Satellite data download time minimization method based on cross-slot scheduling

Abstract

The application discloses a satellite data download time minimization method based on cross-time slot scheduling and belongs to the field of satellite communication. The application realizes the method as follows: evenly dividing a communication time window into multiple time slots; on the basis, establishing and solving a throughput maximization problem under the minimum download time upper and lower bound mean value restriction under the energy constraint, judging whether the satellite data volume download can be completed within the time, and further updating the minimum download time upper and lower bound in a dichotomy search manner and iteratively optimizing the convex optimization until convergence, so that the minimum download time is obtained, the download time slot selection and the energy distribution result of each time slot reaching the minimum download time are obtained, the utilization efficiency of the satellite download time and energy is improved, the time of connecting the ground station required by the satellite data download is reduced, the on-orbit data efficient download under the dynamic satellite channel and energy acquisition is realized. The application also has the advantages of a larger feasible region and no inter-satellite data transmission.

Description

Technical Field

[0001] The present invention relates to a method for minimizing download time in a satellite communication system, and in particular to a method for minimizing satellite data download time based on cross-time slot scheduling, and belongs to the field of satellite communication. Background Art

[0002] Low-Earth Orbit (LEO) satellites are expected to play a key role in the sixth-generation (6G) communications network by providing a variety of services. Some of these services, such as Earth imaging and weather observation, generate large amounts of data in space. This data, collected in space, needs to be downloaded to the ground via communication with ground stations when the satellites are within range.

[0003] However, the amount of data generated by satellites can easily exceed the communication link capacity between satellites and ground stations. On the one hand, lower orbital altitudes result in higher satellite speeds and smaller coverage areas, which further reduces the communication window between satellites and ground stations to less than ten minutes. Furthermore, due to the sparse distribution of ground stations and the continuous shift in the satellite's orbit relative to the Earth's rotation, satellites may only have one communication opportunity with a ground station per day in some cases, forcing them to download data within this less than ten-minute communication window. On the other hand, the time and financial costs associated with applying for and maintaining ground stations also make renting them prohibitively expensive, making it difficult to download the required amount of data within cost constraints. Therefore, given both communication and cost constraints, downloading large amounts of data in the shortest possible time is both beneficial and necessary.

[0004] However, in addition to the limited communication time window, downloading data from satellites also needs to consider the limitations imposed by satellite dynamics and the confined environment of space, including the ever-changing communication channel and the limited and varying available energy. First, due to the ever-changing distance between the satellite and the ground station, there is a path loss fluctuation of approximately 10dB at different times during each communication with the ground station, which makes it necessary to select times with better channel conditions for data download. Second, the energy available for downloading from the satellite is limited and increases over time. When exposed to sunlight, the satellite continuously obtains energy from solar panels, which makes the satellite's available energy continue to grow, but the cost constraints of the satellite payload mean that this energy will not be too abundant, making efficient energy planning a necessity.

[0005] Existing methods for reducing satellite data download time mainly focus on two aspects. The first is to increase the downlink transmission rate per unit time through physical layer signal processing or resource allocation methods. However, there are few solutions that consider satellite dynamics to jointly optimize energy allocation and transmission time selection under energy collection and dynamic channel conditions. The second is to use inter-satellite links to transmit on-board data to satellites with better channel conditions for download. However, most of the satellites currently used to collect in-orbit data do not have inter-satellite links. Therefore, for the application scenario of a single satellite downloading in-orbit data, it is very necessary to jointly consider energy collection and dynamic channel conditions to further improve the utilization efficiency of time and energy, thereby minimizing the time required for satellite data download. Summary of the Invention

[0006] Aiming at the problem of efficient on-orbit data download under dynamic satellite channels and energy acquisition, the present invention provides a satellite data download time minimization method based on cross-time slot scheduling. The method first evenly divides the communication time window into multiple time slots. On this basis, a throughput maximization problem under the mean constraints of the upper and lower bounds of the minimum download time is established and solved under energy constraints to determine whether the satellite data volume can be downloaded within the time. The upper and lower bounds of the minimum download time are further iteratively updated in a binary search manner until convergence, thereby obtaining the minimum download time, and obtaining the download time slot selection that achieves the minimum download time and the energy allocation result of each time slot. The method improves the utilization efficiency of satellite download time and energy, thereby reducing the time required to connect to the ground station for satellite data download, and realizing efficient on-orbit data download under dynamic satellite channels and energy acquisition.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] The method for minimizing satellite data download time based on cross-time slot scheduling disclosed in the present invention includes the following steps:

[0009] Step 1: When the satellite enters the connection range of the ground station, the amount of satellite data D to be downloaded and the initial energy available for communication E0 are sent to the ground station. The amount of satellite data D to be downloaded and the initial energy available for communication E0 are any positive numbers; the ground station estimates the satellite's communication time window t according to the satellite orbit. total . And initialize the upper bound of the minimum download time t max and the lower bound t min , and the convergence error ε of the download time.

[0010] The initialization method of the upper and lower bounds of the minimum download time is

[0011]

[0012] Step 2: Divide the communication time window estimated in step 1 into N time slots of length Δt, with each time slot starting at t i time slot; and estimate the distance d between the satellite and the ground station in each time slot based on the satellite orbit and time slot segmentation i , in order to facilitate further calculation of the channel conditions of each time slot, realize time slot scheduling of satellite energy, and improve the utilization rate of satellite energy resources.

[0013] The time slot length Δt and the time slot start time t i The value of

[0014]

[0015] Step 3: For the satellite time slots divided in step 1, the energy obtained before each time slot must be greater than the energy used before each time slot, and the energy constraint under the satellite energy acquisition condition is established; based on the distance d between the satellite and the ground station obtained in step 2 i According to the Shannon formula and the relationship between satellite channel attenuation and the distance between the satellite and the ground station, the total throughput during the satellite transit and the power P of each time slot are established. i and time slot selection indicator variable y i The relationship between P i The value range of y is any positive number. i The value range is 0 or 1. i =1, it means the satellite uses the i-th time slot for downloading.

[0016] The energy constraint for the satellite to obtain energy is:

[0017]

[0018] Among them, E i (h) E is the energy that the satellite can obtain for communication in the i-th time slot, which is obtained according to the satellite's operating status, parameter design, and its relative position to the sun and the earth; i is the energy used by the satellite in the i-th time slot, which is equal to the power P of the i-th time slot i The relationship is

[0019] E i =ηΔtP i (4)

[0020] Where η represents the energy loss caused by the power amplifier and is a constant greater than 1;

[0021] The total throughput during the satellite transit period is related to the power P in each time slot i The slot selection indicator variable and the slot allocation y i The relationship between

[0022]

[0023] Where B is the system bandwidth, G is the product of the gains of the transmitting and receiving antennas, N0 is the power spectral density of the noise, and L i is the average path loss between the satellite and the ground station in the i-th time slot, which is equal to the distance d between the satellite and the ground station in each time slot obtained in step 2. i The relationship is

[0024]

[0025] Where f is the carrier frequency used for data transmission;

[0026] Step 4: The energy constraint obtained in step 3 and the total occupied time slot are not greater than the mean of the upper and lower bounds of the minimum download time t mid As a constraint, y i and P i As a control variable, establish the minimum download time upper and lower bound mean t mid The satellite download throughput maximization problem as a maximum download time constraint.

[0027] The minimum download time upper and lower bound mean t mid The satellite download throughput maximization problem with the maximum download time constraint is

[0028]

[0029] st(3),

[0030] y i Δt≤t mid ,i∈{1,…,N} (7a)

[0031] 0≤P i ≤P max (7b)

[0032] y i ∈{0,1},i∈{1,…,N} (7c) Among them, the mean of the upper and lower bounds of the minimum download time t mid The value of

[0033]

[0034] P max is the maximum transmission power of the satellite, (7a) constrains the total length of the allocated download time to not exceed the maximum download time limit, (7b) constrains the transmission power to not exceed the maximum value allowed by the satellite, and (7c) constrains the value range of the download time slot indicator variable.

[0035] Step 5: Calculate the mean of the upper and lower bounds of the minimum download time constructed in step 4. mid The satellite download throughput maximization problem with the maximum download time limit is solved to obtain the minimum download time upper and lower bound mean t mid As the maximum satellite download throughput D under the maximum download time constraint max , and the corresponding time slot selection indicator variable y that can achieve the satellite download throughput is obtained i * And the power P of each time slot i * , utilizing the joint allocation of multi-slot resources to improve the efficiency of satellite download time and energy.

[0036] In order to reduce the solution to the minimum download time upper and lower bound mean t mid As the complexity of the satellite download throughput maximization problem with the maximum download time limit, as the preferred method, in step 5, the satellite download throughput maximization problem is solved by using the generalized Benders decomposition and cyclic water injection method to obtain the minimum time upper and lower bound mean t mid The maximum download throughput of the satellite as a limit on the maximum download time.

[0037] Step 6: Convert the t obtained in step 5 mid As the maximum satellite download throughput D under the maximum download time constraint max Compare it with the amount of satellite data D that needs to be downloaded to determine whether it can be downloaded within the value t mid Complete the download of all data within 10 seconds. Based on the judgment result, the binary search method is used to update the upper and lower bounds of the minimum download time, and determine whether the range of the upper and lower bounds of the minimum download time is less than the convergence error. If it is greater than the convergence error, return to step 4 for iteration. If the upper and lower bounds of the minimum download time meet the preset iterative convergence criteria, the optimized minimum satellite data download time and the time slot selection and power of each time slot that can achieve the minimum data download time are output. That is, the satellite data download time is minimized based on cross-time slot scheduling, thereby reducing the time required to connect to the ground station for satellite data download, and realizing efficient download of on-orbit data under dynamic satellite channels and energy acquisition.

[0038] The updating method of updating the upper and lower bounds of the minimum download time by using the binary search method according to the judgment result is as follows: if the satellite download throughput is greater than or equal to the amount of satellite data to be downloaded, that is, D max ≥D, then let the upper bound of the minimum download time be equal to the mean of the upper and lower bounds of the current minimum download time, that is, t max =t mid Otherwise, if the satellite download throughput is less than the amount of satellite data that needs to be downloaded, that is, D max <D, then let the lower bound of the minimum download time be equal to the mean of the upper and lower bounds of the current minimum download time, that is, tmin =t mid ;

[0039] The preset iterative convergence criterion for determining the upper and lower bounds of the minimum download time is:

[0040] t max -t min ≤ε (7)

[0041] Beneficial effects

[0042] 1. The satellite data download time minimization method based on cross-time slot scheduling disclosed in the present invention characterizes the channel and available energy impacts brought about by long-term satellite dynamics to consider the possible reduction in download time brought about by reserved energy. Compared with the download time minimization method that only maximizes the download rate per unit time, the feasible domain of the present invention is larger, thereby achieving more efficient download of in-orbit data under dynamic satellite channels and energy acquisition, thereby saving the time required to occupy the ground station for downloading data.

[0043] 2. The satellite data download time minimization method based on cross-time slot scheduling disclosed in the present invention does not involve inter-satellite data transmission, and thus has no requirements on whether the satellite payload is equipped with inter-satellite link-related components. Compared with the download time minimization method based on inter-satellite links, it is applicable to a wider range of low-orbit satellite application scenarios.

[0044] 3. The satellite data download time minimization method based on cross-time slot scheduling disclosed in the present invention adopts a generalized Benders decomposition and cyclic water filling method to solve the satellite download throughput maximization problem. Compared with the traditional branch-and-bound based mixed integer nonlinear programming problem solving method, the problem is transformed into an integer linear programming problem and an iterative solution of a convex optimization problem, thereby obtaining the optimal download time slot selection and power allocation for each time slot with low complexity.

[0045] 4. The satellite data download time minimization method based on cross-time slot scheduling disclosed in the present invention iteratively updates the upper and lower bounds of the minimum download time in a binary search manner until convergence, thereby obtaining the minimum download time, and obtaining the download time slot selection that achieves the minimum download time and the energy allocation result of each time slot, thereby improving the utilization efficiency of satellite download time and energy, thereby reducing the time required to connect to the ground station for satellite data download, and realizing efficient download of in-orbit data under dynamic satellite channels and energy acquisition. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of an application scenario of the satellite data download time minimization method based on cross-time slot scheduling of the present invention;

[0047] Figure 2 Flowchart of the method for minimizing satellite data download time based on cross-time slot scheduling of the present invention;

[0048] Figure 3 This is a performance comparison diagram of the satellite data download time minimization method based on cross-time slot scheduling under different energy input conditions of the present invention; DETAILED DESCRIPTION

[0049] The present invention will be described in detail below with reference to the accompanying drawings and embodiments, and the technical problems solved by the technical solution of the present invention and its beneficial effects will be discussed. Figure 1 It should be noted that the described embodiments are intended to facilitate understanding of the present invention and do not limit the present invention in any way.

[0050] Example

[0051] This embodiment discusses the application of a satellite data download time minimization method based on cross-time slot scheduling in satellite data downloading. Figure 2 As shown, the specific implementation steps are as follows:

[0052] Step 1: When the satellite enters the ground station connection range, the amount of satellite data to be downloaded D = 17.7GB and the initial energy available for communication E0 = 4.04kW are sent to the ground station; the ground station estimates the satellite's communication time window t according to the satellite orbit. total =562.20s, and initialize the upper bound of the minimum download time t max =562.20s and lower bound t min = 0s, and the convergence error of the download time ε = 1 × 10 -3 .

[0053] Step 2: Divide the communication time window estimated in step 1 into N = 62 slots of length Δt = 9.07s, with each slot starting at t i =9.07(i-1)s time slot; and estimate the distance d between the satellite and the ground station in each time slot based on the satellite orbit and time slot segmentation i , whose values ​​are shown in Table 1, in order to facilitate further calculation of the channel conditions of each time slot, realize time slot scheduling of satellite energy, and improve the utilization rate of satellite energy resources.

[0054] Table 1 Average distance between satellite and ground station at different time slots

[0055]

[0056]

[0057] Step 3: For the satellite time slots divided in step 1, the energy obtained before each time slot must be greater than the energy used before each time slot, and the energy constraint under the satellite energy acquisition condition is established; based on the distance d between the satellite and the ground station obtained in step 2 i According to the Shannon formula and the relationship between satellite channel attenuation and the distance between the satellite and the ground station, the total throughput during the satellite transit and the power P of each time slot are established. i and time slot selection indicator variable y i The relationship between P i The value range of y is any positive number. i The value range is 0 or 1. i =1, it means the satellite uses the i-th time slot for downloading.

[0058] The energy constraint for the satellite to obtain energy is:

[0059]

[0060] In this embodiment, since the satellite is located in the shadow of the earth, the energy that the satellite can obtain for communication in each time slot is 0, that is, E i is the energy used by the satellite in the i-th time slot, which is equal to the power P of the i-th time slot i The relationship is

[0061] E i =30.2×P i

[0062] Among them, the energy loss caused by the power amplifier is η = 3.33;

[0063] The total throughput during the satellite transit period is related to the power P in each time slot i The slot selection indicator variable and the slot allocation y i The relationship between

[0064]

[0065] Where B = 100 MHz is the system bandwidth, G = 1.59 × 10 10 is the product of the gains of the transmitting and receiving antennas, N0 = 3.98 × 10 -21 is the power spectral density of the noise, L i is the average path loss between the satellite and the ground station in the i-th time slot, which is equal to the distance d between the satellite and the ground station in each time slot obtained in step 2. i The relationship is

[0066]

[0067] Wherein, f = 20 GHz is the carrier frequency used for data transmission;

[0068] Step 4: The energy constraint obtained in step 3 and the total occupied time slot are not greater than the mean of the upper and lower bounds of the minimum download time t mid =281.10s as the constraint condition, with y i and P i As a control variable, establish the minimum download time upper and lower bound mean t mid The satellite download throughput maximization problem as a maximum download time constraint.

[0069]

[0070] st(3),

[0071] y i Δt≤t mid ,i∈{1,…N}

[0072] 0≤P i ≤P max

[0073] y i ∈{0,1},i∈{1,…N}

[0074] P max =50W is the maximum transmission power of the satellite, (7a) constrains the total length of the allocated download time to not exceed the maximum download time limit, (7b) constrains the transmission power to not exceed the maximum value allowed by the satellite, and (7c) constrains the value range of the download time slot indicator variable.

[0075] Step 5: Calculate the mean of the upper and lower bounds of the minimum download time constructed in step 4. mid = 281.10s as the maximum download time limit, the satellite download throughput maximization problem is solved, and the minimum download time upper and lower bound mean t is obtained. mid = 281.10s as the maximum satellite download throughput D under the maximum download time limit max =61.1GB, and the corresponding time slot selection indicator variable y that can achieve the satellite download throughput is obtained i * And the power P of each time slot i * , whose values ​​are shown in Table 2 and Table 3 respectively. The joint allocation of multi-slot resources is used to improve the utilization efficiency of satellite download time and energy.

[0076] Table 2 Optimal time slot selection indicator variable y when the contact time with the ground station is limited to less than 281.10s i *

[0077]

[0078]

[0079] Table 3 Optimal power P for each time slot when the contact time with the ground station is limited to less than 281.10s i *

[0080]

[0081] Step 6: Convert the t obtained in step 5 mid = 281.10s as the maximum satellite download throughput D under the maximum download time limit max = 61.1GB and the satellite data volume D = 17.7GB that needs to be downloaded, it is determined that the data can be downloaded within t mid = Complete the download of all data within 281.10s. According to the judgment result D max ≥D uses the binary search method to update the upper bound of the minimum download time, that is, t max =t mid , and judge that the upper and lower bounds of the minimum download time are greater than the convergence error, that is, t max -t min ≤ε, return to step 4 and iterate until the upper and lower bounds of the minimum download time meet the preset iterative convergence criteria. Output the optimized minimum satellite data download time and the time slot selection and power of each time slot that can achieve the minimum data download time. That is, the satellite data download time is minimized based on cross-time slot scheduling, thereby reducing the time required for satellite data download to connect to the ground station, and realizing efficient on-orbit data download under dynamic satellite channels and energy acquisition.

[0082] Comparison of download time performance before and after joint allocation of time slot energy Figure 3 As shown in the figure, the simulation results are the average of 10 simulations with an average download data of 17.59G. When satellite energy is scarce, the satellite data download time minimization method based on cross-time slot scheduling can reduce the download time by 95%. When energy is sufficient, the proposed satellite data download time minimization method based on cross-time slot scheduling can also reduce the download time by an average of 1-2s, thereby improving the utilization efficiency of download time and energy, thereby reducing the time required to connect to the ground station for satellite data download and improving the utilization rate of the ground station.

[0083] The above specific description further illustrates the purpose and technical solution of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for minimizing satellite data download time based on cross-time slot scheduling, characterized by: The following steps are included: Step 1: When the satellite enters the connection range of the ground station, the amount of satellite data D to be downloaded and the initial energy available for communication E0 are sent to the ground station. The amount of satellite data D to be downloaded and the initial energy available for communication E0 are any positive numbers; the ground station estimates the satellite's communication time window t according to the satellite orbit. total ; and initialize the upper bound of the minimum download time t max and the lower bound t min , and the convergence error ε of the download time; Step 2: Divide the communication time window estimated in step 1 into N time slots of length Δt, with each time slot starting at t i time slot; and estimate the distance d between the satellite and the ground station in each time slot based on the satellite orbit and time slot segmentation i , in order to facilitate further calculation of the channel conditions of each time slot, realize time slot scheduling of satellite energy, and improve the utilization rate of satellite energy resources; Step 3: For the satellite time slots divided in step 1, the energy obtained before each time slot must be greater than the energy used before each time slot, and the energy constraint under the satellite energy acquisition condition is established; based on the distance d between the satellite and the ground station obtained in step 2 i According to the Shannon formula and the relationship between satellite channel attenuation and the distance between the satellite and the ground station, the total throughput during the satellite transit and the power P of each time slot are established. i and time slot selection indicator variable y i The relationship between P i The value range of y is any positive number. i The value range is 0 or 1. i =1 means the satellite uses the i-th time slot for downloading; Step 4: The energy constraint obtained in step 3 and the total occupied time slot are not greater than the mean of the upper and lower bounds of the minimum download time t mid As a constraint, y i and P i As a control variable, establish the minimum download time upper and lower bound mean t mid The problem of maximizing satellite download throughput as a maximum download time constraint; Step 5: Calculate the mean of the upper and lower bounds of the minimum download time constructed in step 4. mid The satellite download throughput maximization problem with the maximum download time limit is solved to obtain the minimum download time upper and lower bound mean t mid As the maximum satellite download throughput D under the maximum download time constraint max , and the corresponding time slot selection indicator variable y that can achieve the satellite download throughput is obtained i * And the power P of each time slot i * ,Using the joint allocation of multi-slot resources, the time and energy efficiency of satellite downloading is improved; Step 6: Convert the t obtained in step 5 mid As the maximum satellite download throughput D under the maximum download time constraint max Compare it with the amount of satellite data D that needs to be downloaded to determine whether it can be downloaded within the value t mid The download of all data is completed within 10 seconds; based on the judgment result, the binary search method is used to update the upper and lower bounds of the minimum download time, and it is judged whether the upper and lower bounds of the minimum download time are less than the convergence error. If they are greater than the convergence error, the process returns to step 4 for iteration. If the upper and lower bounds of the minimum download time meet the preset iterative convergence criteria, the optimized minimum satellite data download time and the time slot selection and power of each time slot that can achieve the minimum data download time are output. That is, the satellite data download time is minimized based on cross-time slot scheduling, thereby reducing the time required for satellite data download to connect to the ground station, and realizing efficient download of on-orbit data under dynamic satellite channels and energy acquisition.

2. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 1, wherein: In step one, The initialization method of the upper and lower bounds of the minimum download time is 3. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 2, wherein: In step 2, The time slot length Δt and the time slot start time t i The value of 4. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 3, wherein: In step three, The energy constraint for the satellite to obtain energy is: in, E is the energy that the satellite can obtain for communication in the i-th time slot, which is obtained according to the satellite's operating status, parameter design, and its relative position to the sun and the earth; i is the energy used by the satellite in the i-th time slot, which is equal to the power P of the i-th time slot i The relationship is E i =ηΔtP i (4) Where η represents the energy loss caused by the power amplifier and is a constant greater than 1; The total throughput during the satellite transit period is related to the power P in each time slot i The slot selection indicator variable and the slot allocation y i The relationship between Where B is the system bandwidth, G is the product of the gains of the transmitting and receiving antennas, N0 is the power spectral density of the noise, and L i is the average path loss between the satellite and the ground station in the i-th time slot, which is equal to the distance d between the satellite and the ground station in each time slot obtained in step 2. i The relationship is Where f is the carrier frequency used for data transmission.

5. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 4, characterized in that: In step four, The minimum download time upper and lower bound mean t mid The satellite download throughput maximization problem with the maximum download time constraint is st(3), y i Δt≤t mid ,i∈{1,…N} (7a) 0≤P i ≤P max (7b) the i ∈{0,1},i∈{1,…N} (7c) Among them, the mean of the upper and lower bounds of the minimum download time t mid The value of P max is the maximum transmission power of the satellite, (7a) constrains the total length of the allocated download time to not exceed the maximum download time limit, (7b) constrains the transmission power to not exceed the maximum value allowed by the satellite, and (7c) constrains the value range of the download time slot indicator variable.

6. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 5, characterized in that: In step four, The satellite download throughput maximization problem is solved by using the generalized Benders decomposition and cyclic water injection method, and the minimum time upper and lower bound mean t is obtained. mid The maximum download throughput of the satellite as a limit on the maximum download time.

7. The method for minimizing satellite data download time based on cross-time slot scheduling according to claim 6, characterized in that: In step six, The updating method of updating the upper and lower bounds of the minimum download time by using the binary search method according to the judgment result is as follows: if the satellite download throughput is greater than or equal to the amount of satellite data to be downloaded, that is, D max ≥D, then let the upper bound of the minimum download time be equal to the mean of the upper and lower bounds of the current minimum download time, that is, t max =t mid Otherwise, if the satellite download throughput is less than the amount of satellite data that needs to be downloaded, that is, D max <D, then let the lower bound of the minimum download time be equal to the mean of the upper and lower bounds of the current minimum download time, that is, t min =t mid ; The preset iterative convergence criterion for determining the upper and lower bounds of the minimum download time is: t max -t min ≤ε (7)。

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