# Generating Datasets for Real-Time Scheduling on 5G New Radio
## 6 Evaluation
### Solving Scheduling Problems
#### 6.2.1 Performance Comparison  
We compare the three methods under \(<\)[\(20,30\)], \(4\), \(2\), \(7\), \(40\)\(>\) and modify these parameters in turn to evaluate our method across as many system configurations as possible. Based on our experience, setting \(T\) to \(2\) allows our SMT method to obtain solutions for the majority of scheduling problems. In the following subsection, we will discuss the impact of different values of \(T\) on the solutions. Figure 7 is the comparison of the solution time and satisfiable ratio of the three methods. _Satisfiable ratio_ is the percentage of scheduling problems for which a method can find an optimal solution. For each column, \(10\),\(000\) scheduling problems are generated by Umifast. In Figure 7a, the solution time increases with the number of packets. In the first four columns, OMT is better than OMT_original because OMT introduces fewer variables and significantly reduces the search space; SMT has the best solution time because the determination of the objective value simplifies the search for solutions. In the last two columns, OMT and OMT_original can only find solutions for simple problems under the time limitation, whereas SMT can solve more complicated problems. Thus, the solution time of SMT is higher than the others. This is also shown in the last two columns of Figure 7b, in which the satisfiable ratios of OMT and OMT_original significantly decrease. These two  
Figure 6: Distribution of scheduling problems. methods can no longer solve the problems that SMT needs to consume a lot of time to solve. In Figure 8, we plot the distribution of the objective values of SMT and OMT under \(<\)30, 4, 2, 7, 40\(>\). The objective values of OMT are all zero. In an acceptable time, OMT cannot solve any problems with covering, whereas SMT can still solve complicated problems to make solutions show diversity. We run 16 Z3 threads on our workstation to solve 10,000 problems under parameter \(<\)30, 4, 2, 7, 40\(>\). OMT_original takes 3.92 days, whereas OMT and SMT take 1.36 days and 0.99 days, respectively. Compared to OMT_original, SMT reduces the solution time by 74.7%. In Figure 9, we change the time limitation \(T\) to 10. Although there is a slight difference between Figures 7 and 9, the difference is more due to the randomness of Umifast. The added time has little effect on searching solutions. Since the solution time of solvers grows exponentially with the problem's complexity, for such scheduling problems, the added time is not enough to solve more complicated problems. Therefore, in our evaluation, the time limitation of 2 can effectively avoid time consumption. In Figure 10, we increase the maximum number of transmissions from 4 to 5. Since packets require more resources, it is more difficult to place them in \(L\times P\). Hence, the satisfiable ratios of all methods are reduced. OMT and OMT_original cannot find any solutions when the number of packets is large. Although the solution time of SMT increases, it can still maintain the satisfiable ratio of 34% when the other methods fail to solve problems. Figure 11 changes the frequency bandwidth from 7 to 10, and at the same time increases the number of packets to 40 to use these increased resources. As the number of packets increases, the solution time increases and the satisfiable ratio decreases. OMT and OMT_original consume a lot of time and can only solve a small amount of scheduling problems. The time growth trend of SMT is slower than those of the other methods. Compared to Figures 7 and 11 increases resources by 42.9%, but reduces the solution time to 4.4%. Figure 8: Distribution of objective values. Figure 7: Scheduling problems under \(<\)[\(20,30\)], 4, 2, 7, 40\(>\). Figure 12 increases the period to 60. Figure 12 is similar to Figure 11. Thus, increasing time and bandwidth both have similar effects on scheduling problems, and for the larger problems, the performance improvement of SMT is more significant. Figure 11: Comparison under varying \(L\). Figure 10: Comparison under varying \(M\).