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Abstract
Over years of space laser communication technology advances, satellite optical networks (SONs) have emerged as a pivotal component in 6 G networks. Satellite services are transmitted from the global view, undergoing transmission through SONs, and being downloaded to the targeted areas. However, the transmission capacity of satellites passing through the areas where users are concentrated may be insufficient to download services transmitted worldwide. This problem exists in various kinds of satellite networks and may cause a large amount of service congestion. In this paper, we propose a multi-downlink delivery routing selection (MDD-RS) strategy to study the total utilization of transmission capacity of SONs. We construct an integer linear programming (ILP) model to establish an optimal case study for minimal network capacity occupation. Also, we design an online option, MDD-RS heuristic algorithm, dynamically calculating path routes, considering bandwidth allocation and resource constraints. A comparative analysis against the conventional single-downlink scheme reveals superior performance of the MDD-RS heuristic algorithm, with a reduction in blocking probability of 0.129 and an improvement in bandwidth utilization of 0.032.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past decades, satellites have played a pivotal role in television communications, enabling widespread broadcasts to users in regional areas [1–3]. By exploiting satellite’s high-speed mobility, nearly all television signals can be forwarded, directly attaching homes [1]. Nowadays, satellite communication is regarded as a promising way to achieve connections for global users. It is a complementary composition of 6 G networks to incorporate the spatial and the temporal networks. It helps to address the digital gap between urban and rural areas through remote communications. To ensure a seamless coverage area, satellites are developed into a large-scale constellation, numbering in tens of thousands, so-called mega-constellations [4–6]. Some well-known constellations include Starlink [7,8], which consists of over 6,000 small satellites as of March 2024, and OneWeb [9,10], having a constellation exceeding 648 satellites. In the near future, it is expected that these satellite constellations will be applied in various communication scenarios facilitated by some advanced technologies, such as the direct connection between satellites and mobile phones.
Traditionally, satellites have predominantly served as signal relays in satellite-to-ground (SG) communication processes. Through the satellite-to-ground links (SGLs) [11], signals can be forwarded by satellites in a bent-pipe manner, merely forwarding signals among users without modifying the data. This process may introduce latency on the waiting of satellite moving right over the destination. To improve transmission performances, researchers consider the way of forwarding signals from one satellite to its nearby satellites until finding the satellite right over the destination. Such an inter-satellite way is based on the establishment of inter-satellite links (ISLs). While the microwave communications in space have some disadvantages like relatively low data rates, and thus limit the application efficiency. Over years of advances in optical communications, researcher trends to exploit laser communication to establish ISLs and have an enhanced transmission capacity [12,13]. Laser communication is a viable way, which can potentially support gigabits-per-second data rates to match the projected performances of satellite internetwork. The benefits of using laser communication were demonstrated with numerous experiments in various projects [14–17], like OneWeb and Starlink. Consequently, ISL achieved through laser communication in satellite networks, often referred to as satellite optical networks (SONs), are emerging as promising and forward-looking trends in the evolution of communication networks.
Nowadays, satellite numbers are rapidly increasing to extend the coverage areas and enable more accessibility regardless of time and position. While there are more numbers of ground stations on the ground. Satellites are enabled to connect with several ground stations in visual range at the same time to perform communications. They establish uplinks and downlinks to upload and download services by occupying a certain bandwidth. The connections can generally maintain a short interval until the satellites fly out of the range. During these connection periods, the Satellite-Ground Link (SGL) connections are generally assumed to have similar transmission capacities. This assumption stems from the situation that satellites in the same orbit theoretically maintain consistent speeds and inclinations relative to ground stations, resulting in nearly equal connection durations. However, user distribution across regions varies due to factors like population density and political strategy. Certain regions become primary recipients of a large number of services. During the download process, the satellite’s downlink transmission capacity may be constrained due to the disparity in transmission capacity between ISLs and SGLs. Moreover, a satellite possesses fixed port numbers and link bandwidth for establishing downlinks with ground stations. It will potentially lead to service blockage. Existing solutions, such as the proposal of double-layer constellations to enhance transmission capacity in specific regions [18–20], are constrained by technological maturity and substantial costs. Therefore, the problem of how to use the fixed transmission capacity of downlinks to download more services is inevitable and should have a focus.
In the background of large-scale SONs, this paper focuses on the problem of service blockage caused by limited downlink transmission capacity. We provide case studies to see the network performances of increasing satellite numbers to jointly download services. First, we construct the integer linear programming (ILP) model, to seek the optimal results of minimum network capacity utilization as an optimal case study. Second, we propose an online option, i.e. multi-downlink delivery routing selection (MDD-RS) heuristic algorithm, to dynamically calculate the path routes consisting of ISLs and SGLs. MDD-RS algorithm requires the ISLs and SGLs in multiple paths have the common connection periods. Also, the scheduling is subjected to the following two limitations: i) available transmission capacity of ISLs and SGL, and ii) available port numbers of satellites (to the ground stations) and the port numbers of the ground station (to the satellites) to establish SGLs. With the comparison of one downlink scheme as the benchmark, we analyzed the simulation performances of MDD-RS algorithm. Simulation results show better performances of MDD-RS in the items of blocking probability of service delivery and bandwidth utilization of ISLs and downlinks.
The reminder of this paper is organized into 6 sections. Sec. 2 provides a comprehensive overview of SONs and nowadays popular routing schemes in SONs. Sec. 3 addresses the DD-RS problem with the constructive network model and service model. Sec.4 addresses the DD-RS problem and designs the MDD-RS heuristic algorithm. The numerical results are discussed and presented in Sec. 5. Finally, Sec. 6 draws the paper’s conclusion.
2. Background
2.1 SONs
SONs typically compose the space segment and the ground segment. In the space segment, satellites are divided by the location orbits at different altitudes. Low earth orbit (LEO) is in the range of 400-2000km, medium earth orbit is in the range of 2000-35786 km, and geostationary earth orbit is beyond the altitude of 35786 km [21–26]. Satellites perform laser communication to transmit high-speed data between each other in SONs, enabling the exchange of large volumes of data. In the ground segment, it mainly includes the ground stations [27] and ground terminals [28]. Ground stations are mostly considered on their transmission performances of uplinks and downlinks [29], and the connection relationship with the moving satellites is an important topic in existing papers. Within the coverage area, satellite and the ground station can establish bidirectional communications with two independent links affected by visible distance, inclination angle, atmospheric conditions, users’ demand pattern and other factors [30]. They can be achieved by multibeam technology, which are always studied on the issues of power and bandwidth allocation [31,32]. Without losing practicality, this context mainly considers the background of the ground stations with unbalanced service distribution and delivers them to SONs. In SONs, service delivery in SONs can be divided into three processes, as shown in Fig. 1(i) The upload of services via uplinks. ii) The forwarding of services between satellites. iii) The download of services via downlinks. In a service’s delivery path, the satellite responsible for the service upload is called access satellite, and the satellite responsible for the service download is called feeder satellite.
2.2 Routing schemes in SONs
SONs are attracted significant attention in recent years. In Table 1, it is an overview of relevant literature addressing various service congestion challenges across different types of satellite networks. Additionally, the table summarizes various multipath schemes developed specifically for SONs. Despite lots of existing state-of-art routing schemes were designed in SONs, the problem of how to exploit multiple downlinks for a service delivery was less considered. Motivated and differing from the above strategies, we focused on the service blockage caused by the problem of unbalanced capacity between uplink and downlink in this context.
Table 1. Summary of Routing Schemes in Satellite Optical Networks
3. Network model and problem statement
3.1 SON model
The modeling of SON can be denoted as a graph at arrival time of service request. In the graph G, we formally take satellites and ground stations in the node set V, respectively marked as S and G. E is link set, including ISLs (${L_S}$) and SGLs (${L_G}$). ${L_G}$ includes uplinks (${L_A}$) and downlinks (${L_F}$). The bandwidth of ${L_A}$, ${L_S}$ and ${L_F}$ are marked as ${B_{as}}$, ${B_{ss}}$ and ${B_{sg}}$, respectively. The occupied bandwidth of ${L_A}$, ${L_S}$ and ${L_F}$ are represented as ${B_{a{s_o}}}$, $\textrm{}{B_{s{s_o}}}$ and $\textrm{}{B_{s{g_o}}}$.
3.2 Service model
Service requests are considered as a tuple $r({{s_r},{g_r},{b_r}} )$, where ${s_r}$ is a content and refers to the source satellite, ${g_r}$ is a ground station (i.e., a content), and ${b_r}$ is the required bandwidth. Suppose source satellite ${s_r}$ and $\textrm{G}({V,E} )$ is given. $r({{s_r},{g_r},{b_r}} )$ can be separated into ${r_s}({{s_r},{d_r},{b_r}} )$ and ${r_g}({{s_r},{d_r},{b_r}} )$ for the path calculation in IS process and download process, as shown in Eq. (1). The separation begins from a common source satellite ${s_r}$ to several satellites ${d_r}$, involving x IS paths and x downlinks for service delivery, as depicted in Eq. (2) and Eq. (3). The total bandwidth occupation across x paths equals ${b_r}$. As for the x IS paths and x downlinks of each service request, suppose they belongs to set $\textrm{R}_s^r$ and set $\textrm{R}_g^r$, respectively.
3.3 MDD-RS problem statement
The MDD-RS problem is defined as follows. The above-mentioned models of network topology and service request are taken as an input. Given i) a network graph $\textrm{G}({V,E} )$, ii) the service request model $r({{s_r},{g_r},{b_r}} ),r \in \{{1, \cdots ,|R |} \}$, separated into $r_s^x({{s_r},d_r^x,b_r^x} )$ and $r_g^x({d_r^x,{g_r},b_r^x} )$ . iii) The problem addresses the service blockage caused by a limited downlink transmission capacity, i.e., ${L_{A1}} + {L_{A2}} + {L_{A3}} > {L_F}$, as presented in Fig. 2. Both ILP and MDD-RS heuristic algorithm are constrained by, i) the bandwidth capacity of IS and SG satisfied the service requests at least, and ii) the available port numbers of satellites (to the ground stations) and the port numbers of the ground station (to the satellites).
4. ILP model
In this section, we develop the MDD-ILP model to allocate available transmission capacity for end-to-end services in a static scenario. The ILP model shows the constraints associated with bandwidth scheduling across multiple downlinks, and enables the optimal results. Table 2 summarizes the model parameters.
Table 2. Parameters Description
4.1 Supposes illustration
There are two assumptions outlined below. i) The first assumption is that the enabled transmission capacity of every ISL and SGL remains fixed over time. ii) The second assumption is that when the diagonal distances and elevation angles between feeder satellites and ground stations are feasible, they are allowed to establish SGLs in a physical view. As is customary, the connections of every S and G can be identified by coordinates.
4.2 ILP model
The object is to minimize the total capacity occupation ${C_T}$ in the SON, as shown in Eq. (4). It is composed of ${C_S}$ in Eq. (5) and ${C_G}$ in Eq. (6). It is for the constraints of capacity allocation in IS, as shown in Eq. (7–16). The first constraint, as described in Eq. (7), represents the bandwidth constraint for ISLs. It ensures that the bandwidth occupation of any ISL for a service should not exceed its requirement, which is also less than or equal to the initial bandwidth, as depicted in Eq. (8). Equation (9) ensures the network capacity constraint by ensuring that the total bandwidth demand of all service requests does not exceed the total capacity of the network. Equation (10) states the constraint of occupied numbers for one service in an ISL should not be beyond x. Equation (11) imposes the constraint that the number of services on any ISL should not exceed the total number $\textrm{N}$. Equation (12) constrains the number of ISLs that can be assigned to a service, ensuring it is less than the total number of network links. Equation (13) and Eq. (14) ensures the number of ports that can be occupied by a service cannot exceed the allowable number of ports. The third constraint is the flow conservation in IS, as shown in Eq. (15). It ensures the input and output of every intermediate satellite must be equal. The feeder satellites here are only considered for IS service input and output.
Objective function:
Subjected to,
The following equations are the constraints for the downlink selection. It is for the constraints of capacity allocation in SG, as shown in Eq. (16–21). The first constraint is bandwidth constraint of SGLs, as shown in Eq. (16). Equation (17) refers to the constraint of service numbers assigned in any SGL which cannot beyond the total numbers. Equation (18) imposes a constraint on services where the x paths have a total bandwidth of ${b_r}$ if $m = {g_r}$. It is also the flow conservation for a ground station. In this case, Eq. (19) means that the occupied SGL numbers should be larger than x. Equation (20) and Eq. (21) represent the port number constraints for any ground station or satellite, ensuring that they are less than or equal to ${N_{sg}}$.
Subjected to,
5. Online algorithm
ILP models provide optimal results but can be computationally intensive and spend a long running time, especially in large-scale SONs. This section introduces the MDD-RS strategy and its heuristic algorithm. These methods efficiently select feeder satellites and compute multiple routes under the constraints to ground stations.
5.1 MDD-RS strategy
To find multiple paths and downlinks with available resources, we propose an MDD-RS strategy that decomposes one feeder satellite into multiple assistant satellites, collectively delivering services. In MDD-RS strategy, destination ground stations selectively establish SGLs with certain passing satellites. First, we conduct a potential set of satellites for the destination ground station that can establish connections, which can be obtained in the ephemeris table. Then, it is the selection of assistant satellites to calculate paths with available transmission resources. We calculate possible routes by exploiting several times of the Dijkstra algorithm for surplus resources and putting them in a set. Based on the route set, considering the assistant satellites act as destination nodes for service delivery, we go through the set to find whether they have available port numbers and enough bandwidth to fit the demand of requests. Finally, by traversing the above when the total transmission capacity exceeds requirements, determining the number of assistant feeder satellites needed.
5.2 MDD-RS algorithm
In Algorithm 1, as the inputs, $G({V,E} )$, $r({{s_r},{g_r},{b_r}} )$, $r \in R$, $G({V,E} )$, ephemeris table, ${B_{sg}}$, ${B_{ss}}$, ${N_{gs}}$, represents a network having given links in IS and SG with a certain bandwidth and enabled port numbers to be allocated for a series of service requests. As the outputs, we design the MDD-RS algorithm to find x as the number of paths for the content request, ${P_{MDD}}$ as the calculated routes for the request, ${B_{MDD}}$ as the offered bandwidth set for the request.
Algorithm 1 starts by the arrival of requests $r({{s_r},{g_r},{b_r}} )$. It contains two parts, respectively in IS and SG. Considering iteration process for the scheduling in IS is more complex compared to SG, the algorithm first goes to the scheduling in SG and then in IS. First, it is the source and destination definiteness steps. We extract the destination ground station from the request, and construct a possible-connected satellite set (i.e., ${\textrm{D}_{{g_r}}}$) of this ground station (i.e., ${\textrm{D}_{{g_r}}}\{{d_r^1, \cdots ,d_r^x} \}$) by searching the ephemeris table. The algorithm checked the available port numbers of $d_r^x$ in ${\textrm{D}_{{g_r}}}$, which should have at least one. Otherwise, delete the ineligible ones from the ${\textrm{D}_{{g_r}}}$. Then, it goes to the scheduling in IS, i.e., route calculation steps. Based on the given ${s_r}$ and ${\textrm{D}_{{g_r}}}\{{d_r^1, \cdots ,d_r^x} \}$, we use Dijkstra algorithm to calculate the shortest routes between ${s_r}$ and each $d_r^x$, respectively. The x numbers of paths are put into path set of the request ${P_r}$. Next, it is the resource allocation steps. The algorithm sorts the paths according to their number of hops from smallest to largest. Traversing each link of routes in ${P_r}\{{p_r^1, \cdots ,p_r^x} \}$, the algorithm regards the lowest bandwidth of the link in the path as the available bandwidth of the path. The algorithm puts the available bandwidth of each path in set of the request (i.e., ${B_r}\{{b_r^1, \cdots ,b_r^x} \}$), and compare them one by one with ${b_r}$ in the request to judge whether a path having enough bandwidth. If there are $b_r^x$ bigger than ${b_r}$, allocating one of them to the request and ending the scheduling of this request. If there is no $b_r^x$ bigger than ${b_r}$, traversing the ${P_r}\{{p_r^1, \cdots ,p_r^x} \}$ and allocating ${B_r}\{{b_r^1, \cdots ,b_r^x} \}$ for the request until $\sum b_r^x \ge {b_r}$. If bandwidth requirement can be satisfied in advance, delete the surplus routes in the ${P_r}$ and their corresponding bandwidth in ${B_r}$. If the x numbers routes in ${P_r}$ having $\sum b_r^x < {b_r}$, it means the scheduling of the request is failed, otherwise it is successful. Finally, the algorithm output the route set and bandwidth set of successful scheduled requests.
Table 2. MDD-RS Algorithm
5.3 Complexity analysis
The complexity of MDD-RS algorithm includes three parts, i) complexity of the MDD-RS by traversing satellite set V with O($V$). ii) The complexity of multiple path calculation which is consisted of x times of Dijkstra algorithm which uses two times of “for” loops marked as O(${V^2}$). As for x paths calculated in IS part, the number of iterations needed to transform V satellites for feeder function and converge to a successful route selection solution is in the order of O($V$) times and therefore, since the worst-case complexity of O($x{V^2}$). iii) As for the x downlinks calculation in SG part, the process will go for the bandwidth judgement with O($N$) and N is a constant. It should be noted that will have a relative-high complexity with the increasing numbers of satellites or ground stations.
6. Case study and simulation results
6.1 Simulation settings
In this section, we conduct simulations to evaluate the proposed ILP model and MDD-RS algorithm. As for the basic setting of SON, we consider a Walker constellation (altitude: 1050 km, degree: 89°, planes: 24, phase factor: 9, range: 180°) with 1152 satellites to form a basic topology, whose time-varying connection relationship is shown in Fig. 3(a). We suppose there are 50 ground stations in the terrestrial which have a relative centralized distribution, as shown in Fig. 3(b). The specific connection data between satellites and ground stations was obtained from the simulative constellation data in Satellite Tool Kit. Figure 3(b) is presentation of parts of Ground Stations. The entire holding period was set to 2 hours referred by the practical orbit period, then the whole period was divided into 120 continuous time slices per min by using snapshot. We use part of data as the input of topology to verify the proposed route calculation and bandwidth allocation algorithm. The bandwidth of each ISL was set to 40 Gbps, and the bandwidth of uplinks/downlinks are set to 8 Gbps. We suppose the arrival of services in ground stations followed Poisson distribution. Service numbers (SN) varied in the range of [3000, 4000, 5000, and 6000]. Service request was generated by the program and has the known source satellite, destination ground station, and the required bandwidth. The source and destination satellites were generated by Random distribution within the range of node set, and the generation of required bandwidth follows Normal distribution with 30 standard deviations. Therefore, the services were supposed to transmit in a snapshot topology conducted by the time slices sampled every 1 minute in the algorithm simulation. The designed ILP models are solved by the CPLEX software in version 12.7.1 installed on this computer. The simulations were run on a computer with a 1.8 GHz Intel Core i5-8250U CPU and 8GB RAM. It is noted that ILP may not be suitable for the solution applied in practice due to the complexity of its calculation in time dimension. The simulation results of the ILP model will be referred to refer as an optimal operation diagram, which provides the meaning of model construction and constraint forming. In the dynamic scenario, we developed a C++ event-driven network simulator with a joint constellation with STK To evaluate the performances of the MDD-RS algorithm, with the dynamic route-calculated algorithm always used in existing methods as the benchmark, i.e., Dijkstra-routing selection (D-RS), to calculate the shortest path for services. The numerical performance evaluation for the proposed algorithms with the benchmark is mainly evaluated in terms of blocking probability and bandwidth utilization of downlinks and ISLs.
Fig. 3. (a) 3D presentation of 1152 satellites. (b) The presentation of parts location of 50 ground stations on the Earth.
6.2 Simulation results for MDD-ILP and MDD-RS
Figure 4(a) shows the minimal utilization of network capacity when SN is 3000, 4000, 5000, and 6000, respectively. We counted the total utilization of ISLs and SGLs and their partial utilization, as shown in the legend. When SN increases, the network capacity utilization gradually becomes higher. The capacity utilization of ISLs and SGLs show an upward trend, but the increasing of ISLs is slower than that of SGLs. This is because the transmission capacity of ISLs is large and the increase of ISL is not obvious to it. In Fig. 4(b), it is the average number of feeder satellites used for the delivery of services. This performance also indicates the number of IS paths for the services. The results show that the number is irregular as the increase of SNs, and also has a fewer gap between each two of them. This is because that multiple paths can alleviate the bandwidth occupation conflict when the bandwidth of the downlink is tight. Figure 4(c) shows the counted hops for the averaged deliveries of services. The trends are similar to the multiple paths, which are also irregular as SN increases. Also, it shows a fewer gap between each two of them. While it should be noted that the calculation of paths for services will be detoured and thus have lots of extra hops especially when the resources become tight. The results of ILP model can be seen as a case study to seek the optimal results of minimum resource occupation under various SNs at a time point.
Fig. 4. Performances for the MDD-ILP, i.e., (a) minimal bandwidth utilization of the network respectively when SN = 3000, 4000, 5000 and 6000. (b) The average $x$ under SN = 3000, 4000, 5000 and 6000. (c) The average hops of the minimal results.
Figure 5(a) shows the blocking probability of the MDD-RS and D-RS. This performance is calculated by the average blocking probability of SNs in 120 time slices. The figure illustrates a reduction of approximately 0.129 in the blocking probability achieved by MDD-RS compared to D-RS when SN = 3000. With the increase of SNs, the trend of MDD-RS gradually becomes stable, and the D-RS has an increase trend. It means that gap between the two trends changes from a small value to a big value and then small back until the MDD-RS cannot effectively alleviate the blockage. If it occurs to this situation, the current SN is the limit value that can be carried in the SON in the situation of fixed transmission capacity of the downlinks. Therefore, we can draw two conclusions from this performance. One is that using one feeder satellite for service delivery will indeed have the fixed and limited transmission capacity, and thus resulting in blockage. The second is that MDD-RS can support more services delivered in the SONs. Figure 5(b) shows the impact of different time slices on the blocking probability. There are 10 continuous time slices selected from the entire orbit period, and each of them is with different holding times. We can see from the figure that the blocking probability of time slice became bigger as SN increases. Each fixed SN’s blocking probability has a slight and irregular fluctuation in different time slices. This fluctuation might be caused by the connection changes between satellites and ground stations on each time slice. This means that time slices and their holding time have less impact on the SNs that can be carried in SONs. Furthermore, we can also find that the improvement of MDD-RS over SN in SONs has less affection for the time slice changing. Figure 5(c) shows the real-time SN of the MDD-RS and D-RS dealt by each feeder satellite changing in two time slices. The X-axis shows the downlink ID, and the Y-axis shows four sizes of SNs, respectively in two time slices. The Y-axis is composed of two parts, i.e., the front block belonged to the D-RS and the back block belonged to the MDD-RS. As for the SN changing in a time slice, the density of the back part is significantly greater than that of the front part, indicating that more SNs can be carried in the downlink, which is consistent with the conclusion in Fig. 4(b). As for the same value of SN under different time slices, it shows the SN of each downlink fluctuates slightly, which also means that time slices have little effect on this. As for the SN in two time slices, it shows that the downlink ID from 50 to 150 has relatively continuous and stable SNs than the others. It means that ground stations can always establish downlinks with some fixed and specific satellites. That is to say, no matter which constellation it is in, a specific area on the earth can be always covered by the satellites.
Fig. 5. Blocking probability of services under increased SN (i.e., 3000, 4000, 5000, and 6000). A gradual decomposition of blocking probability, i.e., (a) a total result under the comparison of D-RS and MDD-RS with increased SN, (b) results with the averaged blocking probabilities under different service numbers respectively in 1-10 sampled continuous time slices, and (c) results with a real time count of carried service numbers for every feeder satellite in MDD-RS and D-RS algorithms during 2 sampled time slices.
In Fig. 6(a), the bandwidth utilization of downlinks is presented for both the MDD-RS and D-RS algorithms. As the SN increases, the MDD-RS curve exhibits a gradual rise, contrasting with the stable curve of the D-RS. The gap between them fluctuates, initially small, then widening before contracting again. Notably, the average downlink utilization ratio can be improved by at least 0.032. Figure 6(b) examines the impact of time slices on downlink transmission capacity utilization. Both curves display a similar trend, indicating that the enhanced bandwidth utilization brought by the MDD-RS is less influenced by time slices. However, the maximum downlink bandwidth utilization ratio approximately reaches 0.4576, while the corresponding blocking probability is about 0.075. This illustrates that there is a room for further improvement in bandwidth utilization. Blockages occur even when there is sufficient transmission capacity of downlinks, hinting at potential issues related to insufficient capacity of ISLs. Figure 6(c) delves into the real-time bandwidth utilization of downlinks, featuring various SNs on two time slices, comparing the MDD-RS and D-RS. The front block corresponds to the D-RS, and the rear block to the MDD-RS. As in Fig. 6(c), the proportional relationship between feeder satellites and downlinks persists, showing trends similar to those observed previously. The real-time data reveals that maximum bandwidth utilization ratio approaches 0.9, a significant contrast to the average time slice in Fig. 6(b), the ratio was less than 0.5. This discrepancy underscores the potential generation of fragmented resources through dynamic service allocation, necessitating further exploration in downlink scheduling.
Fig. 6. Bandwidth utilization of downlinks under an increased SN (i.e., 3000, 4000, 5000, and 6000). Also, a gradual decomposition of it, i.e., (a) a total comparison of MDD-RS and D-RS with increasing service numbers, (b) the averaged bandwidth utilization of downlinks to be compared with different service numbers in 10 continuous time slices, and (c) results with a real-time count of downlink bandwidth under different service numbers respectively in 2 time slices.
Figure 7(a) illustrates the bandwidth utilization of ISLs, serving as a reflection of the bandwidth occupation by services. Notably, the bandwidth utilization of ISLs in the MDD-RS scenario exhibits a clear increase with the growing number of services, contrasting with the gradual rise observed in the D-RS. The gap between them widens, reaching a point where the MDD-RS curve stabilizes. Given that ISL bandwidth is generally times larger than that of the downlink, a suitable allocation of bandwidth resources for ISLs becomes imperative. In Fig. 7(b), the influence of time slices on ISL bandwidth utilization is examined. Similarly, the MDD-RS demonstrates a less pronounced sensitivity to variations in time slices, contributing to improved bandwidth utilization of ISLs. Figure 7(c) provides insights into the real-time bandwidth utilization of individual ISLs, with the D-RS occupying the front block and the MDD-RS the rear. Different time slices appear to have a relatively minor impact on real-time bandwidth occupancy. However, both MDD-RS and D-RS show similar uneven utilization of ISLs. The figure depicts concentrated utilization in specific sections, resulting in significantly higher utilization rates, while some ISLs experience lower utilization. This concentration is attributed to the MDD-RS’s ability to support more services, contributing to a relatively focalized utilization pattern. The additional services supported by MDD-RS exacerbate uneven resource utilization among ISLs, potentially leading to partial service blockages, which is an aspect to be explored further in the context of flexible resources within SONs.
Fig. 7. Bandwidth utilization of ISLs under an increased SN (i.e., 3000, 4000, 5000, and 6000), i.e., (a) a total comparison of MDD-RS and D-RS, (b) averaged utilizations changing with different service numbers during 10 continuous time slices, and (c) real-time utilizations of ISLs under different service numbers.
7. Conclusions
In this paper, we propose MDD-RS strategy by using possible satellites as the feeder to jointly download services. The main work of this paper is concluded as follows: i) Construct ILP models to select available satellites and schedule multiple routes for the ground stations under the object of a minimum network capacity and subjected to the constraints of bandwidth and port number. ii) The MDD-RS heuristic algorithm is designed to dynamically compute routes with multiple feeder satellites for service delivery. Comparative analysis illustrates the effectiveness of MDD-RS algorithm in enhancing network capacity while maintaining a certain performance guarantee. The results indicate that a higher number of services can be efficiently delivered within the networks, accompanied by improvements in the utilization of satellites as the feeders. In the future, we will explore methods to efficiently utilize dynamic network resources and optimize their utilization. This could leverage machine learning techniques or enhancing the adaptability of routing algorithms.
Funding
National Natural Science Foundation of China (62350001); Funds for Creative Research Groups of China (62021005).
Acknowledgements
This work has been supported in part by the Funds for Creative Research Groups of China (62021005).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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