CN114609589B - Heuristic backtracking-based real-time phased array radar beam residence scheduling method - Google Patents
Heuristic backtracking-based real-time phased array radar beam residence scheduling method Download PDFInfo
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Abstract
The invention belongs to the field of radar system resource management, and particularly relates to a novel phased array radar real-time self-adaptive residence scheduling method. The invention firstly determines the actual execution task queue, the delay task queue and the deletion task queue in the scheduling interval through the time pointer, ensures the importance and urgency criterion in the beam resident scheduling, and then adjusts the actual execution time of the tasks in the actual execution task queue by a heuristic backtracking method, thereby reducing the offset between the actual execution time of each task and the expected execution time thereof and ensuring the expected execution time criterion in the beam resident scheduling. In addition, the real-time performance of the method is ensured by dividing the actual execution task queue and then carrying out backtracking processing.
Description
Technical Field
The invention belongs to the field of radar system resource management, and particularly relates to a self-adaptive residence scheduling method of a phased array radar.
Background
Since the transmit beam direction of the phased array radar (phased array radar, PAR) can be changed rapidly in a short time, the phased array radar can perform different types of tasks during its operating time to achieve a multi-functional characteristic. In order to realize reasonable allocation of limited system resources among multiple tasks, a high-efficiency beam resident scheduling method with real-time performance needs to be designed.
In recent years, beam-resident scheduling methods, particularly adaptive beam-resident scheduling methods that can match task requests that are time-varying in an online scheduling process, have been widely studied. According to the method for solving the resident scheduling optimization problem, the adaptive beam resident scheduling method can be divided into a beam resident scheduling method based on heuristic rules and a beam resident scheduling method based on intelligent optimization algorithm (see literature: zhang, h., xie, j., ge j., et al: A hybrid adaptively genetic algorithm for task scheduling problem in the phased array radar', european Journal of Operational Research,2019,272, (3), pp.868-878)
The beam resident scheduling method based on the heuristic rule adopts the heuristic rule to solve the beam resident scheduling problem. Literature (Orman, a.j., potts, c.n., shahani, a.k., et al, 'Scheduling for a multifunction phased array radar system', european Journal ofOperational Research,1996,90, (1), pp.13-25) uses the work mode priority of the resident tasks as a scheduling criterion and designs a corresponding scheduling method in a heuristic rule. The literature (Haritsa, J.R., livny, M., carey, M.J.: earliest deadline scheduling for real-time database systems', proceedings Twelfth Real-Time Systems Symposium, san Antonio, TX, USA, december 1991, pp.232-242) schedules tasks in a first-in-first-out (First in First out, FIFO) manner with the deadline of the resident task as the scheduling criteria for the same task. Literature (Lu Jian, hu Weidong, yu Wenxian): multifunctional phased array radar real-time task scheduling study', e-newspaper, 2006,34, (4), pp.732-736) sets a comprehensive priority based on working mode priority and task deadline, and obtains a scheduling task sequence by introducing a time pointer during scheduling analysis. The threat level of the target is further taken into account in the setting of the integrated priority in the literature (Zhang, h., xie, j., zong, b., et al, 'Dynamic priority scheduling method for the air-defence phased array radar', IETRadar Sonar & Navigation,2017,11, (7), pp. 1140-1146). The scheduling method proposed by the above document has the characteristics of high time utilization rate and good real-time performance, but fails to consider the expected execution time criterion, which requires that the actual execution time of the resident task should be as close as possible to the expected execution time of the task. (see documents: zeng Guang, hu Weidong, lu Jian, zhou Wenhui: multifunctional phased array radar adaptive scheduling simulation ', system simulation theory, 2004,16, (9), pp. 2026-2029) based on this problem, documents (Cheng, t., he, z., tang, t.: ' Dwell scheduling algorithm for multifunctionphased array radars based on the scheduling gain ', journal ofSystems Engineering and Electronics,2008,19, (03), pp. 479-485) propose a beam dwell scheduling method based on scheduling interval analysis. The method sorts the tasks according to the task scheduling gain, and distributes actual execution time for each resident task in turn according to the expected time criterion. The method can effectively consider the requirement execution time criterion, but has the problems of low time utilization rate, poor real-time performance and the like.
In order to solve the problem that the beam resident scheduling method based on the heuristic method cannot simultaneously consider the system time utilization rate and the expected time criterion, a series of beam resident scheduling methods based on the intelligent optimization algorithm are provided. The method establishes the beam resident scheduling problem as an optimization problem, and introduces a series of optimization algorithms according to the characteristics of the optimization problem to obtain an optimal actual execution task sequence and the execution time of the actual execution task. Literature (L, hao, X, yang, S, hu.: 'Task scheduling of improved time shifting based on genetic algorithm for phased array radar',2016IEEE 13th International Conference on Signal Processing (ICSP), chengdu, china, november 2016, pp. 1655-1660) designs fitness functions based on importance of tasks, urgency and desired execution time criteria, and uses genetic algorithms to obtain optimal actual execution task queues. Literature (Yang, s., tian, k., liu, r.: task SchedulingAlgorithm Based on Value Optimization forAnti-missile PhasedArray Radar', IET Radar Sonar & Navigation,2019,13, (11), pp.1883-1889.) has designed fitness functions based on specific characteristics of the reverse Radar scheduling problem, which is also solved by genetic algorithms. The literature (Meng, f., tian, k., 'Phased-Array Radar Task Scheduling Method for Hypersonic-Glide Vehicles', IEEE Access,2020,8, pp. 221288-221298) adopts a particle swarm-simulated annealing hybrid algorithm to solve the beam dwell scheduling problem under supersonic target tracking tasks. Literature (shaghi, m., add, r.s., zhen, d.: multifunction Cognitive Radar Task Scheduling Using Monte Carlo Tree Search and Policy Networks', IET Radar Sonar & Navigation,2018,12, (12), pp.1437-1447) designed an objective function of the multi-functional cognitive Radar scheduling problem according to task urgency and desired time criteria, and obtained an optimal actual execution task sequence and actual execution time thereof by using a monte carlo search tree optimization method. The literature (Xu, l., zhang, t.: reinforcement Learning based Dynamic Task Scheduling for Multifunction Radar Network', IEEE Radar Conference, florence, italy 2020, pp.1-5) addresses this problem with minimum loss rate of tasks as an objective function and with reinforcement learning methods. However, the beam resident scheduling method based on the optimization algorithm has poor real-time performance, so that the method cannot be used in actual radar beam resident scheduling.
Based on the problems, the invention provides a real-time phased array radar beam residence scheduling method based on heuristic backtracking. The method first employs a scheduling method in literature (Lu Jian, hu Weidong, yu Wenxian: multifunctional phased array radar real-time task scheduling study', e-newspaper, 2006,34, (4), pp. 732-736) to determine actual execution tasks, delay tasks, and missing tasks within the current scheduling interval. Then, the method traverses all feasible execution sequences of the actual execution tasks, and backtrack optimizes the actual execution time of the tasks corresponding to each possible execution sequence so as to consider the expected execution time criterion. Finally, the method calculates the time offset of all the feasible task execution sequences, and selects the scheduling sequence corresponding to the task execution sequence with the minimum time offset as the optimized scheduling sequence. In addition, the method carries out blocking processing on the scheduling task sequence in the current scheduling interval, thereby reducing the computational complexity of the method. Simulation results show that compared with the existing method, the method can give consideration to priority, deadline and expected execution time criteria, and can realize real-time beam resident scheduling.
Disclosure of Invention
The invention provides a novel beam resident scheduling method based on heuristic backtracking, which is characterized by comprising the following steps of:
assume that at the current scheduling interval t 0 ,t 0 +t SI ]There are N resident tasks t= [ T ] 1 ,T 2 ,...,T N ]Application scheduling, where t 0 T is the starting time of the current scheduling interval SI For the duration of the scheduling interval, the resident task model is T i ＝{W i ,rt i ,st i ,l i ,dw i W, where i For job priority, rt i To expect execution time, st i For the actual execution time, l i For time window dw i Is the residence time period. The phased array radar beam residence scheduling method based on heuristic backtracking comprises the following steps:
step 1: initialization time pointer tp=t 0 Initializing an actual execution task queue T in the scheduling interval ex Delay task queue T dl Delete task queue T dr Is empty.
Step 2: deleting the application scheduling task satisfying the formula (1) in T and adding the application scheduling task to T dr Is a kind of medium.
rt i +l i ＜tp (1)
Step 3: selecting all tasks satisfying the formula (2) from the T, and generating a current time schedulable task set T cd ＝T cd,1 ,T cd,2 ,...,T cd,Q Wherein Q is T cd The number of internal tasks.
Calculating the comprehensive priority p corresponding to each task according to the formula (3) i Wherein Np i Is T cd Sequencing serial numbers of middle tasks from big to small according to working mode priority, nd i Is T cd The middle tasks are sequenced according to the task deadline from small to large.
Step 4: from T cd Selecting the highest composite priorityTask of (1)>Delete it from T and add it to T ex Is a kind of medium.
Step 5: update tp=tp+dw i . If tp>t 0 +t SI Or T is null, let T dl =t, and go to step 6; otherwise, the process returns to the step 2.
Step 6: assume thatThe number of tasks in the system is N 1 Will T ex Is divided into->Sub-execution task queue T l ,l＝1,2,...,N 1 K, each sub-execution task queue containing at most K tasks, wherein the symbol +.>Representing an upward rounding. First sub-execution task queue T 1 ＝[T 1 ,T 2 ,...,T K ]The second sub-execution task queue T 2 ＝[T K+1 ,T K+2 ,...,T 2K ]And so on, the first sub-execution task queue T l ＝[T (l-1)K+1 ,T (l-1)K+2 ,...,T lK ]. Each sub-execution task queue T l Corresponds to a sub-scheduling interval t a,l ,t b,l ]Wherein t is a,l And t b,l The calculation method of (2) is as follows:
step 7: traversing sub-execution teamsAll possible execution orders of execution tasks in the column. By T l For example, define T l The j-th execution sequence of (C) is [ T ] (l-1)K+1,j ,T (l-1)K+2,j ,...,T (l-1)K+i,j ,....,T lK,j ]J=1, 2,..k-! . For example T (l-1)K+i,j For sub-execution queue T l The j-th task in the execution order. The actual execution time is allocated to the execution task under each execution sequence of each sub-execution task queue according to the following formula:
the actual execution time of the allocation is then determined according to the following equation:
if the condition is satisfied, the execution sequence is a feasible execution sequence, and the actual execution time of the corresponding task under the execution sequence is obtained, otherwise, the permutation and combination is an infeasible execution sequence.
Step 8: and backtracking the actual execution time of the actual execution task in all the sub-execution task queues according to all the feasible execution sequences. In execution order T 1 ＝[T 1 ,T 2 ,...,T K ]For example, specific backtracking steps are as follows:
step 8.1: and carrying out backtracking processing on the tasks sequentially from short to long according to the time window length. Assume that the current task to be backtraced is T i The expected execution time is rt i The actual execution time is st i . If st i -rt i > 0, go to step 8.2; if st i -rt i < 0, go to step 8.4; if st i -rt i =0, jump to step 8.6.
Step 8.2: by T i As a starting point, the first task that has been traced back is found forward. Assuming that the task is T j Definition t end ＝st j +dw j The method comprises the steps of carrying out a first treatment on the surface of the If T i Tasks not previously traced back, t end ＝t a,1 . If at [ t ] end ,st i ]In total P tasks [ T ] P,1 ,T P,2 ,...,T P,P ]Optimizing T according to i Is the actual execution time of (a):
if at [ t ] end ,st i ]None of them, optimize T according to i Is the actual execution time of (a):
st i ＝max(t end ,rt i ) (9)
step 8.3: update according to the following [ T ] P,1 ,T P,2 ,...,T P,P ]Is the actual execution time of (a):
and goes to step 8.6.
Step 8.4: by T i As a starting point, the first task that has been traced back is found back. Assuming that the task is T j Definition t end ＝st j . If T i Tasks not followed by backtracking, t end ＝t b,1 . If at [ st ] i ,t end ]In total P tasks [ T ] P,1 ,T P,2 ,...,T P,P ]Optimizing T according to i Is the actual execution time of (a):
if at [ st ] i ,t end ]None of them, optimize T according to i Is the actual execution time of (a):
st i ＝min(t end -dw i ,rt i ) (12)
step (a)8.5: update according to the following [ T ] P,1 ,T P,2 ,...,T P,P ]Is the actual execution time of (a):
step 8.6: record task T i Backtracking has been completed. If all tasks have completed backtracking, go to step 9, otherwise go to step 8.1.
Step 9: and calculating the time offset degree of each sub-execution task queue under all feasible execution sequences. By T 1 The order result in the j-th order is exemplified by the time offset bias j The calculation formula is as follows:
wherein b i,j The calculation formula is as follows:
and selecting the task execution time corresponding to the task execution sequence with the lowest time offset from the sub-execution queues as the actual execution time of the task, and integrating all the sub-execution queues to acquire an actual execution task queue again. And (5) finishing the analysis of the scheduling process.
Principle of the invention
The invention ensures the importance criterion and the urgency criterion of the dispatch when determining the actual execution task, delaying the task and deleting the task, and ensures the expected execution time criterion of the dispatch by backtracking the actual execution time of the actual execution task. The principle thereof will be explained below.
Assume that there are N task applications scheduled in this scheduling interval, denoted t= [ T ] 1 ,T 2 ,...,T N ]. When scheduling, importance criteria and urgency criteria respectively require tasks with high working mode priority and early deadlinesTasks should be performed as much as possible. Equation (3) embodies the two criteria described above. The desired execution time criteria requires that the actual execution time of the actual execution task should be as close as possible to the desired execution time. Equation (14) embodies this criterion. Since the search task does not include the desired execution time, the search task b is searched in the formula (15) i Is 0.
According to the three criteria of the scheduling, the objective function of the beam resident scheduling problem is established as follows
G i (st i ,rt i ,l i ,w i ,t 0 )＝g 1 (w i )g 2 (rt i ,l i ,t 0 )g 3 (st i ,rt i ,l i ) (16)
Wherein g 1 (w i )＝w i Due to g 1 (w i ) As the priority of the task work mode increases, the priority increases, so that the importance criterion of scheduling is embodied;wherein c 1 Is a positive constant due to g 2 (rt i ,l i ,t 0 ) Increasing with decreasing deadlines for tasks, so this term embodies the urgency criterion of scheduling;wherein c 2 Is a positive constant due to g 3 (st i ,rt i ,l i ) The value of (c) decreases with increasing deviation between the actual execution time and the desired execution time, so this term embodies the scheduled desired execution time criterion. Comprehensively considering an objective function and constraint conditions in the beam resident scheduling problem, and establishing a mathematical model of the beam resident scheduling problem as follows:
wherein N is 2 And N 3 Number and deletion of tasks respectivelyThe number of transactions, obviously n=n 1 +N 2 +N 3 . In the optimization model, the last two inequalities reflect the conditions that the deferred task and the delete task should meet.
The invention adopts a heuristic backtracking-based method to solve the optimization problem, and the specific analysis method is as follows:
in the scheduling process, in order to maximize the time utilization rate and schedule as many tasks with high priority as possible, the invention adopts a beam resident scheduling method based on a time pointer to confirm the actually executed tasks in the scheduling interval, and delays the tasks and deletes the tasks. The present invention then considers backtracking optimizing the actual execution time of each task to minimize the deviation of the desired execution time from it. According to the invention, all possible task execution sequences are traversed at first, and screened, and infeasible task execution sequences are removed so as to ensure that actual execution moments which do not meet constraint conditions cannot appear in the subsequent backtracking process. And then backtracking the actual execution time of the task. From g 3 (st i ,rt i ,l i ) As can be seen from the expression of (a), at the time offset |rt i -st i When the values of l are the same, time window l i G corresponding to smaller task 3 (st i ,rt i ,l i ) Smaller, so the invention firstly backtracks the task with shorter time window. As shown in fig. 1, assume T k Time window of (1) is minimum, T i Second, T j The method is first to T k Backtracking is performed to realize the actual execution time st k As close as possible to its desired execution instant rt k . Subsequently the method is applied to T i Backtracking is performed to realize the actual execution time st i As close as possible to its desired execution instant rt i . At adjustment st i At the time of preventing T i And T is j Overlapping of residence times, T j Actual execution time st of j Should be adjusted accordingly. When T is j Adjust to T k Execution completion time, T i Adjust to T j When the execution is completed, T is because the previous backtracking result cannot be changed i Is completed. When (when)T i And T is k After backtracking is completed, T j The actual execution time of (a) cannot be further adjusted, so the method considers that the backtracking process is completed. In addition, step 6 reduces the computational complexity of the method by performing a blocking process on the actual execution task queue.
Drawings
FIG. 1 is a schematic diagram of a backtracking process
FIG. 2 is TDR for four methods;
FIG. 3 is an HVR of four methods;
FIG. 4 is TUR for four methods;
fig. 5 is an ATSR for four methods.
FIG. 6 is a run length of four methods
FIG. 7 is a run length of method A and the inventive method
Detailed Description
TABLE 1 radar beam dwell task parameter table
Five tasks of verification, precise tracking, common tracking, horizon searching and airspace searching are considered in the simulation scene. The simulation time length is 12s, the scheduling interval time length is set to be 50ms, the ratio of the number of precision tracking targets to the number of common tasks targets is 1:4, and K in the step 6 is set to be 5. The radar task parameters are shown in table 1.
In order to comprehensively evaluate the performance of the invention, the section adopts a task loss rate (TDR), an implementation Value rate (HVR), a Time utilization rate (Time Utilization Ratio), an Average Time offset rate (Average Time ShiftingRatio, ATSR) and a running duration as performance evaluation indexes. The above index is defined as follows:
the task loss rate (TDR) is the ratio of the number of lost tasks to the number of scheduled tasks applied in the simulation duration:
TDR＝N drop /N total (18)
wherein N is drop Indicating the number of lost tasks, N total Indicating the number of tasks to be scheduled；
The realization value rate (HVR) is the ratio of the sum of the working mode priorities of the actual execution tasks and the sum of the working mode priorities of the application scheduling tasks in the simulation time length:
wherein N is exe Indicating the number of tasks actually performed. The index is used for reflecting the proportion of successfully scheduled high-priority tasks;
time Utilization (TUR): the ratio of the sum of the actual execution task residence time to the total simulation time is defined as:
wherein t is total Is the total simulation duration.
Average time offset (ATSR): reflecting the average offset rate between the actual execution time and the expected execution time of all the tracking tasks:
wherein N is tra Indicating the number of tracking tasks actually performed.
Duration of operation: the run length within one scheduling interval.
The heuristic backtracking-based real-time phased array radar beam resident scheduling method is adopted to carry out beam resident scheduling, and performance comparison is carried out between the method A, the method B and the method C. Wherein method A is a phased array radar beam-resident scheduling method based on a time pointer (see documents: lu Jian, hu Weidong, yu Wenxian: multifunctional phased array radar real-time task scheduling research ', electronic report, 2006,34, (4), pp.732-736), method B is a phased array radar beam-resident scheduling method based on scheduling interval analysis (see documents: cheng, T., he, Z., tang, T: dwell scheduling algorithm for multifunctionphased array radars based on the scheduling gain ', journal of Systems Engineering and Electronics,2008,19, (03), pp.479-485), and method C is a phased array radar beam-resident scheduling method based on a genetic algorithm (see documents: L, hao., X, yang, S, hu.: task scheduling of improved time shifting based on genetic algorithm for phased array radar ',2016IEEE 13th International Conference on Signal Processing (ICSP), chengdu, china, november 2016, pp.1655-1660). The simulation platform is MATLAB R2016a, the computer processor is Core i7-10700, and the memory is 16G. Fig. 2 to 6 show statistics of 100 monte carlo at different indices.
Fig. 2 is a task loss rate curve. When the target number is raised to 30, method C begins to appear task loss first. This is because the method C performs scheduling using the idea of allocating an actual execution time closest to the desired execution time to each task, which inevitably results in an underutilized time slot within the scheduling interval, and thus the scheduling sequence obtained by the method C has the highest task loss rate. Compared with the method C, the method B adopts a genetic algorithm to directly optimize the actual execution time of each task, has relatively low task loss rate, but still cannot thoroughly eliminate the time gap in the scheduling interval. The method A introduces the time pointer to schedule, so that the tasks in the scheduling interval can be closely arranged, and therefore, the method A has the lowest task loss rate. The invention adjusts the actual execution time of the task only on the basis of the actual execution task queue obtained by the method A, and does not change the scheduled task. Therefore, the task loss rate obtained by the method is completely consistent with that of the method A.
Fig. 3 is a graph showing the implementation of a value rate curve that reflects whether tasks with higher priority of the operating mode are performed as much as possible. The realization value rate curve obtained by the four methods and the task loss rate curve trend in opposite directions can be seen, namely, when the task loss rate is higher, the realization value rate is lower.
Fig. 4 is a time utilization curve. When the target number is small, the time utilization rate curve is linearly increased along with the increase of the target number; when the number of targets is increased to a certain degree, task loss occurs, and the time utilization rate of the system tends to be saturated. The method A and the method provided by the invention have the maximum time utilization rate.
Fig. 5 is an average time offset rate curve. It can be seen that the time offset rate of method a is higher, while the time offset rates of method B and method C are lower. This is because both method B and method C consider the desired time criteria when scheduling, while method a does not consider the desired time criteria when scheduling. Compared with the time offset rate obtained by the method A, the method provided by the invention has the advantages that the feasible task actual execution time is obtained by traversing all execution task sequences, and the feasible actual execution time is further backtracking optimized, so that the time offset rate is greatly reduced.
Fig. 6 shows the operating times of the four methods. The genetic algorithm needs to be repeated for a plurality of times to calculate the fitness function of a large number of individuals, so that the operation amount of the method C is maximum and the operation time is longest; method B has a run time that is better than method C, but worse than the present invention release and method a. It can be seen that the operation time of both method B and method C exceeds one scheduling interval time (50 ms), so that both methods have no real-time performance.
Fig. 7 shows the operation time of method a and the inventive method. It can be seen that method a has the lowest run length. Because the method of the invention adds the step of backtracking on the basis of the method A, the method of the invention has longer operation time compared with the method A. However, the operation time length of the method is far less than the scheduling interval time length (50 ms), so that the method and the method A have real-time performance.
In summary, compared with the scheduling method based on the time pointer, the scheduling method provided by the invention can give consideration to the time offset rate of the task under the condition of realizing completely consistent task loss rate and realization value rate; compared with a scheduling method based on scheduling interval analysis and a genetic algorithm, the method has lower task loss rate and higher realization value rate, and the method ensures the real-time performance of scheduling analysis. The invention relates to a real-time beam resident scheduling algorithm which simultaneously considers priority, deadline and expected execution time criteria.
Claims (1)
1. A novel beam resident scheduling method based on heuristic backtracking is characterized by comprising the following steps:
assume that at the current scheduling interval t 0 ，t 0 +t SI ]There are N resident tasks t= [ T ] 1 ，T 2 ，...，T N ]Application scheduling, where t 0 T is the starting time of the current scheduling interval SI For the duration of the scheduling interval, the resident task model is T i ＝{W i ，rt i ，st i ，l i ，dw i W, where i For job priority, rt i To expect execution time, st i For the actual execution time, l i For time window dw i Is the residence time length; the phased array radar beam residence scheduling method based on heuristic backtracking comprises the following steps:
step l: initialization time pointer tp=t 0 Initializing an actual execution task queue T in the scheduling interval ex Delay task queue T dl Delete task queue T dr Is empty;
step 2: deleting the application scheduling task satisfying the formula (1) in T and adding the application scheduling task to T dr In (a) and (b);
rt i +l i ＜tp (1)
step 3: selecting all tasks satisfying the formula (2) from the T, and generating a current time schedulable task set T cd ＝[T cd，1 ，T cd，2 ，...，T cd，Q ]Wherein Q is T cd The number of internal tasks;
calculating the comprehensive priority p corresponding to each task according to the formula (3) i Wherein Np i Is T cd Sequencing serial numbers of middle tasks from big to small according to working mode priority, nd i Is T cd Sequencing the middle tasks according to the sequence number from small to large of the task deadline;
step 4: from T cd Selecting the highest composite priorityTask T of (1) i * Delete it from T and add it to T ex In (a) and (b);
step 5: update tp=tp+dw i The method comprises the steps of carrying out a first treatment on the surface of the If tp > t 0 +t SI Or T is null, let T dl =t, and go to step 6; otherwise, turning back to the step 2;
step 6: assume thatThe number of tasks in the system is N 1 Will T ex Is divided into->Sub-execution task queueEach sub-execution task queue contains K tasks at most, wherein the symbol +.>Represents rounding up; first sub-execution task queue T 1 ＝[T 1 ，T 2 ，...，T K ]The second sub-execution task queue T 2 ＝[T K+1 ，T K+2 ，...，T 2K ]And so on, the first sub-execution task queue T l ＝[T (l-1)K+1 ，T (l-1)K+2 ，...，T lK ]The method comprises the steps of carrying out a first treatment on the surface of the Each sub-execution task queue T l Corresponds to a sub-scheduling interval t a，l ，t b，l ]Wherein t is a，l And t b，l The calculation method of (2) is as follows:
step 7: traversing sub-execution queue T l All possible execution orders of the execution tasks; definition T l The j-th execution sequence of (C) is [ T ] (l-1)K+1，j ，T (l-1)K+2，j ，...，T (l-1)K+i，j ，....，T lK，j ]J=1, 2,..k-! Wherein T is (l-1)K+i，j For sub-execution queue T l An ith task in the jth execution order; the actual execution time is allocated to the execution task under each execution sequence of each sub-execution task queue according to the following formula:
the actual execution time of the allocation is then determined according to the following equation:
if the condition is satisfied, the execution sequence is a feasible execution sequence, and the actual execution time of the corresponding task under the execution sequence is obtained, otherwise, the execution sequence is an infeasible execution sequence;
step 8: t in the queue of all sub-execution tasks according to all feasible execution sequences l The actual execution time of the actual execution task is traced back, and the specific tracing step is as follows:
step 8.1: sequentially carrying out backtracking processing on the tasks from short to long according to the time window length; assume that the current task to be backtraced is T i The expected execution time is rt i The actual execution time is st i The method comprises the steps of carrying out a first treatment on the surface of the If st i -rt i > 0, go to step 8.2; if st i -rt i < 0, go to step 8.4; if st i -rt i =0, jump to step 8.6;
step 8.2: by T i As a starting point, the first task which is traced back is found forward; assuming that the task is T j Definition t end ＝st j +dw j The method comprises the steps of carrying out a first treatment on the surface of the If T i Tasks not previously traced back, t end ＝t a，1 The method comprises the steps of carrying out a first treatment on the surface of the If at [ t ] end ，st i ]In total P tasks [ T ] P，1 ，T P，2 ，...，T P，P ]Optimizing T according to i Is the actual execution time of (a):
if at [ t ] end ，st i ]None of them, optimize T according to i Is the actual execution time of (a):
st i ＝max(t end ，rt i ) (9)
step 8.3: update according to the following [ T ] P，1 ，T P，2 ，...，T P，P ]Is the actual execution time of (a):
and go to step 8.6;
step 8.4: by T i As a starting point, finding the first traced task backwards; assuming that the task is T j Definition t end ＝st j The method comprises the steps of carrying out a first treatment on the surface of the If T i Tasks not followed by backtracking, t end ＝t b，1 The method comprises the steps of carrying out a first treatment on the surface of the If at [ st ] i ，t end ]In total P tasks [ T ] P，1 ，T P，2 ，...，T P，P ]Optimizing T according to i Is the actual execution time of (a):
if at [ st ] i ，t end ]None of them, optimize T according to i Is the actual execution time of (a):
st i ＝min(t end -dw i ，rt i ) (12)
step 8.5: update according to the following [ T ] P，1 ，T P，2 ，...，T P，P ]Is the actual execution time of (a):
step 8.6: record task T i Backtracking has been completed; if all tasks have completed backtracking, turning to step 9, otherwise turning to step 8.1;
step 9: calculate each sub-execution task queue T l Time offset under all feasible execution orders; definition T l In j-th execution order [ T ] (l-1)K+1，j ，T (l-1)K+2，j ，...，T (l-1)K+i，j ，....，T lK，j ]Is (b) the time offset bias of (b) j The calculation formula is as follows:
wherein b (l-1)K+i，j The calculation formula is as follows:
can be according to T (l-1)K+i，j Work mode priority W of (2) (l-1)K+i，j The value of the task is judged to be a searching task or a tracking task; selecting task execution corresponding to task execution sequence with lowest time offset from sub-execution queueThe time is taken as the actual execution time of the task, and all sub-execution queues are integrated to acquire an actual execution task queue again; and (5) finishing the analysis of the scheduling process.
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