Throughput Analysis and On-Board Buffer Sizing for Hybrid RF and Optical LEO Satellites Cao-Vien Phung, Thomas Röthig, and Admela Jukan
arXiv:2605.02001v1 [cs.NI] 3 May 2026
Technische Universität Braunschweig, Germany Email: {c.phung, t.roethig, a.jukan}@tu-bs.de
Abstract—Low Earth Orbit (LEO) satellite networks are increasingly adopting laser (Free Space Optics, FSO) links to provide high-capacity communications. Although laser intersatellite links offer high throughput and low latency, RF upand downlinks remain necessary to maintain connectivity during optical outages caused by adverse atmospheric conditions. In such hybrid link scenarios, satellite buffer design remains a key challenge, since up- and downlink traffic must be buffered and forwarded among satellite nodes. The hybrid RF/FSO scenario requires careful transmission scheduling, especially at envisioned optical transmission rates of 100Gb/s and beyond, making buffer sizing critical under strict onboard energy and weight constraints. Thus, this paper analyzes throughput performance and buffer sizing in hybrid RF/laser satellite networks with finite buffer capacity, interference-aware scheduling, and weather-dependent laser link outage probabilities. Numerical results indicate that laser communications bring significant performance gains. Instead of increasing the transmission power of the satellite to maximize the throughput, we can select a suitable transmission scheduling priority to achieve a maximum throughput, while minimizing the buffer requirement, and lowering packet loss probability under realistic operational conditions and constraints.
I. I NTRODUCTION Modern satellite networks increasingly consider laser communication for optical up- and downlinks (LaserCom), as well as laser inter-satellite links (LISLs), driven by ever-increasing capacity requirements [1]. However, relying solely on laser links remains challenging: weather effects, including clouds, fog, and turbulence, keep optical up- and downlink performance variable. In addition, optical wavelength reuse causes co-channel interference [2]. Therefore, hybrid FSO/RF links still remain necessary [3]. Moreover, since current LEO satellite constellations rely on electronic packet processing rather than optical switching, traffic must be routed and buffered onboard before forwarding [4]. Although such buffering can reduce packet loss during outages or contention [5], onboard processing and memory resources remain limited by satellite SWaP (size, weight, power) budgets, making arbitrarily large buffers impractical for high-speed transmission toward hundreds of Gb/s [5]. In contrast, future optical satellite networks can incorporate transparent all-optical forwarding to reduce electronic processing, lower latency, and improve scalability. Ideally, such systems would operate with little or no buffering or electronic processing. However, fully bufferless operation is not feasible in practice, for a myriad of reasons, most notably because optical feeder links may be intermittently unavailable
due to weather effects, while contention can still arise from traffic dynamics and wavelength reuse. As weather-induced outages increase buffering requirements, higher transmit power can reduce the optical link outage probability [3], thereby lowering required onboard buffering. However, this shifts the resource burden from storage to power rather, and may still be impractical to SWaP constraints in satellites [6]. Before a fully bufferless all-optical operation becomes feasible, a practical intermediate step is to minimize onboard buffering while maintaining network throughput performance. This paper investigates the minimum onboard buffer capacity required to maintain throughput performance under adverse weather conditions affecting optical satellite up- and downlinks. To this end, we propose a Markov chain model for the evaluation of throughput and onboard buffer sizing in satellite networks. The model characterizes system performance as a function of finite satellite buffer capacity, transmission scheduling parameter, and link outage probabilities under various weather conditions. The transmission scheduling parameter is optimized to solve outages, reduce required buffer size, decrease packet dropping probability, and improve throughput. Numerical results show that instead of increasing the transmission power of the satellite to maximize the performance, as it is commonly the case, we can select a suitable optical transmission scheduling priority to achieve maximum throughput and minimum buffer size, while lowering the packet dropping probability. The rest of this paper is organized as follows. Section II presents the related work. Section III provides the analysis. Section IV presents performance evaluation. We conclude the paper in Section V. II. R ELATED WORK Paper in [3] analyzes the probability of an outage link of a weather-dependent hybrid RF/laser link for improved power efficiency. We extend this paper with an analysis of interference-avoiding transmission scheduling strategies to solve the outage problem, while maximizing the throughput and minimizing the buffer. Papers [7], [8] analyze the performance with interference-avoiding transmission scheduling strategies in a general wireless network with a limit for the relay node buffer, using the Markov chain model. Paper [9] builds an analytical model for mixed laser/RF UAV-aided mobile relaying with a buffer, which we use in this paper to analyze foggy weather. However, neither of these papers
either directly or by handover, under the assumption of a satellite grid, and SAI can serve one or more GSs during its movements. For simplicity and without loss of generality, assume that SAI can connect with one SAs and one GS only. Table I summarizes the main notations in the paper. Table II: Link selections between SAI and GS [3].
Figure 1: Reference scenario under different weather effects.
analyzes outages and throughput performance in the same framework, which is our goal. The models in [5], [10] are applied for satellite networks with limited buffer/cache used to retransmit error/lost bursts/chunks. These studies focus on selecting a data burst/chunk size transferred during its burst/chunk time, which is different from our study. It should be noted that many of the related work listed are specifically referred in the analysis, whenever re-used from other models. In a nutshell, the novelty of our paper is that it combines the aspects of traffic, satellite buffer limit, transmission scheduling parameters, and outage link parameters under different weather effects (thin cloud, fog, and rain) which as combination is novel, and required in hybrid RF/FSO scenario. Table I: List of main parameters. Notation
Meaning
Aγ
Average queue length [bits], Aγ = {AC : cloud, AF : f og, AR : rain}. f,C f,R Capacity [bps], Cγ = {CSG : cloud with laser, CSG : r,C r,F rain, CSG : cloud with RF, CSG : f og, CSS : LISL}. Buffer length limit of satellite SAI , L [packets], Lb [bits]. Total time observed in the weather using RF link [seconds]. Average packet dropping probability, Pγ = {PC : cloud, PF : f og, PR : rain}. State probability of i packets in the buffer. Transition probability from state i ∈ (0, L) to itself. Transition probability from state i = L to itself. Transition probability from state i ∈ (0, L] to state i − 1. Probability that SAI sends unsuccessfully data to GS. Transition probability from state i ∈ (0, L) to state i + 1. Probability that SAs sends unsuccessfully data to SAI . Timeout for transmission via SAI -GS link [seconds]. Timeout for transmission via SAs -SAI link [seconds]. Average size of a packet [bits]. Probability Wγ = {WC : cloud, WR : rain, WF : f og}. SAI priority of accessing medium (real value). Outage probability, ργ = {ρSG,C : cloud, ρSG,F : f og, ρSG,R : rain, ρSS : LISL}. Average throughput [bps], τγ = {τC : cloud, τF : f og, τR : rain}.
Cγ L, Lb Ot Pγ P (i) Pl ′ Pl PSAI ′ PSAI PSAs ′ PSAs o TSG o TSS X Wγ α ργ τγ
III. B UFFER AND THROUGHPUT ANALYSIS A. Reference scenario Our reference scenario in Fig. 1 includes one LEO Satellite source (SAs ), one intermediate LEO Satellite (SAI ), and one GS (destination node), where SAI always connects with SAs ,
Weather condition SAI to GS link Thin cloud Both laser and RF links (dual channels) Rain laser link Fog RF link
The system always has packets to send from SAs . The capacity of the SAs -SAI LISL is given by: CSS = Wf · log2 (1 + SN RSS ),
(1)
where Wf is the bandwidth and SN RSS is the signal-tonoise ratio [11]. The SAs -SAI laser link has the probability of o [5]. After a timeout, outage ρSS causing a timeout time TSS any unsuccessful packet can be resent, akin to [5]. SAI does not generate packets itself, as it only relays packets received from SAs . The SAI -GS weather-link selections are summarized in Table II. For thin cloud, the identical rate information is transmitted by both RF and laser channels in parallel [3], where the selection combining technique is to combine received signals at GS to maximize performance. For simplicity and without loss of generality, we assume that there exists only one link (either laser or RF) whose performance is calculated on average between laser and RF. Let ρSG,C , ρSG,R , and ρSG,F be the probability of outage of SAI -GS links in thin cloud, rain, and fog, respectively, [3], causing the timeout o . Note that due to optical interference in the same time TSG frequency band [2], transmitting data to GS and receiving data from SAs at SAI for weather conditions using SAI -GS laser links cannot be simultaneously performed, whereas SAI can simultaneously transmit data to GS for weather conditions using RF and receive data from SAs using laser. The SAI -GS f,C f,R r,C r,F link capacities CSG , CSG , CSG , CSG are for thin cloud with laser link, rain, thin cloud with RF link, and fog, respectively, which are similar to Eq. (1), where their SNRs are referred to [3]. Assume that the switching time between laser and RF is negligible, including signal processing at SAI . For weather using SAI -GS laser links, SAs is scheduled to send one packet of X bits on average to SAI during its access. Let L be the SAI buffer limit in packets (Lb in bits) [5]. Each packet in the buffer occupies one unit. We define α "priority" (real value) for accessing the transmission medium from SAI to GS, i.e., α times of transmission opportunities, whereas SAs competes to get one time for accessing the transmission medium from SAs to SAI . SAI and SAs will not compete for access, if the SAI buffer is empty. If the number of packets stored in the queue is equal to L, SAI will drop any new packet that arrives at its buffer. When SAI wins a transmission chance, it can transport a packet to GS, i.e., remove a packet
the probability PSAI that the nonempty SAI queue decreases one packet (SAI sends successfully one to GS) is given by: 0
2
1
PSAI =
α(1 − ρSG,C ) , 1+α
(5)
′
Figure 2: Embedded Markov chain model applied. from its buffer. In case of weather conditions using SAI -GS RF, SAI does not use the priority α because SAs -SAI links are optical, i.e., they do not interfere. B. Thin cloud weather model 1) Queue length analysis (thin cloud):
whereas the probability PSAI that the nonempty SAI queue keeps unchanged (SAI sends unsuccessfully one to GS) is: ′ α · ρSG,C . (6) PSAI = 1+α With Eqs. (4), (6), the transition probability Pl from state i ∈ (0, L) to itself, i.e., the probability that the nonempty SAI queue keeps unchanged (SAs or SAI sends unsuccessfully one packet to SAI or GS, respectively) is given as follows: ′
Lemma 1. The average queue length of the SAI buffer in the thin cloud using SAI -GS laser/RF link can be given as follows: 1 AC = (AC,f + AC,r ), 2
(2)
where AC,f and AC,r are the average queue length of SAI if using SAI -GS laser and SAI -GS RF, respectively. AC,f and AC,r are calculated by using Lemmas 4 and 5, respectively. With cloud (SAI -GS laser), we design a Markov chain (Fig. 2) to obtain the throughput, queue length of buffered packets, and packet dropping probability at SAI , where each state i ∈ [0, L] is the number of buffered packets in the SAI queue (queue state). Observations in the Markov chain occur before each packet transmission from SAs or SAI . Let P0→1 and P0→0 be the transition probability from state i = 0 (empty buffer) to state i = 1 and to itself, respectively. Since the SAI buffer is empty, the transmission chance is only from SAs which increases one unit in the queue. So, we get P0→1 = 1 − ρSS in case of which SAs sends successfully one packet to SAI , whereas we get P0→0 = ρSS in case of which SAs sends unsuccessfully one due to SAs -SAI link outage. Let PSAs be the transition probability that nonempty queue state i ∈ (0, L) to i + 1, i.e., queue increases one, in case of transmission chance from SAs occupied. As the SAI buffer is not empty, its transmission competition chance is "α priority" over SAs . Hence, with the transmission chance of SAs occupied and SAs -SAI link outage probability ρSS , probability PSAs that the nonempty SAI queue increases one packet (SAs sends successfully one to SAI ) is given by: PSAs =
1 − ρSS , 1+α
(3)
′
whereas the probability PSAs that the nonempty SAI queue keeps unchanged (SAs sends unsuccessfully one to SAI ) is: ′ ρSS PSAs = . (4) 1+α Let PSAI be the transition probability that nonempty queue state i ∈ (0, L] to i − 1, i.e., queue decreases one packet, in case of transmission chance from SAI occupied with the "α priority". With ρSG,C of SAI -GS laser link outage probability,
′
Pl = PSAs + PSAI =
ρSS + α · ρSG,C . 1+α
(7)
At i = L, any new packet that arrives at SAI when SAs sends data with the probability PSAs will be dropped. With Eqs. (4), (6), (7), the transition probability from i = L to itself is given as follows: ′
Pl = PSAs + Pl =
1 + α · ρSG,C . 1+α
(8)
Lemma 2. The Markov chain is finite, irreducible, aperiodic. The proof is provided in Appendix 1. Lemma 3. Let P (i) be the state probability that the SAI buffer has i packets. P (i) in thin cloud (SAI -GS laser link) is:
P (i) =
1 PL
,
(9)
(PSAs )i−1 (1 − ρSS )P (0), ∀i ∈ [1, L]. (PSAI )i
(10)
P (0) =
1 + (1 − ρSS )
i=1
(PSAs )i−1 (PSAI )i
The proof is provided in Appendix 2. Lemma 4. The average queue length of SAI buffer in the thin cloud using SAI -GS laser link can be given as follows: AC,f = X(1 − ρSS )P (0)
L X (PSAs )i−1 i , (PSAI )i i=1
(11)
where P (0) is referred to Lemma 3. PL Lemma 4 proves by using X i=1 i · P (i) and Lemma 3. Lemma 5. The queue length of SAI buffer (i.e., using SAI -GS RF) is the difference between the capacities of SAs -SAI laser and RF links with observed time Ot s. So, it is given by: Ot 1 X A min (Lb , i · [β − ϕ]) , if β > ϕ, C,r = Ot + 1 i=0 AC,r = 0, if β ≤ ϕ, (12) where β = (1 − ρSS ) · CSS is the amount of arriving data at r,C SAI from SAs and ϕ = (1 − ρSG,C ) · CSG is the amount of data released from SAI to GS.
2) Packet dropping probability analysis (thin cloud): We define the packet dropping probability to be packets that arrives at SAI where refuses buffering them due to full buffer. Lemma 6. The packet dropping probability at the SAI buffer in the thin cloud using SAI -GS laser/RF link is given by: PC =
1 (PC,f + PC,r ), 2
(13)
and the average transmission slot length is given as follows: X o + P (0) · ρSS · TSS CSS ′ X o + [1 − P (0)]PSAs + [1 − P (0)]PSAs · TSS CSS ′ X o , + [1 − P (0)]PSAI f,C + [1 − P (0)]PSAI · TSG CSG (20)
TC,f = P (0) · (1 − ρSS )
where PC,f and PC,r are the packet dropping probability at SAI buffer in the thin cloud if using SAI -GS laser and RF links, respectively. PC,f and PC,r are from Lemmas 7, 8.
where P (0) is referred to Lemma 3.
Lemma 7. The packet dropping probability at SAI in the thin cloud using SAI -GS laser link is given as follows:
Lemma 11. The average network throughput in the thin cloud using SAI -GS RF link is given as follows:
L
τC,r = min([1 − PC,r ]β, ϕ),
PC,f =
PSAs PSAI
(1 − ρSS )P (0),
(14)
where P (0) is referred to Lemma 3.
I
Lemma 8. The packet dropping probability at SA in the thin cloud using SAI -GS RF is given as follows: " # Ot 1 X Sez + ϕ (15) , min 1, PC,r = 1 − Ot i=1 β where the remaining SAI buffer space in bits at the observed time z = i−1 (previously observed time i) is given as follows: ( Sez = Lb − min (Lb , z · [β − ϕ]) , if β > ϕ, (16) Sez = Lb , if β ≤ ϕ, All parameters in Lemma 8 can be referred to Lemma 5. 3) Throughput analysis: We define the average throughput to be the ratio of the average amount of data per transmission slot that SAI forwards to the average transmission slot length. Lemma 9. The average throughput in the thin cloud using SAI -GS laser/RF link can be given as follows: (17)
where τC,f and τC,r are the throughput in the thin cloud if using SAI -GS laser and SAI -GS RF link, respectively. τC,f and τC,r are from Lemma 10 and Lemma 11. Lemma 10. The average network throughput in the thin cloud using SAI -GS laser link is given as follows: τC,f =
DC,f , TC,f
(18)
where the average amount of data per transmission slot that SAI forwards can be given as follows: DC,f = [1 − P (0)]PSAI · X,
(21)
where all parameters are referred to Lemma 5, and PC,r is from Lemma 8. C. Rain weather model
Lemma 7 is proved by using PSA · P (L) and Lemma 3.
1 τC = (τC,f + τC,r ), 2
The proof is provided in Appendix 3.
(19)
With the rain (SAI -GS laser link), the average queue length AR , packet dropping probability PR , and throughput τR can be similarly calculated using Lemmas 4, 7, and 10. D. Foggy weather model In foggy weather (SAI -GS RF link), the average queue length AF , packet dropping probability PF , and throughput τF can be similarly calculated using Lemmas 5, 8, and 11. E. Combined weather models As the satellite moves, it can experience different weather effects. Let WC , WR , and WF be the probability of thin cloud, rain, and fog, respectively. Theorem 1. The queue length of SAI under three weather effects (thin cloud, rain, and fog) combined is given as follows: At = WC · AC + WR · AR + WF · AF .
(22)
Theorem 2. The packet dropping probability at SAI under the thin cloud, rain, and fog combined is given as follows: Pt = WC · PC + WR · PR + WF · PF .
(23)
Theorem 3. The network throughput under three weather effects (thin cloud, rain, and fog) combined is given as follows: τt = WC · τC + WR · τR + WF · τF .
(24)
IV. P ERFORMANCE EVALUATION We start the evaluation with the system configuration assumptions. The satellite and GS altitudes are set at 500 km and 0.8 km, respectively. The average SAs -SAI distance is 500 km. The bandwidth Wf for the optical and Wr for RF is 500 MHz and 50 MHz, respectively. The RF frequency is 40 GHz, while the laser wavelength is 1550 nm. The satellite and GS gains are 52 dBi. The evaluation angle is 30o . The transmission t s o power PSA is 0.7 watt. The timeouts TSS for SAs s of SA o SAI link and TSG for SAI -GS link are 0.01 s. Each packet
10 9
2
0.7
Average queue length (bits)
Throughput (bps)
5
PtSAI =-20dBm
4.5
PtSAI =-10dBm
4
PtSAI =0dBm 3.5
3
PtSAI =-20dBm
PtSAI =-20dBm
1.9 1.8
PtSAI =-10dBm
1.7
PtSAI =0dBm
1.6
Packet dropping probability
10 9
5.5
1.5 1.4 1.3 1.2 1.1
2.5
1 0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
PtSAI =-10dBm
0.65
PtSAI =0dBm
0.6
0.55
0.5
0.45
10
0
1
2
3
4
5
6
Priority
Priority
Priority
(a)
(b)
(c)
7
8
9
10
Figure 3: Satellite system performance over different SAI priorities α, where the SAI buffer limit is fixed at L = 100 packets.
5.5
10 9
Throughput (bps)
5
4.5
PtSAI =-20dBm PtSAI =-10dBm PtSAI =0dBm
4
3.5
3 10
20
30
40
50
I
60
70
80
SA buffer length limit (packets)
90
100
PtSAI =-20dBm 0.54
10 9
Packet dropping probability
Average queue length (bits)
0.545
PtSAI =-20dBm PtSAI =-10dBm PtSAI =0dBm
10 8 10
20
30
40
50
60
70
80
SAI buffer length limit (packets)
(a)
90
100
PtSAI =-10dBm PtSAI =0dBm
0.535
0.53
0.525
0.52
0.515
0.51 10
20
30
40
(b) I
50
60
70
80
90
100
SAI buffer length limit (packets)
(c) I
Figure 4: Satellite system performance over different SA buffer limits L, where the SA priority is fixed at α = 1.
X has 20 Mbits on average. Assume that the average outage probability of SAs -SAI link is small, e.g., 0.0001. For fairness, assume that the probabilities of the different weather types (WC , WR , and WF ) are equal. The observed time Ot in case of weather, such as fog, only needs a few dozen seconds to get convergent results which were also proved in [8], while the weather effects may be occurred in a longer duration. The remaining parameters are selected according to [3], [11], [12]. We focus on evaluating the throughput (Theorem 3), queue length of SAI buffer (Theorem 1), and packet dropping probability (Theorem 2) under three weather effects (thin cloud, rain, and fog) combined. In Fig. 3, we consider a SAI buffer with L = 100 packets, different SAI transmission scheduling priorities α = [0.5, 10] in step of 0.5 (α is only used for SAI -GS laser), and transt mission power of SAI PSA I = {−20, −10, 0} dBm. As we analyze results under combined weather effects. The smaller t the PSA I value is, the worse the performance is because the probability of SAI -GS link outage increases with decreasing t PSA I . Also, the throughput in Fig. 3a increases with increasing α. This is because the buffered packets can be removed faster with a higher α (average queue length in Fig. 3b and packet dropping probability in Fig. 3c decrease with increasing t α). At a fixed transmission power PSA I , we can increase
the performance by adjusting the priority α without needing t an increment of PSA I . However, the throughput achieves a maximum at α ≥ 1.5 and configuring α larger than 1.5 is unnecessary because the packet dropping probability at α ≥ 1.5 is constant. The reason is that setting a SAI priority α higher than 1.5 will occupy more redundant transmission chance over SAs , leading to sometime less data transmitted from SAs due to using an inefficient frequency resource. In Fig. 3, in case of the weather using SAI -GS RF link, the performance does not depend on the SAI priority α. The performance is constant after observed time Ot because the arrival data rate of SAs -SAI laser link is much larger than the released data rate of SAI -GS RF link. Thus, the queue length of SAI buffer is always approximately full, and the packet dropping probability is only the ratio of the amount of released data to the amount of arrival data. Hence, the variant performance over different α values mainly comes from the case of the weather using SAI -GS laser link. Due to after α ≥ 1.5, the performance is constant. Thus, to get a much better quality of service, we need to sacrifice the t consumed energy of satellite by increasing PSA I . In addition, the average queue length and packet dropping probability t are relatively high, even increasing PSA I and α. This is I due to bad performance by using SA -GS RF link which
is independent with using the priority α. Thus, the satellite systems prioritize using the laser technology, while the RF technology is used as the backup [8]. We now show the benefit of using the laser links. Assume that we only consider the foggy weather using SAI -GS laser link with adjusting α. The system achieves a maximum performance at α = 1.5: t The throughput achieves 3.8768 Gbps at PSA I = −20 dBm, t 4.9615 Gbps at PSAI = −10 dBm, and 6.1077 Gbps at t PSA I = 0 dBm; the queue length is optimally minimized t at 0.0936 Gbits for PSA I = −20 dBm, at 0.0740 Gbits for t t PSAI = −10 dBm, and at 0.0647 Gbits for PSA I = 0 dBm; the packet dropping probability achieves zero for all cases. Next, we consider a SAI buffer with L = [10, 100] packets t in step of 10, SAI priority α = 1, and PSA I = {−20, −10, 0} dBm. The throughput shown (Fig. 4a) increases with increasing L because the SAI buffer with a higher L value can save more data which is proved via the average queue length (Fig. 4b), so this leads to lower packet dropping probabilities (Fig. 4c). However, the total satellite system performance slowly increases with increasing L because of the inefficiency in case of the weather using SAI -GS RF link as analyzed above.
3) Proof of Lemma 10: Based on Fig. 2, if the buffer is empty with the state probability P (0), the transmission probability of SAs without competing with SAI that sends successfully one packet to SAI is 1−ρSS with the transmission slot length CXSS , i.e., P (0) · (1 − ρSS ) CXSS . In case of empty o buffer, the timeout time TSS for the SAs -SAI laser link due to its outage probability ρSS causing packets unsuccessfully o sent is P (0) · ρSS · TSS . If the buffer is nonempty with the probability P (0̄) = 1 − P (0), the transmission probability of SAs with competing with SAI that sends successfully one to SAI is PSAs with the transmission slot length CXSS , i.e., P (0̄) · PSAs CXSS . Also, in case of nonempty buffer, the transmission probability of SAs with competing with SAI that ′ sends unsuccessfully one to SAI is PSAs with timeout time ′ o o TSS , i.e., P (0̄) · PSAs · TSS . Similarly as explained above, we have the transmission slot length if SAI wins transmission ′ o chances, i.e., P (0̄) · PSAI CX f,C + P (0̄) · PSAI · TSG . So, we get SG Eq. (20). If the buffer is nonempty, the transmission probability of SAI with competing with SAs that sends successfully one packet (X bits) to GS is PSAI , i.e., Eq. (19). R EFERENCES
V. C ONCLUSION We proposed an analytical framework based on Markov chain model to calculate the throughput and on-board buffering requirements for hybrid RF/FSO networks. The analytical results also show that instead of increasing transmission power, which increases energy and weight requirements, a suitable optical transmission scheduling priority can be used to maximize throughput and minimize electronic buffer size. We observed best results when using laser downlinks, resulting in a small buffer and zero packet dropping probability. RF improves the FSO reliability, but it requires comparably larger buffers, also due to reduced capacity. Our analysis also showed that even with smaller power, we can minimize the buffer, which carries potential for future all-optical transparent network solutions. A PPENDIX 1) Proof of Lemma 2: As the state space in the Markov chain has L states, it is finite. In addition, this Markov chain is irreducible because we observe Fig. 2 that any state i ∈ [0, L] can be reachable from any other state j ∈ [0, L]\i with a nonzero probability. Finally, we prove that if any state from this Markov chain is aperiodic, then it is aperiodic. Any state i with the period d(i) has the greatest common denominator from all integer values larger than 0, whereby there exists a transition probability larger than 0 from any state i traversing to the other states, and then going back to itself. In this Markov chain, there always exists a state i with a non-zero self-transition probability, d(i) = 1. Thus, the state i is aperiodic. 2) Proof of Lemma 3: In Fig. 2, the balance equations can be given as follows: PSAs 1 − ρSS P (0); P (i + 1) = P (i), ∀i ∈ [1, L). PSAI PSAI (25) PL With Eqs. (25), and i=0 P (i) = 1, we get Lemma 3. P (1) =
[1] M. Cardakli, “Challenges and opportunities in free space optical satellite communication,” Journal of Lightwave Technology, vol. 44, no. 3, pp. 903–912, 2026. [2] M. E. Hosney, H. A. I. Selmy, and K. M. F. Elsayed, “Co-channel interference reduction by optimizing field of view angle of angular diversity receiver in vlc systems,” in 2020 22nd International Conference on Transparent Optical Networks (ICTON), 2020, pp. 1–4. [3] O. B. Yahia, E. Erdogan, G. K. Kurt, I. Altunbas, and H. Yanikomeroglu, “A weather-dependent hybrid rf/fso satellite communication for improved power efficiency,” IEEE Wireless Communications Letters, vol. 11, no. 3, pp. 573–577, 2022. [4] S. Ma, Y. C. Chou, H. Zhao, L. Chen, X. Ma, and J. Liu, “Network characteristics of leo satellite constellations: A starlink-based measurement from end users,” in IEEE INFOCOM 2023 - IEEE Conference on Computer Communications, 2023, pp. 1–10. [5] H. He, Y. Hou, J. Yang, X. Jiang, S. Chen, and L. Hanzo, “Towards reliable space-ground integrated networks: From system-level design to implementation,” IEEE Network, vol. 37, no. 5, pp. 154–161, 2023. [6] B. Lin, H. Li, and Y. Long, “A buffer-limited maximum throughput routing algorithm for satellite network,” in 2015 22nd International Conference on Telecommunications (ICT), 2015, pp. 378–383. [7] K. Chi, Y.-h. Zhu, X. Jiang, and X. Tian, “Practical throughput analysis for two-hop wireless network coding,” Computer Networks, vol. 60, pp. 101–114, 2014. [Online]. Available: https://www.sciencedirect.com/ science/article/pii/S1389128613004283 [8] C. V. Phung, A. C. Drummond, and A. Jukan, “Achievable throughput and on-board buffer sizing in ris-uav relay-assisted satellite-aerialground integrated networks (sagins),” IEEE Transactions on Aerospace and Electronic Systems, vol. 61, no. 6, pp. 16 666–16 691, 2025. [9] J.-H. Lee, K.-H. Park, Y.-C. Ko, and M.-S. Alouini, “Throughput maximization of mixed fso/rf uav-aided mobile relaying with a buffer,” IEEE Transactions on Wireless Communications, vol. 20, no. 1, pp. 683– 694, 2021. [10] H. D. Le, V. V. Mai, C. T. Nguyen, and A. T. Pham, “Design and analysis of sliding window arq protocols with rate adaptation for burst transmission over fso turbulence channels,” Journal of Optical Communications and Networking, vol. 11, no. 5, pp. 151–163, 2019. [11] Z. Niu, H. Yang, Q. Yao, B. Wu, S. Yin, S. Shen, B. Wei, J. Zhang, and A. V. Vasilakos, “Reliable low-latency routing for vleo satellite optical network: A multiagent reinforcement learning approach,” IEEE Internet of Things Journal, vol. 12, no. 3, pp. 2309–2321, 2025. [12] R. Samy, H.-C. Yang, T. Rakia, and M.-S. Alouini, “Parallel fso-rf transmissions for high-throughput remote access with satellite communications,” IEEE Transactions on Aerospace and Electronic Systems, vol. 59, no. 6, pp. 9417–9426, 2023.