers and users, along with the maximum-biased-average-power association rule that splits users between satellite and cloud tiers. Coverage probabilities are computed by converting Shadowed-Rician fading on satellite links to a Gamma approximation with a tight CDF bound, then integrating against the contact-distance distribution of the binomial point process. The delay analysis chains these coverage expressions into queuing models: M/M/1/N for satellites with bounded buffers and M/G/1 for cloud servers, with arrival rates obtained from the association probabilities.

What would settle it

Run the same Monte Carlo scenario with co-channel interference from non-serving satellites and ground servers included, and compare the resulting uplink and downlink coverage probabilities and average delay to the paper's closed-form curves; a systematic gap would show that the predicted absolute delays hold only in the interference-free case.

Watch

Extended reading notes

Core claim

The central claim is that a LEO satellite-assisted space caching MEC network can be analyzed tractably by combining stochastic geometry with queuing theory: satellites are placed according to a binomial point process on a sphere, cloud servers and users according to Poisson point processes, and each user associates with either a satellite or a cloud server based on maximum biased average power. From this setup the paper derives closed-form expressions for the uplink and downlink coverage probabilities of both the satellite and terrestrial links, along with an average-delay expression that accounts for multiple task types, satellite buffer limits, and the mean load on each server. Monte Carlo simulations are shown to match the analytical curves, and the results indicate that increasing satellite altitude or satellite count reduces average delay, with the integrated satellite-terrestrial system outperforming either satellite-only or terrestrial-only operation.

Load-bearing premise

The whole analysis assumes the network is noise-limited: packets from users and servers with different tasks and service types do not interfere with each other, so every link's success depends only on its own signal and receiver noise.

Editorial extensions

If this is right

  • Increasing the number of LEO satellites reduces average delay at every altitude, and the reduction is steepest when the satellite count is small.
  • Higher satellite altitude lowers average delay for a fixed satellite count, because coverage probability improves with altitude.
  • The satellite-assisted MEC network achieves lower average delay than networks relying only on satellites or only on terrestrial cloud servers.
  • In dense user regions, more satellites are the effective way to limit delay; in sparse regions, fewer satellites at higher altitude can maintain delay performance while saving deployment cost.
  • The closed-form expressions let constellation parameters such as altitude and satellite count be tuned directly toward a target average-delay requirement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the analysis is noise-limited and assumes nodes with different tasks and service types do not interfere with each other, including co-channel interference from non-serving satellites and ground servers would likely compress the coverage gains and raise the predicted delays.
  • The tier decomposition by task and service type is modular, so the same framework could be extended to intra-constellation relaying or multiple cached services per satellite without reworking the core distance distributions.
  • Replacing the mean-load approximation with full load statistics could change predicted delays in low-density regimes, since bandwidth sharing per server depends on load variability.
  • A natural testable extension is to compare the closed-form coverage probabilities against a network simulator that models interference explicitly; the gap would quantify how much of the reported performance depends on the interference-free assumption.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a stochastic-geometry and queuing-theoretic framework for a LEO satellite-assisted space-caching MEC network. It models LEO satellites as a binomial point process, terrestrial cloud servers and user equipment as Poisson point processes, defines a biased maximum-average-power association strategy, derives downlink and uplink coverage probabilities for satellite and terrestrial links, and combines association probabilities with M/M/1/N and M/G/1 queueing models to obtain an average-delay expression. Monte Carlo simulations are used to validate the analytical results across satellite altitude, number of satellites, and UE density, and the paper reports design insights such as the trade-off between satellite altitude and constellation size.

Significance. If the derivations were fully justified, this framework would be a useful first tractable model for space-caching MEC, giving closed-form coverage expressions that depend on satellite altitude, number of satellites, and node densities. The Monte Carlo validation in Figs. 4-12 suggests the final delay expressions are numerically accurate under the stated assumptions. The paper also delivers practical insights, e.g., that increasing satellite altitude can compensate for a smaller constellation, and it explicitly builds on recent BPP-based LEO satellite analysis. However, the central claim of an exact analytical framework is weakened by unquantified approximations at load-bearing steps of the coverage derivation, which propagate into all delay formulas.

major comments (3)
  1. [Appendix A, Lemma 2, Eq. (22)-(23)] In step (c) of the proof of Lemma 2, the one-sided Gamma CDF bound from Eq. (22) is used as an equality: the manuscript writes F_H(A x^2) = (1 - exp(-mu A x^2 / beta_s))^{alpha_s}. For alpha_s > 1, which holds for the SR parameters in Table II (alpha_s is approximately 2.58), Eq. (22) only gives F_H(t) > (1 - exp(-mu t / beta_s))^{alpha_s}. Consequently the complementary probability is not equal to 1 minus the bound, and the coverage probability P_D_Si(tau) in Eq. (23) is an upper bound, not an exact expression. Since the delay formulas in (40), (41), and (46) divide by these coverage probabilities, the error is unquantified in the final delay results. The authors should either state explicitly that Eq. (23) is a bound, quantify the resulting error, or replace this step with a valid equality.
  2. [Appendix A, step (d) and Appendix C, Lemma 5, Eqs. (23) and (35)] The binomial expansion (1 - y)^{alpha_s} = sum_{j=0}^{alpha_s} binom(alpha_s, j)(-1)^j y^j used in step (d) of Appendix A and in Appendix C is valid only when alpha_s is a nonnegative integer. For the shadowed-Rician parameters SR(1.29, 0.158, 19.4) in Table II, the shape parameter is alpha_s = m(2b0+Omega)^2 / (4 m b0^2 + 4 m b0 Omega + Omega^2), which is approximately 2.58 and is not an integer. The finite sum with upper limit alpha_s is therefore not a valid identity. This invalidates the closed-form coverage expressions in Lemma 2 and Lemma 5 as derived, and all downstream results inherit the issue. The authors should correct this, for example by using the generalized (infinite) binomial series and a truncation bound, or by re-framing the results as an approximation with a controlled error.
  3. [Section IV, Eqs. (40)-(41)] The manuscript computes the average transmission time by using E[W log2(tau+1) 1{SNR > tau}] = W log2(tau+1) P(SNR > tau), replacing the ergodic rate E[W log2(1+SNR)] with a step function that assigns rate W log2(tau+1) when the SNR exceeds the threshold and zero otherwise. This is an approximation or a specific truncated-rate model, but it is not stated or justified as such. Because the average delay is the sum of these transmission times and the queuing response times, the claim that Eq. (46) gives the exact average delay is overstated. The authors should clarify this modeling choice or derive the transmission time from the actual rate expression.
minor comments (5)
  1. [Abstract and Introduction] There are several typographical errors, including 'reigon' in the abstract and Section I, 'tecgnology' in Section I, and 'U A V' in the related-work discussion; these should be corrected.
  2. [Appendix B, Eq. (56)] In the derivation of the association probability, the text writes 'F_Dc(Qs x^{2/alpha}) = exp(-lambda_c pi Q_s^2 x^{4/alpha})', but this is the complementary CDF, not the CDF itself; the notation should be fixed to avoid confusion.
  3. [Eqs. (9) and (42)] The task arrival rate at a satellite with service S_i is first defined in Eq. (9) as Lambda_{s,i} = A_{s,i} lambda_u / lambda_s, but Eq. (42) later includes an additional factor q_i P_U_Si(tau). The consistency between these two definitions should be clarified.
  4. [Lemma 5, Eq. (64)] The probability w is written as 1 - ((1+cos theta_c)/2)^{N_i - 1}; it would be helpful to explain why the exponent is N_i - 1 rather than N_i, since the presence of at least one satellite in the spherical cap should involve all N_i satellites.
  5. [Section III, SNR definitions] The analysis is noise-limited and ignores all co-channel interference, justified only by the statement that nodes with different tasks and service types do not interfere. The paper should state this limitation more prominently and discuss how frequency reuse among satellites or CSs would affect the absolute delay predictions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: coverage and delay expressions are derived from model assumptions and independent published lemmas, not from the simulation curves they claim to predict.

full rationale

The paper's derivation chain is self-contained in the sense required here. The coverage probabilities (Lemmas 2, 3, and 5) are obtained by applying stated model assumptions (PPP/BPP spatial models, Shadowed-Rician and Rayleigh fading, maximum-biased-power association) together with external mathematical results: the SR-to-Gamma approximation in Proposition 1 is attributed to [47]-[48], the Alzer Gamma-CDF bound in Eq. (22) is attributed to [49]-[50], and the contact-distance distributions in Lemmas 1 and 4 are cited from [30] and [32]. These cited results are published, parameter-free mathematical statements that do not encode the average-delay outputs of this paper; citing them is not circular even when some are authored by the same research group. The average-delay expressions in Section IV are built directly from these coverage probabilities, association probabilities, and M/G/1 and M/M/1/N queueing models; no parameter is fitted to the Monte Carlo curves shown in Figs. 4-12. Parameter values in Table II are taken from prior literature or standard system settings, not tuned to make the analytical curves match simulation. The skeptic's concern about replacing the one-sided Alzer inequality with an equality and applying a finite binomial expansion for non-integer shape parameter alpha_s is a mathematical validity or approximation-accuracy issue, not a circularity issue: even if Eqs. (23) and (35) are bounds or approximations rather than exact identities, they are still derived from the model rather than being equivalent to their own inputs. No quoted step reduces a claimed prediction to a fitted parameter, a self-referential definition, or a uniqueness theorem imported from the authors' own prior work. Therefore no circular step meets the evidentiary threshold.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The framework relies on standard stochastic geometry identities, several domain assumptions about channel and queuing models, and approximations from prior literature. The most consequential choices are the noise-limited assumption and the Gamma-bound-as-equality step, both of which shape the numerical results. No new physical entities are introduced.

free parameters (6)
  • Association bias ratio B_s/B_c = 200
    Chosen by hand in Table II to steer users toward satellites; directly shapes association probabilities in Lemma 3 and therefore the average delay. It is a design knob, not fitted to data.
  • Shadowed-Rician fading parameters (Ω, b0, m) = (1.29, 0.158, 19.4)
    Taken from prior empirical channel modeling [48]; these set the Gamma approximation parameters α_s ≈ 2.58 and β_s, which enter the coverage expressions. Not fitted here, but load-bearing.
  • Finite buffer capacity Ns = 2
    Hand-chosen in Table II; controls SAT blocking probability in Eq. (10) and the M/M/1/N response time, strongly affecting SAT delay results.
  • Task generation probability q_i = 0.25
    Each of the M task types is generated with equal probability 0.25 in the simulations; affects arrival rates and delay.
  • Path loss exponent for terrestrial links α = 2.7
    Chosen in Table II from literature; affects CS coverage and association expressions.
  • SNR threshold τ = 0 dB
    Hand-chosen; all coverage probabilities are evaluated at this threshold, and the delay calculation uses it as the rate cutoff.
assumptions (8)
  • standard math Slivnyak's theorem and the void probability of a PPP are used to analyze the typical UE and nearest-CS distance distribution (Eqs. (16)-(17)).
    Standard results in stochastic geometry, invoked without proof in Section III-A.
  • standard math The BPP contact distance distributions on a sphere (Lemma 1 and Lemma 4) are taken from prior BPP satellite work [30], [32].
    The distance CDF/PDF expressions in Eqs. (14)-(15) and (28)-(29) are cited, not derived in this paper.
  • domain assumption Satellite links experience Shadowed-Rician fading and free-space path loss with exponent 2 (Eqs. (1)-(3)).
    Assumed in the channel model for all SAT links; the SR parameters are taken from [48].
  • domain assumption Terrestrial links experience Rayleigh fading with path loss exponent α (Eqs. (4), (6)).
    Standard assumption for ground cellular links.
  • domain assumption There is no inter-cell interference; coverage is SNR-based (Section III, before Eq. (12)).
    The paper states that nodes with different tasks and service types do not interfere, which removes interference terms from the coverage analysis.
  • domain assumption The mean load approximation: the number of UEs per server equals its mean value (Assumption 1, Section IV).
    Used to compute per-user bandwidth in Eq. (37)-(39); an approximation imported from [46].
  • domain assumption The finite-buffer satellite is modeled as an M/M/1/N queue and the CS as an M/G/1 queue (Section II-D).
    Queuing model choice; service times are exponential (M/M/1/N) or general (M/G/1) as stated.
  • standard math The squared Shadowed-Rician fading is approximated by a Gamma distribution (Proposition 1), and its CDF is replaced by the tight bound (1 - e^{-µt/βs})^{αs} (Eq. (22)).
    Imported from [47]-[50] to obtain tractable coverage integrals; the bound is one-sided, which is used as an equality in the derivation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stochastic Geometry-Based Performance Evaluation for LEO Satellite-Assisted Space Caching." pith.science (2026). https://pith.science/paper/UUDY6SH7

@misc{pith2026250521259,
  author       = {Pith},
  title        = {Pith review of: Stochastic Geometry-Based Performance Evaluation for LEO Satellite-Assisted Space Caching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UUDY6SH7}},
  note         = {Machine review of arXiv:2505.21259}
}
read the original abstract

To achieve the Internet of Things (IoT) vision,Mobile Edge Computing (MEC) is a promising technology aimed at providing low-latency computing services to user equipment (UE). However, terrestrial MEC network struggles to provide service to UEs in remote and maritime region. Low Earth Orbit (LEO) satellite networks have the potential to overcome geographical restrictions and provide seamless global coverage for UEs. In this paper, we provide the first attempt to use stochastic geometry to investigate the performance of implementing space caching with LEO satellites (SATs) in the MEC network. We study a LEO satellite-assisted space caching MEC network, and LEO SATs can be equipped with servers to enable space caching, with the advantage of seamless coverage to assist terrestrial CSs for serving UEs in remote or maritime reigon. Using stochastic geometry and queuing theory, we establish an analytical framework for this MEC network. Meanwhile, we develop association strategies for UEs to connect with LEO SATs or CSs and utilize stochastic geometry to derive uplink and downlink coverage probabilities, considering the diversity of task and service types. On this basis, we employ the queuing theory to calculate the average delay to evaluate the system performance. Through Monte Carlo simulations and numerical results, the system performance is evaluated. The results show the potential of SAT spatial caching in improving the performance of the MEC network. Additionally, our results reveal useful insights such as the significant impact of the altitude and number of LEO SATs on the average delay of the network, providing helpful system-level recommendations for the design and configuration of the space-caching MEC network.

Figures

Figures reproduced from arXiv: 2505.21259 by the authors.

Figure 1
Figure 1. Schematic diagram of the network system. 1The Doppler frequency caused by the mobility of the LEO satellite can be estimated and mitigated by the mature pre-compensation method for UEs [38]. B. Channel model The channel link is responsible for transmitting the data of offloaded tasks from the UEs to the server, and after the server executes the task calculations, the UEs download the calculated results through the c… view at source ↗
Figure 2
Figure 2. S-U downlink geometry diagram. The CDF and PDF of the distance Dd,C−U between typical UE and the nearest CS can be easily obtained using the void probability of PPP as follows FDd,C−U (x) = 1 − exp −λcπx2  , (16) and fDd,C−U (x) = 2λcπx exp −λcπx2  , (17) where λc is the density of CS. Applying the law of total probability, the downlink coverage probability for each task generated is obtained as the sum of the pro… view at source ↗
Figure 3
Figure 3. U-S uplink geometry diagram. For the U-C link, the CDF and PDF of the distance Du,U−C between serving CS and UE are [16] FDu,U−C (x) = 1 − exp −λcπx2  , (30) and fDu,U−C (x) = 2λcπx exp −λcπx2  . (31) The uplink coverage probability of this system is given by P U cov(τ )=X M i=1 qiP(SNRU > τ |T ypical UE with task Ti ) = X M i=1 qi [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: shows the impact of satellite altitude on the perfor￾mance of the considered network system analyzed through analysis and simulation results. As the number of SATs Table II: The value of parameters. Parameter Value Parameter Value pu 23 dBm Du i 0.5 kb pc 45 dBm Dd i 0…
Figure 6
Figure 6. Figure 6: Comparison of average delay for different LEO SAT constellations [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Effect of λu with 500 km of SAT. 500 1000 1500 2000 2500 The number of satellites 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Average delay (s) u = 53 points/km2 Analy. u = 53 points/km2 Simu. u = 45 points/km2 Analy. u = 45 points/km2 Simu. u = 35 points/km2 Analy. u = …
Figure 10
Figure 10. Figure 10: Effect of λu with 1000 SATs. 30 35 40 45 50 55 60 u points/km2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Average delay (s) a s=1000km Analy. a s =1000km Simu. a s=800km Analy. a s =800km Simu. a s=500km Analy. a s =500km Simu [PITH_FULL_IMAGE:figures/full_fig…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

54 extracted references · 50 canonical work pages

  1. [1]

    Cache in the air: Exploiting content caching and delivery techniques for 5G systems,

    X. Wang, M. Chen, T. Taleb, A. Ksentini, and V . C. Leung, “Cache in the air: Exploiting content caching and delivery techniques for 5G systems,” IEEE Communications Magazine , vol. 52, no. 2, pp. 131–139, 2014

    work page 2014

  2. [2]

    Modeling and analysis of stochastic mobile-edge computing wireless networks,

    Y . Gu, Y . Yao, C. Li, B. Xia, D. Xu, and C. Zhang, “Modeling and analysis of stochastic mobile-edge computing wireless networks,” IEEE Internet of Things Journal , vol. 8, no. 18, pp. 14 051–14 065, 2021

    work page 2021

  3. [3]

    Computation offloading and service caching in heterogeneous MEC wireless networks,

    Y . Zhang, M. A. Kishk, and M.-S. Alouini, “Computation offloading and service caching in heterogeneous MEC wireless networks,” IEEE Transactions on Mobile Computing, vol. 22, no. 6, pp. 3241–3256, 2021

    work page 2021

  4. [4]

    Wireless networks for mobile edge computing: Spatial modeling and latency analysis,

    S.-W. Ko, K. Han, and K. Huang, “Wireless networks for mobile edge computing: Spatial modeling and latency analysis,” IEEE Transactions on Wireless Communications, vol. 17, no. 8, pp. 5225–5240, 2018

    work page 2018

  5. [5]

    Space/aerial-assisted computing offloading for IoT applications: A learning-based approach,

    N. Cheng, F. Lyu, W. Quan, C. Zhou, H. He, W. Shi, and X. Shen, “Space/aerial-assisted computing offloading for IoT applications: A learning-based approach,” IEEE Journal on Selected Areas in Commu- nications, vol. 37, no. 5, pp. 1117–1129, 2019

    work page 2019

  6. [6]

    Cooperatively constructing cost-effective content distribution networks upon emerging Low Earth Orbit satellites and clouds,

    Z. Lai, H. Li, Q. Zhang, Q. Wu, and J. Wu, “Cooperatively constructing cost-effective content distribution networks upon emerging Low Earth Orbit satellites and clouds,” in Proc. IEEE 29th ICNP , 2021, pp. 1–12. 14

    work page 2021

  7. [7]

    Remote peering: More peering without internet flattening,

    I. Castro, J. C. Cardona, S. Gorinsky, and P. Francois, “Remote peering: More peering without internet flattening,” in Proceedings of the 10th ACM International on Conference on emerging Networking Experiments and Technologies, 2014, pp. 185–198

    work page 2014

  8. [8]

    Dynamic caching in space over heterogeneous mega-constellations: A drl-guided approach,

    Y . Zhang, M. A. Kishk, and M.-S. Alouini, “Dynamic caching in space over heterogeneous mega-constellations: A drl-guided approach,” IEEE Transactions on Aerospace and Electronic Systems , pp. 1–13, 2024

    work page 2024

Show all 54 references
  1. [9]

    High throughput satellite systems: An analytical approach,

    H. Fenech, S. Amos, A. Tomatis, and V . Soumpholphakdy, “High throughput satellite systems: An analytical approach,” IEEE Transac- tions on Aerospace and Electronic Systems , vol. 51, no. 1, pp. 192–202, 2015

    2015

  2. [10]

    LCT for EDRS: LEO to GEO optical com- munications at 1, 8 Gbps between Alphasat and Sentinel 1a,

    H. Zech, F. Heine, D. Tr ¨ondle, S. Seel, M. Motzigemba, R. Meyer, and S. Philipp-May, “LCT for EDRS: LEO to GEO optical com- munications at 1, 8 Gbps between Alphasat and Sentinel 1a,” in Unmanned/Unattended Sensors and Sensor Networks XI; and Advanced Free-Space Optical Comm...

  3. [11]

    Envisioned wireless big data storage for low-earth-orbit satellite-based cloud,

    H. Huang, S. Guo, and K. Wang, “Envisioned wireless big data storage for low-earth-orbit satellite-based cloud,” IEEE Wireless Communica- tions, vol. 25, no. 1, pp. 26–31, 2018

    2018

  4. [12]

    Collaborative data downloading by using inter-satellite links in LEO satellite networks,

    X. Jia, T. Lv, F. He, and H. Huang, “Collaborative data downloading by using inter-satellite links in LEO satellite networks,” IEEE Transactions on Wireless Communications, vol. 16, no. 3, pp. 1523–1532, 2017

    2017

  5. [13]

    Improvement of the global connectiv- ity using integrated satellite-airborne-terrestrial networks with resource optimization,

    A. Alsharoa and M.-S. Alouini, “Improvement of the global connectiv- ity using integrated satellite-airborne-terrestrial networks with resource optimization,” IEEE Transactions on Wireless Communications, vol. 19, no. 8, pp. 5088–5100, 2020

    2020

  6. [14]

    Task-oriented intelligent net- working architecture for the space-air-ground-aqua integrated network,

    J. Liu, X. Du, J. Cui, M. Pan, and D. Wei, “Task-oriented intelligent net- working architecture for the space-air-ground-aqua integrated network,” IEEE Internet of Things Journal , vol. 7, no. 6, pp. 5345–5358, 2020

    2020

  7. [15]

    Computation offloading in LEO satellite networks with hybrid cloud and edge computing,

    Q. Tang, Z. Fei, B. Li, and Z. Han, “Computation offloading in LEO satellite networks with hybrid cloud and edge computing,” IEEE Internet of Things Journal , vol. 8, no. 11, pp. 9164–9176, 2021

    2021

  8. [16]

    A primer on cel- lular network analysis using stochastic geometry,

    J. G. Andrews, A. K. Gupta, and H. S. Dhillon, “A primer on cel- lular network analysis using stochastic geometry,” available online: https://arxiv.org/abs/1604.03183 [accessed on May 24th, 2024]

    2024 arXiv

  9. [17]

    Analysis on cache-enabled wireless heterogeneous networks,

    C. Yang, Y . Yao, Z. Chen, and B. Xia, “Analysis on cache-enabled wireless heterogeneous networks,” IEEE Transactions on Wireless Com- munications, vol. 15, no. 1, pp. 131–145, 2015

    2015

  10. [18]

    Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis,

    A. H. Sakr and E. Hossain, “Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis,” IEEE Transactions on Communications , vol. 63, no. 5, pp. 1867–1880, 2015

    2015

  11. [19]

    Stochastic geometry analysis of spatial-temporal performance in wireless networks: A tutorial,

    X. Lu, M. Salehi, M. Haenggi, E. Hossain, and H. Jiang, “Stochastic geometry analysis of spatial-temporal performance in wireless networks: A tutorial,” IEEE Communications Surveys & Tutorials , vol. 23, no. 4, pp. 2753–2801, 2021

    2021

  12. [20]

    Modeling and analysis of cellular networks using stochastic geometry: A tutorial,

    H. ElSawy, A. Sultan-Salem, M.-S. Alouini, and M. Z. Win, “Modeling and analysis of cellular networks using stochastic geometry: A tutorial,” IEEE Communications Surveys & Tutorials, vol. 19, no. 1, pp. 167–203, 2016

    2016

  13. [21]

    Modeling and performance analysis of stochastic mobile edge computing wireless networks,

    Y . Gu, C. Li, B. Xia, D. Xu, and Z. Chen, “Modeling and performance analysis of stochastic mobile edge computing wireless networks,” in Proc. IEEE VTC, Spring, 2019 , pp. 1–5

    2019

  14. [22]

    Space-air-ground-sea integrated networks: Modeling and coverage analysis,

    J. Xu, M. A. Kishk, and M.-S. Alouini, “Space-air-ground-sea integrated networks: Modeling and coverage analysis,” IEEE Transactions on Wireless Communications, 2023

    2023

  15. [23]

    A vision of 6G wireless systems: Applications, trends, technologies, and open research problems,

    W. Saad, M. Bennis, and M. Chen, “A vision of 6G wireless systems: Applications, trends, technologies, and open research problems,” IEEE Network, vol. 34, no. 3, pp. 134–142, 2019

    2019

  16. [24]

    Non-terrestrial networks in the 6G era: Challenges and opportunities,

    M. Giordani and M. Zorzi, “Non-terrestrial networks in the 6G era: Challenges and opportunities,” IEEE Network, vol. 35, no. 2, pp. 244– 251, 2020

    2020

  17. [25]

    Hierarchical aerial computing for Internet of Things via cooperation of HAPs and UA Vs,

    Z. Jia, Q. Wu, C. Dong, C. Yuen, and Z. Han, “Hierarchical aerial computing for Internet of Things via cooperation of HAPs and UA Vs,” IEEE Internet of Things Journal , vol. 10, no. 7, pp. 5676–5688, 2022

    2022

  18. [26]

    An analytic approach for modeling the coverage per- formance of dense satellite networks,

    A. Al-Hourani, “An analytic approach for modeling the coverage per- formance of dense satellite networks,” IEEE Wireless Communications Letters, vol. 10, no. 4, pp. 897–901, 2021

    2021

  19. [27]

    Modeling and analysis of LEO mega- constellations as nonhomogeneous Poisson point processes,

    N. Okati and T. Riihonen, “Modeling and analysis of LEO mega- constellations as nonhomogeneous Poisson point processes,” in Proc. 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring) . IEEE, 2021, pp. 1–5

    2021

  20. [28]

    Optimal beamwidth and altitude for maximal uplink coverage in satellite networks,

    B. Al Homssi and A. Al-Hourani, “Optimal beamwidth and altitude for maximal uplink coverage in satellite networks,” IEEE Wireless Communications Letters, vol. 11, no. 4, pp. 771–775, 2022

    2022

  21. [29]

    Downlink coverage and rate analysis of low earth orbit satellite constellations using stochastic geometry,

    N. Okati, T. Riihonen, D. Korpi, I. Angervuori, and R. Wichman, “Downlink coverage and rate analysis of low earth orbit satellite constellations using stochastic geometry,” IEEE Transactions on Com- munications, vol. 68, no. 8, pp. 5120–5134, 2020

    2020

  22. [30]

    Stochastic geometry-based analysis of LEO satellite communication systems,

    A. Talgat, M. A. Kishk, and M.-S. Alouini, “Stochastic geometry-based analysis of LEO satellite communication systems,” IEEE Communica- tions Letters, vol. 25, no. 8, pp. 2458–2462, 2020

    2020

  23. [31]

    Nearest neighbor and contact distance distribution for binomial point process on spherical surfaces,

    A. Talgat, M. A. Kishk, and M.-S. Alouini, “Nearest neighbor and contact distance distribution for binomial point process on spherical surfaces,” IEEE Communications Letters , vol. 24, no. 12, pp. 2659– 2663, 2020

    2020

  24. [32]

    Stochastic geometry-based uplink performance analysis of IoT over LEO satellite communication,

    A. Talgat, M. A. Kishk, and M.-S. Alouini, “Stochastic geometry-based uplink performance analysis of IoT over LEO satellite communication,” IEEE Transactions on Aerospace and Electronic Systems , 2024

    2024

  25. [33]

    Ultra reliable low latency routing in LEO satellite constellations: A stochastic geometry approach,

    R. Wang, M. A. Kishk, and M.-S. Alouini, “Ultra reliable low latency routing in LEO satellite constellations: A stochastic geometry approach,” IEEE Journal on Selected Areas in Communications , 2024

    2024

  26. [34]

    Toward data collection and transmission in 6G space–air–ground integrated networks: Cooperative HAP and LEO satellite schemes,

    Z. Jia, M. Sheng, J. Li, and Z. Han, “Toward data collection and transmission in 6G space–air–ground integrated networks: Cooperative HAP and LEO satellite schemes,” IEEE Internet of Things Journal , vol. 9, no. 13, pp. 10 516–10 528, 2021

    2021

  27. [35]

    Energy- Efficient Caching and User Selection for Resource-Limited SAGINs in Emergency Communications,

    Q. Wei, Y . Chen, Z. Jia, W. Bai, T. Pei, and Q. Wu, “Energy- Efficient Caching and User Selection for Resource-Limited SAGINs in Emergency Communications,” IEEE Transactions on Communications , 2024

    2024

  28. [36]

    Online joint data offloading and power control for space-air-ground integrated networks,

    L. He, Z. Jia, K. Guo, H. Gan, Z. Han, and C. Yuen, “Online joint data offloading and power control for space-air-ground integrated networks,” IEEE Transactions on Wireless Communications , 2024

    2024

  29. [37]

    Edge-assisted multi-layer offloading optimization of LEO satellite-terrestrial integrated networks,

    X. Cao, B. Yang, Y . Shen, C. Yuen, Y . Zhang, Z. Han, H. V . Poor, and L. Hanzo, “Edge-assisted multi-layer offloading optimization of LEO satellite-terrestrial integrated networks,” IEEE Journal on Selected Areas in Communications, vol. 41, no. 2, pp. 381–398, 2022

    2022

  30. [38]

    Near optimal timing and frequency offset estimation for 5G integrated LEO satellite communication system,

    W. Wang, Y . Tong, L. Li, A.-A. Lu, L. You, and X. Gao, “Near optimal timing and frequency offset estimation for 5G integrated LEO satellite communication system,” IEEE Access , vol. 7, pp. 113 298–113 310, 2019

    2019

  31. [39]

    Analysis of LEO, MEO, and GEO global mobile satellite systems in the presence of inter- ference and fading,

    F. Vatalaro, G. E. Corazza, C. Caini, and C. Ferrarelli, “Analysis of LEO, MEO, and GEO global mobile satellite systems in the presence of inter- ference and fading,” IEEE Journal on selected areas in communications, vol. 13, no. 2, pp. 291–300, 1995

    1995

  32. [40]

    Coverage and rate analysis of mega- constellations under generalized serving satellite selection,

    N. Okati and T. Riihonen, “Coverage and rate analysis of mega- constellations under generalized serving satellite selection,” in Proc. IEEE Wireless Communications and Networking Conference (WCNC) . IEEE, 2022, pp. 2214–2219

    2022

  33. [41]

    Sum of squared shadowed-rice random variables and its application to communication systems performance prediction,

    G. Alfano and A. De Maio, “Sum of squared shadowed-rice random variables and its application to communication systems performance prediction,” IEEE Transactions on Wireless Communications , vol. 6, no. 10, pp. 3540–3545, 2007

    2007

  34. [42]

    Heterogeneous cellular networks with flexible cell association: A comprehensive downlink sinr analysis,

    H.-S. Jo, Y . J. Sang, P. Xia, and J. G. Andrews, “Heterogeneous cellular networks with flexible cell association: A comprehensive downlink sinr analysis,” IEEE Transactions on Wireless Communications , vol. 11, no. 10, pp. 3484–3495, 2012

    2012

  35. [43]

    Towards energy-efficient routing in satellite networks,

    Y . Yang, M. Xu, D. Wang, and Y . Wang, “Towards energy-efficient routing in satellite networks,” IEEE Journal on Selected Areas in Communications, vol. 34, no. 12, pp. 3869–3886, 2016

    2016

  36. [44]

    Power budgeting of leo satellites: An electrical power system design for 5G missions,

    A. J. Ali, M. Khalily, A. Sattarzadeh, A. Massoud, M. O. Hasna, T. Khattab, O. Yurduseven, and R. Tafazolli, “Power budgeting of leo satellites: An electrical power system design for 5G missions,” IEEE Access, vol. 9, pp. 113 258–113 269, 2021

    2021

  37. [45]

    Queue systems, volume I: Theory,

    L. Kleinrock, “Queue systems, volume I: Theory,” Jonh Wiley & Sons , 1975

    1975

  38. [46]

    Offloading in heterogeneous networks: Modeling, analysis, and design insights,

    S. Singh, H. S. Dhillon, and J. G. Andrews, “Offloading in heterogeneous networks: Modeling, analysis, and design insights,” IEEE Transactions on Wireless Communications, vol. 12, no. 5, pp. 2484–2497, 2013

    2013

  39. [47]

    User selection for multi- beam satellite channels: A stochastic geometry perspective,

    M. Sellathurai, S. Vuppala, and T. Ratnarajah, “User selection for multi- beam satellite channels: A stochastic geometry perspective,” in Proc. 2016 50th Asilomar Conference on Signals, Systems and Computers . IEEE, 2016, pp. 487–491

    2016

  40. [48]

    A new simple model for land mobile satellite channels: First-and second-order statistics,

    A. Abdi, W. C. Lau, M.-S. Alouini, and M. Kaveh, “A new simple model for land mobile satellite channels: First-and second-order statistics,” IEEE Transactions on Wireless Communications, vol. 2, no. 3, pp. 519– 528, 2003

    2003

  41. [49]

    On some inequalities for the incomplete gamma function,

    H. Alzer, “On some inequalities for the incomplete gamma function,” Mathematics of Computation , vol. 66, no. 218, pp. 771–778, 1997

    1997

  42. [50]

    Uplink interference and performance analysis for megasatellite constellation,

    H. Jia, Z. Ni, C. Jiang, L. Kuang, and J. Lu, “Uplink interference and performance analysis for megasatellite constellation,” IEEE Internet of Things Journal, vol. 9, no. 6, pp. 4318–4329, 2021. 15

    2021

  43. [51]

    Computation offloading and resource allocation in leo satellite-terrestrial integrated networks with system state delay,

    B. Xie, H. Cui, I. W.-H. Ho, Y . He, and M. Guizani, “Computation offloading and resource allocation in leo satellite-terrestrial integrated networks with system state delay,” IEEE Transactions on Mobile Com- puting, 2024

    2024

  44. [52]

    Performance evaluation of a satellite communication-based MEC ar- chitecture for IoT applications,

    M. Luglio, M. Marchese, F. Patrone, C. Roseti, and F. Zampognaro, “Performance evaluation of a satellite communication-based MEC ar- chitecture for IoT applications,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 5, pp. 3775–3785, 2022

    2022

  45. [53]

    An Updated Comparison of Four Low Earth Orbit Satellite Constellation Systems to Provide Global Broadband,

    N. Pachler, I. del Portillo, E. F. Crawley, and B. G. Cameron, “An Updated Comparison of Four Low Earth Orbit Satellite Constellation Systems to Provide Global Broadband,” in Proc. IEEE ICC Workshops, 2021, pp. 1–7

    2021

  46. [9647]

    SPIE, 2015, pp. 85–92

    2015

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.