Summary and Summary and

Abdul Samad Shibghatullah 110 30052008 Total Matches of All Schedules 100 200 300 400 500 600 Ma x Me d Mi n Ma x Me d Mi n Ma x Me d Mi n Large Medium Small Total Type of Schedules Number of Events Total Experiments Total Matched Figure 4.15: Number of Total Matches in Different Schedule Type and Distribution Average Time for Successful Matches 0.00 0.50 1.00 1.50 2.00 Max Med Mi n Max Med Mi n Max Med Mi n Large Medium Small Total Type of Schedules Timing Minutes Average Time for Matching Process Figure 4.16: Average Time for Successful Matches in Different Type and Distribution

4.8 Summary and

Conclusion This chapter presents the experiment’s results and analysis of the proposed system CRSMAS that was developed based on the approach presented in Chapter Three. The purpose of the single event experiments is to evaluate the capability of CRSMAS in performing rescheduling in all conditions, and also to identify characteristics in crew schedules that influence the possibility of matching. Different types of events lateness, delay, and unavailability, different types of schedules large, medium, and small, different duties distributions maximum, median, and minimum, and different time of events are used for the experiment’s purposes. The analysis of the results reveals a new Abdul Samad Shibghatullah 111 30052008 factor that affects the possibility of rescheduling the spreading of duties in a particular time. If the spread is equal or nearly equal between them then the possibility of finding a match is high. In short, the factors in crew schedules that influence the possibility of rescheduling are duty distribution, duty spreading, types of schedules and timing. The analysis also shows that the rate of successful matches is 44.07, which is good but still not satisfactory. There are many things we can do to improve the matching rate. For example, the duties should be equally spread, and the relief should be long enough to absorb any lateness. The average time for successful matches is 1.64 seconds, which is fast and acceptable in a real time scenario where a quick solution is required. In conclusion, from this experiment we identified the factors that affect the matching rate and we are satisfied with CRSMAS with regard to time factors but not in relation to the matching rate, which is still low. Chapter Six will evaluate the weaknesses of CRSMAS after analysing findings from the two experiments Chapters Four and Five and will propose modifications where necessary. . Abdul Samad Shibghatullah 112 30052008 Chapter Five: Multiple Events Experiments

5.1 Introduction

The previous chapter presented results and analysis from the single event experiments. This chapter presents further experiments where a number of events take place simultaneously and randomly. The purpose is to simulate the real world scenario where UE take place any time and several occur at a time. This will show the robustness of CRSMAS in dealing with different types of events with different types of schedules facing different numbers of events with different event timings at any time. The results will be analysed based on the successful rescheduling and the time taken to execute it. Findings from the two experiments will then form the basis for the approach analysis that is presented in the next chapter where the research evaluates the two outcomes in order to identify the weaknesses in CRSMAS and propose modifications where appropriate.

5.1.1 Chapter Objective

The objective of Chapter Five is to present the results and analysis of the multiple events experiments to the proposed approach CRSMAS. The purpose of multiple events experiments is to evaluate the capability of CRSMAS in facing different Abdul Samad Shibghatullah 113 30052008 numbers of events taking place with different event timings in different types of schedules at any time. The results will be analysed based on successful matches and the time taken to execute them. The outcomes of the analysis will be used to assess the CRSMAS and proposed modifications wherever appropriate in Chapter Six.

5.1.2 Chapter Outline

The chapter starts with an introduction in Section 5.1 describing the objective of the chapter and its relationship to the rest of the chapters see Figure 5.1. Section 5.2 presents the experiment plan and discusses types of events and schedules, rescheduling assumptions and rules, data selection process, and experimental environment. There are two types of events, lateness LFSO, LFR, and LFSW and unavailability UNV and three types of schedules, large, medium, and small. Section 5.3 presents the experimental results and provides an analysis of the results and finally, Section 5.4 concludes and summarises the chapter. Results and Analysis -lateness LFSO, LFR, LFSW -unavailability UNV -overall results and analysis Experimentation Plan -types of events and schedules -rescheduling assumptions and rules -data selection process -experiments environment Summaries and Conclusion Chapter Objectives and Outline Figure 5.1: The Structure of Chapter Five Abdul Samad Shibghatullah 114 30052008

5.2 Experiment Plan

This section explains details of types of events, types of schedules, rules and assumptions, the data selection process, and the experimental environment we used for this experiment.

5.2.1 Type of Events and Schedules

The events are the same as discussed in Section 4.2.1 except that there is no delay event. The events are lateness LFSO, LFR, and LFSW and unavailability UNV. The reasons that we do not test delay events is because the duration is quite long and generally it requires more than one round of rescheduling. Two or more than one rounds of rescheduling need manual intervention and adjustments, and when there are many events simultaneously this becomes quite complex. In this experiment, we do not consider more than one round of rescheduling. The types of schedules are the same as in the single event experiments; large, medium and small schedules.

5.2.2 Rescheduling Assumptions and Rules

The rescheduling assumptions and rules are similar to those discussed in Section 4.2.2. The difference is that there is not more than one round of rescheduling because two or more rounds of rescheduling need manual adjustments which are complex. In this experiment, we only consider one round of rescheduling.

5.2.3 Data Selection Process

In these experiments, multiple events take place randomly. Therefore, we should know how to sample the number of events we need and how to select random data. The minimum number of events is 2 and the maximum number is 20 of the total number of duties of the schedule. For a large schedule it is 18 20 of 88 duties, for a medium 10 20 of 51 and for a small 5 20 of 23. To select data randomly, we used the random formula in Microsoft Excel to generate random numbers and the numbers were used to refer to the duty number. For the lateness event we used the formula below: RAND the maximum number-the minimum number + the minimum number Abdul Samad Shibghatullah 115 30052008 The maximum number is the total number of duties and the minimum number is 1. For example, for a medium schedule that has 51 duties the formula will look like this: RAND 51-1 +1 Table 5.1 shows the selected data for a lateness event according to the type of schedule. The full data for the experiments is shown in Appendix G. For the unavailability event, we selected the start time of the event randomly based on the finish work 2 time. Below is the formula. Table 5.2 illustrates the selected data for an unavailability event. RAND the latest time for ‘Finish Work 2’ - the earliest time for ‘Finish Work 2’ + the earliest time for ‘Finish Work 2’ Table 5.1: The Selected Data for Lateness Event Large Medium Small No of Events Crew ID Crew ID Crew ID 1 E K C 2 P O H 3 V Q L 4 W T M 5 X U O 6 AB AG 7 AC AH 8 AD AL 9 AL AP 10 AQ AW 11 AU 12 AW 13 AX 14 BK 15 BN 16 BR 17 BT 18 CA Abdul Samad Shibghatullah 116 30052008 Table 5.2: The Selected Data for UNV Event Large Medium Small No of Events Crew ID Crew ID Crew ID 1 11:48:00 14:30:00 19:12:00 2 12:45:00 14:48:00 20:54:00 3 12:54:00 15:00:00 22:18:00 4 14:24:00 16:30:00 23:54:00 5 15:28:00 17:12:00 6 15:42:00 22:18:00 7 15:54:00 23:36:00 8 16:06:00 23:54:00 9 16:24:00 24:48:00 10 17:24:00 11 17:48:00 12 18:30:00 13 18:54:00 14 19:00:00 15 19:36:00 16 20:12:00 17 20:48:00 In this experiment, we also tested the event with different timing. For lateness except LFSO the event timing started from 15 minutes and was increased by 5 minute intervals until 60 minutes was reached. LFSO is only 15 minutes and 20 minutes because when the timing is more it requires second round rescheduling, which is not considered in this experiment. For unavailability, the event started from 30 minutes increasing by 15 minute intervals until 120 minutes was reached. Table 5.3 demonstrates the overall picture of the experiments. For example, in the event of LFSO- Large schedule there were 34 experiments. The maximum number of duties affected in the large schedule was 18 as discussed in the previous paragraph but the experiment shows only 17 because the event started from 2 events and went to 18 events. The grand total number of the experiments was 870. Abdul Samad Shibghatullah 117 30052008 Table 5.3: The Overall Picture of the Experiments Type of EventsType of SchedulesNumber of Experiments Total Large Schedule 17 x 2 34 Medium Schedule 9 x 2 18 LFSO Small Schedule 4 x 2 8 Large Schedule 17 x 10 170 Medium Schedule 9 x 10 90 LFR Small Schedule 4 x 10 40 Large Schedule 17 x 10 170 Medium Schedule 9 x 10 90 LFSW Small Schedule 4 x 10 40 Large Schedule 17 x 7 119 Medium Schedule 9 x 7 63 UNV Small Schedule 4 x 7 28 Grand Total 870

5.2.4 Experimental Environment

A PC with Pentium IV 1.2 GHz and Windows XP operating system was used for the experiments the same as in single event experiments.

5.3 Results and

Analysis This section presents the results and analysis for every event. Full results are shown in Appendix G.

5.3.1 Lateness

This subsection presents the results and analysis of lateness events. There are three types of lateness, LFSO, LFR, and LFSW, and three types of schedules, large, medium, and small. LFSO-Large The results of LFSO-large are shown in Table 5.4. EV describes how many events large schedule is from 2 to 18, medium schedule 2 to 10, and small 2 to 5, 15 and 20 show the minutes that the crews are late, M shows the number of matches, explains the percentage of matched crews from the number of events, Ts indicates how fast in seconds the system performed the rescheduling process, and the last row gives the total. Abdul Samad Shibghatullah 118 30052008 Total is the full results, TE refers to total events, TM stands for total matched, TTs explains the total time for rescheduling in seconds, indicates the percentage of total successfully matched, and AVs shows the average time taken for the rescheduling process in seconds. The percentage of matched is 100 at the beginning, but when more events are incorporated, the number of matched decreases slowly see Table 5.4 and Figure 5.2. In the event of 6 crews being late for 20 minutes the match is 5 but in the event of 7 crews, the match is reduced to 4. The result is quite strange. Further investigation reveals that one of the crew who is matched in the event of 6 is unavailable in the event of 7 because the crew becomes one of the events, which is the seventh. The overall number successfully matched is 159 out of 340 events and equal to 44. The average time taken for every event is 1.66 seconds, which is very quick and acceptable for a large schedule. Table 5.4: LFSO-Large Schedule EV 15 Minutes 20 Minutes Total M Ts M Ts TE TM TTs AVS 2 2 100 2.85 2 100 3.86 4 4 6.71 100 1.68 3 3 100 5.20 3 100 5.54 6 6 10.74 100 1.79 4 3 75 5.75 3 75 7.16 8 6 12.91 75 1.61 5 4 80 8.92 4 80 8.84 10 8 17.76 80 1.78 6 5 83 10.59 5 83 10.66 12 10 21.25 83 1.77 7 5 71 12.63 4 57 12.41 14 9 25.04 64 1.79 8 5 63 14.52 4 50 14.21 16 9 28.73 56 1.80 9 5 56 15.46 4 44 15.59 18 9 31.05 50 1.73 10 5 50 17.11 4 40 16.62 20 9 33.73 45 1.69 11 6 55 18.58 4 36 18.76 22 10 37.34 45 1.70 12 6 50 20.90 4 33 18.96 24 10 39.86 42 1.66 13 6 46 21.50 4 31 22.00 26 10 43.50 38 1.67 14 6 43 22.90 4 29 23.23 28 10 46.13 36 1.65 15 6 40 25.74 4 27 23.38 30 10 49.12 33 1.64 16 6 38 26.15 4 25 24.52 32 10 50.67 31 1.58 17 6 35 27.85 4 24 25.73 34 10 53.58 29 1.58 18 6 33 28.66 4 22 28.51 36 10 57.17 28 1.59 170 85 50 285 65 38 280 340 150 565.29 44 1.66 Abdul Samad Shibghatullah 119 30052008 LFSOLarge-Total Matched 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Number of Events Percentage of Matched Total Events Matched Figure 5.2: The Relationship between Total Events and Total Matches for LFSO Large LFSO-Medium Table 5.5 and Figure 5.3 show the results for LFSO-medium. The overall matches is very low, only 14 out of 108 events and equates to 13. The reason for this is that most of the events happen at a time when not many crews sign-on see Table G.2 in Appendix G. As a result, this is very hard to reschedule. The average time taken for every event is 0.88 seconds; this is very quick and reasonable for a medium schedule. Table 5.5: LFSO-Medium Schedule EV 15 Minutes 20 Minutes Total M Ts M Ts TE TM TTs AVS 2 0 0 1.81 0 0 1.85 4 0 3.66 0 0.92 3 0 0 2.80 0 0 2.75 6 0 5.55 0 0.93 4 1 25 3.73 1 25 3.70 8 2 7.43 25 0.93 5 1 20 4.67 1 20 3.66 10 2 8.33 20 0.83 6 1 17 5.31 1 17 5.28 12 2 10.59 17 0.88 7 1 14 6.15 1 14 5.93 14 2 12.08 14 0.86 8 1 13 6.77 1 13 6.91 16 2 13.68 13 0.86 9 1 11 7.74 1 11 7.46 18 2 15.20 11 0.84 10 1 10 8.52 1 10 8.42 20 2 16.94 10 0.85 54 7 13 47.5 7 13 46 108 14 93.46 13 0.87 Abdul Samad Shibghatullah 120 30052008 LFSOMedium-Total Matched 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 Number of Events Percentage of Matched Total Events Matched Figure 5.3: The Relationship between Total Events and Total Matched for LFSO Medium LFSO-Small Table 5.6 shows the results for LFSO-small. Out of 28 events, none were successful. The reason for this is that the schedule is small and the events happened outside peak time see Table G.3. The average time taken for every event is 0.42 seconds, which is very fast and reasonable for a small schedule. Table 5.6: LFSO-Small Schedule EV 15 Minutes 20 Minutes Total M Ts M Ts TE TM TTs AVS 2 0 0 0.95 0 0 0.91 4 0 1.86 0 0.47 3 0 0 1.28 0 0 1.31 6 0 2.59 0 0.43 4 0 0 1.68 0 0 1.65 8 0 3.33 0 0.42 5 0 0 1.95 0 0 2.04 10 0 3.99 0 0.40 14 5.86 5.91 28 11.77 0.42 LFR-Large Table 5.7 and Figure 5.4 illustrate the results for LFR-large. The number of matched is 100 when the late time is 15-30 minutes but when the times is longer and the events more the percentage decreases gradually. The overall percentage of matched is only 37, which is low. The reason is that in the large schedule the relief is not long just 45 minutes or a bit more compared to a medium schedule where the relief time is long. Abdul Samad Shibghatullah 121 30052008 When the relief time is just enough, lateness cannot be absorbed. The average time for rescheduling is 1.5 seconds, which is good for a large schedule. Table 5.7: LFR-Large Schedule EV 15 Min. 20 Min. 25 Min. 30 Min. 35 Min. 40 Min. 45 Min. 50 Min. 55 Min. 60 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 2 100 3.27 2 100 3.36 2 100 3.38 2 100 3.15 1 50 3.21 1 50 3.29 1 50 3.50 1 50 3.49 1 50 3.81 1 50 3.43 20 14 33.90 70 1.69 3 3 100 4.66 2 67 4.99 2 67 4.88 2 67 4.59 1 33 4.34 1 33 4.86 1 33 4.42 1 33 4.56 1 33 4.31 1 33 4.71 30 15 46.31 50 1.54 4 4 100 6.45 2 50 6.44 2 50 6.11 2 50 6.45 1 25 6.58 1 25 6.07 1 25 6.76 1 25 6.38 1 25 6.82 1 25 6.72 40 16 64.77 40 1.62 5 5 100 7.74 2 40 8.03 2 40 7.54 2 40 8.14 1 20 8.16 1 20 7.22 1 20 7.88 1 20 7.48 1 20 7.84 1 20 7.43 50 17 77.45 34 1.55 6 6 100 9.56 3 50 9.03 3 50 9.04 3 50 9.48 2 33 9.19 2 33 9.14 2 33 9.02 2 33 9.48 2 33 9.36 1 17 9.35 60 26 92.65 43 1.54 7 7 100 10.65 4 57 10.89 4 57 11.11 4 57 10.59 2 2910.71 2 2910.82 2 2910.53 2 2911.02 2 29 10.80 1 1411.07 70 30 108.19 43 1.55 8 8 100 12.91 4 50 11.97 4 50 12.93 4 50 12.72 3 3813.00 3 3812.81 3 3813.20 3 3812.46 3 38 13.04 2 2512.37 80 37 127.40 46 1.59 9 9 100 14.03 4 44 14.01 4 44 15.95 4 44 13.43 3 3313.57 3 3315.80 3 3313.88 3 3315.77 3 33 13.77 2 2216.11 90 38 146.32 42 1.63 10 10 100 15.57 5 50 15.42 4 40 13.90 4 40 14.45 3 3014.45 3 3013.85 3 3014.25 3 3013.99 3 30 13.91 2 2013.77 100 40 143.55 40 1.44 11 11 100 16.97 5 45 16.88 4 36 16.98 4 36 16.41 3 2716.32 3 2717.32 3 2716.17 3 2717.57 3 27 16.25 2 1817.44 110 41 168.32 37 1.53 12 12 100 18.37 6 50 18.40 4 33 17.52 4 33 17.37 3 2517.31 3 2517.19 3 2517.19 3 2517.05 3 25 17.40 2 1717.36 120 43 175.16 36 1.46 13 12 92 18.75 5 38 19.75 4 31 19.06 4 31 18.99 3 2318.69 3 2318.95 3 2318.42 3 2318.69 3 23 18.10 2 1518.63 130 42 188.04 32 1.45 14 13 93 21.25 6 43 20.88 5 36 21.62 4 29 19.98 3 2120.13 3 2121.53 3 2120.06 3 2121.76 3 21 19.81 2 1421.96 140 45 208.98 32 1.49 15 14 93 21.47 6 40 21.25 5 33 22.63 4 27 22.11 3 2022.38 3 2022.49 3 2022.09 3 2022.66 3 20 22.08 2 1322.99 150 46 222.15 31 1.48 16 15 94 23.20 7 44 23.68 6 38 23.99 5 31 23.19 4 2523.49 4 2524.09 4 2523.14 4 2524.04 3 19 22.82 2 1324.20 160 54 235.84 34 1.47 17 16 94 24.75 7 41 24.64 6 35 24.94 5 29 24.64 4 2424.52 4 2424.76 4 2424.86 4 2424.53 3 18 24.81 2 1224.21 170 55 246.66 32 1.45 18 17 94 25.20 8 44 24.90 7 39 25.83 6 33 26.63 5 28 27 5 2825.87 5 2826.76 5 28 24.8 4 22 26.4 3 17 25.9 180 65 259.16 36 1.44 170164 96 255 78 46 255 68 40 257.4163 37 252 4526 253 4526 256 4526 252 4526 256 42 25 251 29 17 258 17006242544.8637 1.50 LFRLarge-Total Matched 50 100 150 200 1 3 5 7 9 11 13 15 17 Number of Events Percentage of Matched Total Events Matched Figure 5.4: The Relationship between Total Events and Total Matched for LFR Large LFR-Medium The results see Table 5.8 and Figure 5.5 show that the overall matching rate is very high at 72. For 15 to 55 minutes from 2 to 5 events, the matching rate is 100. The results are very encouraging. Further investigation revealed that the relief time is long enough to absorb lateness and increase the possibility of finding another crew for Abdul Samad Shibghatullah 122 30052008 replacement. The average time is 0.90 seconds, which is more or less the same for any type of event in a medium schedule. Table 5.8: LFR-Medium Schedule EV 15 Min. 20 Min. 25 Min. 30 Min. 35 Min. 40 Min. 45 Min. 50 Min. 55 Min. 60 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 2 1002.07 2 1002.15 2 100 2.23 2 1002.22 2 1002.47 2 1002.38 2 1002.82 2 1002.55 2 100 2.45 1 50 2.56 20 19 23.90 95 1.20 3 3 1002.87 3 1002.58 3 100 2.71 3 1002.77 3 1002.91 3 1002.69 3 1003.07 3 1003.00 3 100 2.89 2 67 3.07 30 29 28.55 97 0.95 4 4 1003.92 4 1004.04 4 100 3.77 4 1003.99 4 1003.95 4 1003.86 4 1003.72 4 1003.67 4 100 3.88 3 75 3.73 40 39 38.53 98 0.96 5 5 1004.80 5 1004.40 5 100 4.45 5 1004.51 5 1004.62 5 1004.83 5 1004.61 5 1004.49 5 100 4.43 4 80 4.38 50 49 45.52 98 0.91 6 5 83 5.53 5 83 5.35 5 83 5.55 5 83 5.55 5 83 5.85 5 83 5.61 5 83 5.91 5 83 5.35 5 83 5.87 4 67 5.61 60 49 56.17 82 0.94 7 6 86 6.20 6 86 6.12 5 71 6.02 5 71 6.22 5 71 6.24 5 71 5.94 5 71 6.14 5 71 5.85 5 71 6.21 4 57 5.87 70 51 60.81 73 0.87 8 6 75 7.01 6 75 6.59 5 63 7.14 5 63 6.82 5 63 7.49 5 63 6.86 5 63 7.25 5 63 6.99 5 63 7.38 4 50 7.08 80 51 70.61 64 0.88 9 6 67 7.71 6 67 7.73 5 56 7.48 5 56 7.39 5 56 7.73 5 56 7.28 5 56 7.38 5 56 7.17 5 56 7.64 4 44 7.87 90 51 75.39 57 0.84 10 6 60 8.48 6 60 8.83 5 50 8.58 5 50 8.12 5 50 8.42 5 50 7.99 5 50 8.70 5 50 7.97 5 50 8.79 4 40 8.76100 51 84.65 51 0.85 54 43 80 48.6 43 80 47.8 39 72 47.939 72 47.639 72 49.739 72 47.439 72 49.639 72 47 39 72 49.530 56 48.9540 389484.1472 0.90 LFRMedium-Total Matched 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 Number of Events Percentage of Matched Total Events Matched Figure 5.5: The Relationship between Total Events and Total Matched for LFR Medium LFR-Small Table 5.9 illustrates the results for LFR-small. The overall match is very low at 7 2 out of 28. The matching rate for a small schedule is expected to be low because there are not many duties in the schedule. The experiments were carried out until 20 minutes only, because there was no single match for 20 minutes late and therefore no point in continuing the experiment. Abdul Samad Shibghatullah 123 30052008 Table 5.9: LFR-Small Schedule EV 15 Minutes 20 Minutes Total M Ts M Ts TE TM TTs AVS 2 0 0 0.93 0 0 0.92 4 0 1.85 0 0.46 3 0 0 1.27 0 0 1.13 6 0 2.40 0 0.40 4 1 25 1.75 0 0 1.93 8 1 3.68 13 0.46 5 1 20 2.06 0 0 2.03 10 1 4.09 10 0.41 14 2 45 6.01 6.01 28 2 12.02 7 0.43 LFSW-Large Table 5.10 and Figure 5.4 illustrate the results for LFSW-large. The overall matching rate is very low at 18 matched 312 out of 1,700. The reason is same as mentioned for LFR-large, that is the relief time is not long enough and the distribution of the duty is not equally spread in an hour as discovered in Chapter Four. A large schedule has many duties, but relief timing and spreading also influence the success of rescheduling. Table 5.10: LFSW-Large Schedule 15 Min. 20 Min. 25 Min. 30 Min. 35 Min. 40 Min. 45 Min. 50 Min. 55 Min. 60 Min. Total E M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 1 50 3.32 1 50 3.25 1 50 3.41 1 50 3.28 1 50 3.45 1 50 3.39 1 50 3.34 1 50 3.28 1 50 3.16 1 50 3.27 20 10 33.16 50 1.66 3 1 33 4.53 1 33 4.49 1 33 4.49 1 33 4.57 1 33 4.53 1 33 4.70 1 33 4.62 1 33 4.68 1 33 4.58 1 33 4.62 30 10 45.83 33 1.53 4 1 25 6.42 1 25 6.46 1 25 6.37 1 25 6.39 1 25 6.36 1 25 6.31 1 25 6.48 1 25 6.32 1 25 6.32 1 25 6.37 40 10 63.80 25 1.60 5 1 20 7.85 1 20 7.81 1 20 7.87 1 20 7.70 1 20 7.94 1 20 7.59 1 20 7.89 1 20 7.89 1 20 8.04 1 20 7.51 50 10 78.09 20 1.56 6 2 33 9.56 2 33 9.55 2 33 9.58 2 33 9.54 2 33 9.69 1 17 9.48 1 17 9.64 1 17 9.81 1 17 9.82 1 17 9.39 60 15 96.04 25 1.60 7 2 29 10.74 2 2910.81 2 29 10.72 2 2910.80 2 2910.75 1 1410.68 1 1410.89 1 1410.99 1 1410.88 1 14 10.83 70 15 108.08 21 1.54 8 3 38 12.97 3 3812.83 3 38 13.05 3 3812.77 3 3813.01 2 2512.67 1 1313.12 1 1313.04 1 1313.02 1 13 12.53 80 21 129.02 26 1.61 9 3 33 13.98 3 3313.88 3 33 13.87 3 3314.01 3 3313.95 2 2213.95 1 1114.03 1 1114.18 1 1114.16 1 11 13.99 90 21 139.99 23 1.56 10 3 30 15.52 3 3015.55 3 30 15.38 3 3015.48 3 3015.37 2 2015.62 1 1015.37 1 1015.43 1 1015.57 1 10 15.75 100 21 155.03 21 1.55 11 3 27 17.02 3 2716.97 3 27 17.04 3 2717.08 3 2716.96 2 1816.97 1 9 16.92 1 9 16.92 1 9 16.86 1 9 17.05 110 21 169.79 19 1.54 12 3 25 18.38 3 2518.25 3 25 18.41 3 2518.31 3 2518.45 2 1718.24 1 8 18.31 1 8 18.24 1 8 18.33 1 8 18.36 120 21 183.29 18 1.53 13 3 23 18.80 3 2318.87 3 23 18.93 3 2318.78 3 2318.91 2 1518.92 1 8 19.00 1 8 18.90 1 8 18.83 1 8 18.90 130 21 188.85 16 1.45 14 3 21 21.33 3 2121.42 3 21 21.26 3 2121.28 3 2121.13 2 1421.23 1 7 21.10 1 7 21.05 1 7 20.98 1 7 21.21 140 21 211.99 15 1.51 15 3 20 21.49 3 2021.63 3 20 21.48 3 2021.67 3 2021.34 2 1321.55 1 7 21.22 1 7 21.17 1 7 21.20 1 7 21.42 150 21 214.17 14 1.43 16 4 25 23.08 3 1923.03 3 19 23.10 3 1922.97 3 1923.14 2 1323.04 1 6 23.13 1 6 23.03 1 6 23.04 1 6 22.97 160 22 230.53 14 1.44 17 4 24 24.05 3 1824.06 3 18 24.19 3 1824.08 3 1824.09 2 1224.02 1 6 24.06 1 6 24.00 1 6 24.17 1 6 23.88 170 22 240.61 13 1.42 18 5 28 24.46 4 2225.26 4 22 24.46 4 2225.11 4 2224.42 3 1725.23 2 1124.41 2 1124.31 1 6 24.26 1 6 25.19 180 30 247.11 17 1.37 170 4526 254 42 25 254 4225 254 4225 254 4225 253 2917 254 1811 254 1811 253 1710 253 17 10 253 17003122535.3818 1.49 Abdul Samad Shibghatullah 124 30052008 LFSWLarge-Total Matched 50 100 150 200 1 3 5 7 9 11 13 15 17 Number of Events Percentage of Matched Total Events Matched Figure 5.6: The Relationship between Total Events and Total Matched for LFSW Large LFSW-Medium The matching rate for LFSW-medium 39 is higher than that of the large schedule as discussed above because of the long relief time and spreading of duties in an hour see Table 5.11 and Figure 5.7. The results show that in the beginning the matching rate is high but when the time is longer and involves more events, the matching rate slowly declines. Table 5.11: LFSW-Medium Schedule EV 15 Min. 20 Min. 25 Min. 30 Min. 35 Min. 40 Min. 45 Min. 50 Min. 55 Min. 60 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 2 1002.00 2 1002.11 1 50 2.09 1 50 2.04 1 50 1.99 0 0 2.03 0 0 1.97 0 0 2.09 0 0 2.07 0 0 1.98 20 7 20.38 35 1.02 3 3 1002.24 3 1002.15 2 67 2.18 2 67 2.12 2 67 2.09 0 0 2.13 0 0 2.04 0 0 2.16 0 0 2.13 0 0 2.29 30 12 21.53 40 0.72 4 4 1002.93 4 1002.88 3 75 2.89 3 75 2.72 3 75 2.66 1 25 2.54 1 25 2.42 1 25 2.51 1 25 2.54 1 25 2.46 40 22 26.56 55 0.66 5 5 1003.60 4 80 3.50 3 60 3.53 3 60 3.60 3 60 3.43 2 40 3.29 2 40 3.31 2 40 3.22 2 40 3.09 2 40 3.21 50 28 33.77 56 0.68 6 5 83 4.28 4 67 4.33 3 50 4.28 3 50 4.20 3 50 4.31 2 33 4.32 2 33 4.20 2 33 4.07 2 33 4.19 2 33 4.09 60 28 42.27 47 0.70 7 5 71 4.57 4 57 4.54 3 43 4.67 3 43 4.72 3 43 4.81 2 29 4.90 2 29 4.84 2 29 4.83 2 29 4.84 2 29 4.92 70 28 47.66 40 0.68 8 5 63 6.87 4 50 6.97 3 38 6.88 3 38 6.71 3 38 6.71 2 25 6.62 2 25 6.67 2 25 6.66 2 25 6.53 2 25 6.37 80 28 66.99 35 0.84 9 5 56 7.91 4 44 7.89 3 33 7.84 3 33 7.98 3 33 7.98 2 22 7.87 2 22 7.96 2 22 7.87 2 22 8.04 2 22 7.70 90 28 79.04 31 0.88 10 5 50 8.24 4 40 8.46 3 30 8.37 3 30 8.61 3 30 8.40 2 20 8.09 2 20 8.30 2 20 8.02 2 20 8.22 2 20 7.96100 28 82.67 28 0.83 54 39 72 42.6 33 61 42.8 24 44 42.7 24 44 42.7 24 44 42.4 13 24 41.8 13 24 41.7 13 24 41.4 13 24 41.6 13 24 41 540209420.8739 0.78 Abdul Samad Shibghatullah 125 30052008 LFSWMedium-Total Matched 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 Number of Events Percentage of Matched Total Events Matched Figure 5.7: The Relationship between Total Events and Total Matched for LFSW Medium LFSW-Small Table 5.12 shows the results where none of the events find any match. From all the experiments for a small schedule in multiple events for lateness, there is a very low or zero possibility of successful rescheduling. Table 5.12: LFSW-Small Schedule EV 15 Minutes Total M Ts TE TM TTs AVS 2 0 0 0.88 2 0 0.88 0.44 3 0 0 1.37 3 0 1.37 0.46 4 0 0 1.68 4 0 1.68 0.42 5 0 0 2.06 5 0 2.06 0.41 14 5.99 14 5.99 0.43

5.3.2 Unavailability

This subsection explains the results and analysis for unavailability events for large, medium, and small schedules. UNV-Large The results show that the matching rate is average at 67 see Table 5.13 and Figure 5.8. The reason for this is that some of the sign-off times for the duties are same, and the gap between end work 2 and sign-off is not very consistent in large schedules. If the Abdul Samad Shibghatullah 126 30052008 sign-off time is the same, it reduces the possibility of finding a match. The longer the gap between end work 2 and sign-off, the higher the possibility of finding a match. The average time is 1.56 seconds, which is very quick. Table 5.13: UNV-Large Schedule EV 30 Min. 45 Min. 60 Min. 75 Min. 90 Min. 105 Min. 120 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 1 50 2.79 1 50 3.01 1 50 3.16 1 50 2.96 1 50 3.20 1 50 3.03 1 50 3.04 14 7 21.20 50 1.51 3 2 67 4.10 2 67 4.39 2 67 4.60 2 67 4.36 2 67 4.49 2 67 4.48 2 67 4.60 21 14 31.02 67 1.48 4 2 50 4.28 2 50 6.59 2 50 6.63 2 50 6.35 2 50 6.34 2 50 6.54 2 50 6.30 28 14 43.02 50 1.54 5 3 60 6.23 3 60 7.92 3 60 7.71 3 60 7.75 3 60 7.93 3 60 7.87 3 60 7.85 35 21 53.27 60 1.52 6 4 67 6.76 4 67 9.48 4 67 9.56 4 67 9.45 4 67 9.69 4 67 9.58 4 67 9.42 42 28 63.93 67 1.52 7 5 71 8.40 5 71 10.65 5 71 10.76 5 71 10.93 5 71 10.96 5 71 10.71 5 71 10.94 49 35 73.36 71 1.50 8 6 75 8.61 6 75 12.68 6 75 12.98 6 75 12.95 6 75 12.81 6 75 12.96 6 75 12.75 56 42 85.73 75 1.53 9 7 78 9.09 7 78 13.88 7 78 13.81 7 78 13.72 7 78 13.74 7 78 14.03 6 67 14.03 63 48 92.29 76 1.46 10 8 80 13.31 8 80 15.63 8 80 15.59 8 80 15.68 8 80 15.39 8 80 15.55 7 70 15.44 70 55 106.58 79 1.52 11 9 82 15.43 9 82 17.14 9 82 17.02 9 82 16.94 9 82 17.07 9 82 16.98 7 64 16.86 77 61 117.43 79 1.53 12 9 75 16.09 9 75 18.33 9 75 18.26 9 75 18.20 9 75 18.09 9 75 18.35 7 58 18.32 84 61 125.64 73 1.50 13 9 69 17.28 9 69 18.96 9 69 18.79 9 69 18.71 9 69 18.94 9 69 19.02 7 54 18.89 91 61 130.59 67 1.44 14 10 71 18.54 10 71 21.45 10 71 21.36 10 71 21.53 10 71 21.28 10 71 21.38 8 57 21.44 98 68 146.98 69 1.50 15 10 67 19.48 10 67 21.80 10 67 21.47 10 67 22.53 10 67 21.74 10 67 21.76 8 53 21.55 105 68 150.33 65 1.43 16 10 63 20.71 10 63 22.95 10 63 23.11 10 63 23.01 10 63 23.16 10 63 23.03 8 50 22.92 112 68 158.88 61 1.42 17 10 59 21.98 10 59 24.03 10 59 24.14 10 59 23.94 10 59 23.97 10 59 24.07 8 47 23.95 119 68 166.08 57 1.40 18 11 61 24.40 11 61 25.12 11 61 25.04 11 61 24.8 11 61 25.38 10 56 25.29 8 44 25.42 126 73 175.42 58 1.39 170 116 68 217 116 68 254 116 68 254 116 68 254 116 68 254 115 68 255 97 57 254 1190 792 1742 67 1.46 UNVLarge-Total Matched 20 40 60 80 100 120 140 1 3 5 7 9 11 13 15 17 Number of Events Percentage of Matched Total Events Matched Figure 5.8: The Relationship between Total Events and Total Matched for UNV Large Abdul Samad Shibghatullah 127 30052008 UNV-Medium Table 5.14 and Figure 5.9 illustrate the results for UNV-medium. The overall matched is 71, which is higher than for the UNV-large schedule. The explanation for this is that the sign-off time one of the factors for finding a match in UNV event for a medium schedule is distributed unlike that of a large schedule where some of the time is the same. When there is different timing, the possibility of finding a match is high. The average time taken is 0.77 seconds, which is very fast. Table 5.14: UNV-Medium Schedule EV 30 Min. 45 Min. 60 Min. 75 Min. 90 Min. 105 Min. 120 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 2 100 1.83 2 100 1.87 2 100 2.08 2 100 1.94 2 100 2.01 2 100 1.93 2 100 2.10 14 14 13.75 100 0.98 3 2 67 1.98 2 67 2.13 2 67 2.15 2 67 2.31 2 67 2.10 2 67 2.19 2 67 2.15 21 14 15.02 67 0.72 4 3 75 3.17 3 75 2.89 3 75 3.05 3 75 3.00 3 75 2.84 2 50 3.10 2 50 2.97 28 19 21.01 68 0.75 5 4 80 3.23 4 80 3.50 4 80 3.51 4 80 3.65 4 80 3.75 3 60 3.45 2 40 3.67 35 25 24.76 71 0.71 6 5 83 3.26 5 83 4.31 5 83 4.15 5 83 4.45 5 83 4.17 4 67 4.37 3 50 4.25 42 32 28.96 76 0.69 7 6 86 3.68 6 86 4.41 6 86 4.54 6 86 4.72 6 86 4.40 5 71 4.51 4 57 4.68 49 39 30.94 80 0.63 8 6 75 5.19 6 75 6.86 6 75 6.93 6 75 6.89 6 75 7.02 5 63 6.71 4 50 6.78 56 39 46.37 70 0.83 9 6 67 5.59 6 67 8.02 6 67 7.81 6 67 7.98 6 67 7.80 5 56 8.06 4 44 7.79 63 39 53.06 62 0.84 10 7 70 7.94 7 70 8.41 7 70 8.27 7 70 8.40 7 70 8.41 6 60 8.29 5 50 8.26 70 46 57.98 66 0.83 54 41 76 35.9 41 76 42.4 41 76 42.5 41 76 43.3 41 76 42.5 34 63 42.6 28 52 42.7 378 267 291.8 71 0.77 UNVMedium-Total Matched 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 Number of Events Percen tag e o f Match e d Total Event Matched Figure 5.9: The Relationship between Total Events and Total Matched for UNV Medium Abdul Samad Shibghatullah 128 30052008 UNV-Small Table 5.15 and Figure 5.10 show the results for UNV-small. The overall matched is 47, which is better than expected for a small schedule. The average time taken is 0.39 seconds, which is very fast. Table 5.15: UNV-Small Schedule EV 30 Min. 45 Min. 60 Min. 75 Min. 90 Min. 105 Min. 120 Min. Total M Ts M Ts M Ts M Ts M Ts M Ts M Ts TE TM TTs AVS 2 1 50 0.87 1 50 0.72 1 50 0.85 1 50 0.86 1 50 0.87 1 50 0.82 1 50 0.94 14 7 5.93 50 0.42 3 2 67 1.27 2 67 1.40 2 67 1.11 2 67 1.19 2 67 1.30 2 67 1.28 1 33 1.43 21 13 8.98 62 0.43 4 2 50 1.47 2 50 1.60 2 50 1.32 2 50 1.36 2 50 1.42 2 50 1.61 1 25 1.50 28 13 10.28 46 0.37 5 2 40 1.91 2 40 1.85 2 40 1.94 2 40 1.96 2 40 1.95 2 40 1.88 1 20 1.89 35 13 13.38 37 0.38 14 7 50 5.52 7 50 5.57 7 50 5.22 7 50 5.37 7 50 5.55 7 50 5.59 4 29 5.76 98 46 38.57 47 0.39 UNVSmall-Total Matched 10 20 30 40 50 60 70 1 2 3 4 Number of Events Percentage of Matched Total Events Matched Figure 5.10: The Relationship between Total Events and Total Matched for UNV Small

5.3.3 Overall Results and Analysis

The overall results show that the highest matching rate is LFR-medium followed by UNV-medium, UNV-large, and UNV-small respectively. This shows that the type of schedule does not necessarily guarantee a match, but other factors like distribution and the relief period also influence the match. The reason why LFR-medium is the highest is because the schedule has longer break periods so lateness can be absorbed. Unlike in large schedules, the relief period is just enough more or less than 50 minutes and gives no chance for lateness absorption. The LFSO event is different because the time is Abdul Samad Shibghatullah 129 30052008 fixed; after sign-on the starting time is after 15 minutes. So the chance to reschedule depends on the size of the schedule. Table 5.16 shows that LFSO-large is 44.1, LFSO-medium is 13, and LFSO-small 0. In the event of UNV, the factor depends on end work 2 and sign-off. In the medium schedule, there are different times for signing off which is why UNV-medium is the highest 70.6. However, in large schedules, some crews have the same time for sign-off although their end work 2 is different. This reduces the chances for a successful match UNV-Large is 66.6. Out of 4 events LFSO, LFR, LFSW, and UNV, the highest matched is UNV 66, 70.6, and 46.9. The overall match is 42.1, which gives 2,805 successes out of 6,664 events. The result is good but still not satisfactory. There are many ways of increasing the percentage matched, for example by building the schedule with characteristics that support rescheduling. The next chapter will explain more about this. The time is different with different schedule types and nothing to do with different events. For large schedules, the average time is between 1.46 to 1.66 seconds, medium 0.77 to 0.9 seconds, and small 0.39 to 0.42 seconds. The time is quick and acceptable for a real- time scenario. Table 5.16: Total Analysis Type of Events TE TM TTS AVS LFSO-LARGE 340 150 565 44.1 1.66 LFSO-MEDIUM 108 14 93.5 13 0.87 LFSO-SMALL 28 11.8 0.42 LFR-LARGE 1700 624 2545 36.7 1.5 LFR-MEDIUM 540 389 484 72 0.9 LFR-SMALL 28 2 12 7.14 0.43 LFSW-LARGE 1700 312 2535 18.4 1.49 LFSW-MEDIUM 540 209 421 38.7 0.78 LFSW-SMALL 14 5.99 0.43 UNV-LARGE 1190 792 1742 66.6 1.46 UNV-MEDIUM 378 267 292 70.6 0.77 UNV-SMALL 98 46 38.6 46.9 0.39 TOTAL 6664 2805 8740 42.1 1.31 Abdul Samad Shibghatullah 130 30052008 Total Matched for All Events 10 20 30 40 50 60 70 80 LF SO- S MALL LFS W- S MA LL LF R- SMAL L LF SO -ME DI UM LFS W- LA R G E LF R -L AR GE LF SW -ME D IU M LF S O -L AR GE U N V-S M AL L UNV -L ARGE UNV -MED IUM LF R- MED IU M TOTAL Type of Events Percentage of Matched Figure 5.11: The Overall Matched According to Events

5.4 Summary and

Conclusion This chapter presents the results and analysis for multiple events experiments. The purpose of multiple events experiments is to evaluate the capability of CRSMAS the proposed system in facing different numbers of events taking place with different event timings in different types of schedules at any time. In these experiments we carried out a total of 870 experiments using four different events - LFSO, LFR, LFSW, and UNV. The analysis of the results shows that the time taken for rescheduling average is 1.31 seconds is very quick for all types of schedule and events and excellent for real-time scenarios. CRSMAS is also capable of handling multiple events at a single time. The largest number of events is 18, which takes more or less 25 seconds. However, the percentage of successfully matched 42.1 is not satisfactory. There are many ways in which we can increase the matching rate, for example, the duties spreading, and the relief timing. In the next chapter these issues will be discussed further. In short, from these experiments, CRSMAS is capable of handling multiple events at any time and giving quick solutions in real-time but with a low matching rate. Chapter Six will evaluate the weaknesses of CRSMAS and propose modifications to it. . Abdul Samad Shibghatullah 131 30052008 Chapter Six: Approach Analysis and the Modifications to CRSMAS

6.1 Introduction