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Level . Intermediate Schedule Building Chapter 3. Schedule Building When evaluating alter- Tip 3.2 A Slightly More Intricate Schedule nate scheduling frequen- cies on a route, always recalculate Let's continue from where we left off. Again we assume you are building the sched- the round trip cycle time and check LEVEL ule in the spreadsheet, but many of the approaches carry over into computerized the efficiency of the headway against the cycle. You may find that 2A scheduling. Suppose you have done a fabulous job of constructing this schedule, just as a good scheduler should, and you have beaten the cost estimate contained you can increase service by making in the operating budget. There is enough funding left over to provide additional the cycle more efficient. peak hour service. Peak hours have been defined for us as : : AM and : : PM ( : : ). Running "hot" or ahead Tip We have some options. (We generally do...that is what makes scheduling seem so daunting for of schedule is a much new schedulers.) We could provide a -minute service, which would double the service of the more serious problem for riders than running behind schedule. The existing schedule, or we could go from our present - to a -minute headway, an approxi- timetable is essentially a "contract" mate % increase in service. Of course, we could provide even better peak service than between the passenger and the minutes. Since our remaining service budget is not unlimited, we want to look at both options. transit system that promises that if This is a very typical task asked of schedulers--"how much will it cost for this frequency, that the passenger arrives at the stop frequency, or span of service?" on time the bus will be there to Back again to our old friend the Round trip Cycle. To refresh our memory, the minimum ac- pick them up. Leaving a stop early ceptable cycle (round-trip running time of minutes plus the prescribed minimum layover) is means that passengers who arrive minutes. To provide a -minute service, look at how multiples of work with that cycle: at the stop on time may have to wait more than an entire headway , , , , etc. A cycle of would yield layover of minutes, which is %. Therefore, for the bus to come. an increase to minute service would require one more bus (for a total of four-- minutes divided by the -minute headway) in the cycle. For a -minute headway we need to look at multiples of : , , , , , , etc. A - minute cycle would allow for layover of nine minutes, which is acceptable under our contrac- tual requirements (or operating practices, if there is no provision in the contract). But the real question is whether, knowing the practical conditions of traffic congestion and operating time variability, nine minutes of layover every minutes is enough to reasonably guarantee that buses will recover from delays and leave on time for their next trip. A -minute round trip cycle would require buses, one more than the minute headway solution, and more than the initial -minute service proposed. Of course we could also use the -minute base period cycle, which would preserve the minutes or so at each end of the route, but that would be considered excessive if a better alternative were available. 3-19

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Chapter 3. Schedule Building Level . Intermediate Schedule Building Let's now apply a quick rule-of-thumb about costs: the periods of the day when additional split run buses would operate total about seven hours (two three-hour periods during the morning and A run containing two or more pieces afternoon peak periods plus the in and out deadhead time). So, a -minute peak headway of work separated by a break over would add seven hours, while a -minute peak would add (seven hours x buses). Apply one hour in length. Also known as your system's cost per hour to that and you get a reasonably accurate cost estimate even be- a "swing run." At some systems, fore you start building (or in our case, revising) your schedule--again the point of knowing the three-piece split runs are allowed, outcomes before any real schedule writing is undertaken. but one of the breaks (or "swings") is usually paid whereas in two-piece Which do you choose? The ideal choice is the option that provides the greatest amount of split runs the break is generally not service for which funding is available. But transit systems face the economic problem of unlim- paid. Split runs tend to be used to ited wants and limited resources. Therefore we do not want to commit more resources than allow both peaks to be covered by justified either by the known or the projected ridership--service standards, or your service one operator since the work day planners, will be able to assist in making this decision. Then too, there is the concern that peak would otherwise be too long for a hour buses add to the inefficiency of the schedule in that they require equipment that only gets straight run. used for part of the day. They could potentially make for a less efficient runcut, increasing the number of split runs that will have to be built or ultimately winding up as pieces that cannot be pieces worked into a full run. As you can see, the scheduler is torn between these two positions. Portions of a run, especially distinct In this particular case, the decision has been made to go with the -minute service, as the sys- portions separated by a break. tem can afford it and it offers a better connection strategy with other routes that operate on a -minute headway (at a -minute headway, this route would miss one of two hourly connec- two-piece run tions with other -minute routes--this is not a minor consideration). Remembering our round trip cycle calculation, five buses would give us a -minute cycle (we need a minimum of ) A run made up of two pieces of while six buses would take us to the same -minute cycle that we currently use during the day work separated by an interval of for our -minute service. There is no question here. Five buses work within our minimums. We time. The pieces will usually be do not need all of the layover we currently apply in the base period. We would cut that down if on different blocks and may be on we could. different routes. To create the schedule, we simply insert a few rows during the peaks and add in the extra trips three-piece run between the schedules--right? A run made up of three pieces of But wait. It is not quite as easy as that. You can fill in-between trips eastbound beginning with work separated by two intervals of the blank row after : under time point "A." Continue until you reach the : trip. This will time. Generally, one of the intervals add new trips beginning at : and continuing at : and : up to : . That will meet the in a three-piece run is paid time. criteria we set for the AM peak period. Beginning with the : trip, we resume our -minute service and can leave these trips just as we wrote them on the first iteration of the schedule. We can do this also for the PM peak period. We add trips between the : and : trips, giving us a solid -minute service for this three hour period, as shown on the following page: 3-20

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Level . Intermediate Schedule Building Chapter 3. Schedule Building Even if your system Tip 1 Example Headway Sheet #2 does not have a required 2 ROUTE 97 Broad Street amount of layover, always ask 3 DAY Weekday yourself whether the route can 4 Eastbound Westbound 5 Block # Pull Out A B C D D C B A Next Trip Pull In be expected to run on time given 6:00 traffic conditions and a designated 63 5:55 6:15 6:26 6:40 6:48 7:00 amount of layover. 6:30 71 5:50 6:00 6:08 6:22 6:33 6:45 6:56 7:10 7:18 7:30 6:15 7:00 82 6:20 6:30 6:38 6:52 7:03 7:15 7:26 7:40 7:48 8:00 6:45 7:30 93 7:00 7:08 7:22 7:33 7:45 7:56 8:10 8:18 8:30 7:15 8:00 10 1 7:30 7:38 7:52 8:03 8:15 8:26 8:40 8:48 9:00 AM peak period 11 2 7:45 8:00 8:08 8:22 8:33 8:30 8:45 8:56 9:10 9:18 9:30 The period in the morning when the 8:15 9:00 12 3 8:30 8:38 8:52 9:03 9:15 9:26 9:40 9:48 10:00 greatest level of service is provided, 8:45 typically 6 to 9 AM. 13 1 9:00 9:08 9:22 9:33 9:45 9:56 10:10 10:18 10:30 14 2 9:30 9:38 9:52 10:03 10:15 10:26 10:40 10:48 11:00 15 3 10:00 10:08 10:22 10:33 10:45 10:56 11:10 11:18 11:30 PM Peak period 16 17 1 2 10:30 11:00 10:38 11:08 10:52 11:22 11:03 11:33 11:15 11:45 11:26 11:56 11:40 12:10 11:48 12:18 12:00 12:30 The period in the afternoon when 18 3 11:30 11:38 11:52 12:03 12:15 12:26 12:40 12:48 13:00 19 1 12:00 12:08 12:22 12:33 12:45 12:56 13:10 13:18 13:30 the greatest level of service is 20 2 12:30 12:38 12:52 13:03 13:15 13:26 13:40 13:48 14:00 provided, typically 3 to 7 PM. 21 3 13:00 13:08 13:22 13:33 13:45 13:56 14:10 14:18 14:30 22 1 13:30 13:38 13:52 14:03 14:15 14:26 14:40 14:48 15:00 23 2 14:00 14:08 14:22 14:33 14:45 14:56 15:10 15:18 15:30 24 3 14:30 14:38 14:52 15:03 15:15 15:26 15:40 15:48 16:00 25 15:30 1 15:00 15:08 15:22 15:33 15:45 15:56 16:10 16:18 16:30 26 15:15 16:00 2 15:30 15:38 15:52 16:03 16:15 16:26 16:40 16:48 17:00 27 15:45 16:30 3 16:00 16:08 16:22 16:33 16:45 16:56 17:10 17:18 17:30 28 16:15 17:00 1 16:30 16:38 16:52 17:03 17:15 17:26 17:40 17:48 18:00 29 16:45 17:30 2 17:00 17:08 17:22 17:33 17:45 17:56 18:10 18:18 18:30 30 17:15 18:00 3 17:30 17:38 17:52 18:03 18:15 18:26 18:40 18:48 19:00 31 17:45 32 1 18:00 18:08 18:22 18:33 18:45 18:56 19:10 19:18 19:28 33 2 18:30 18:38 18:52 19:03 19:15 19:26 19:40 19:48 19:58 34 3 19:00 19:08 19:22 19:33 19:53 3-21

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Chapter 3. Schedule Building Level . Intermediate Schedule Building Slipping and Sliding slipping and sliding We mentioned the possibility of wanting to "slip or slide" trips before we filled in intermediate The process of shifting one or more times. Basically the term relates to moving the trips in one or both directions. We might want trips forward or backward in time to to do this for the following reasons: achieve a specific purpose. Also known as "trip shifting." To give more or less layover at one end of the route due to operational reasons, such as the lack of a decent place to park a bus To adjust an intermediate time for a particular reason, such as a positive meet with peak vehicles another route The maximum number of vehicles To meet school bell times (in which case we might want to move only one or two trips) required to operate the route at the required headway. Quickly Revising this eastbound direction was simple. But this was done without regard to blocking calculated as: cycle time divided by impacts (remember we said--know the answer before you get into the detailed schedule writ- headway. Also referred to as "peak ing). Our previous schedule pattern had minutes of layover at either end, and now we have vehicle requirement." decided that a total of minutes per round-trip is going to be applied. base vehicles We have minutes of running time within a -minute window ( x -minute headway). We can divide the layover equally between both terminals or give more or most to one terminal. The number of vehicles required to It is not wise to give none at all, because that provides no relief valve for late arriving buses. operate the route at the required Since this is a theoretical schedule and we really do not know the traffic conditions at Terminal headway during the base period. Quickly calculated as: cycle time in A versus D, we can pretty much decide our own strategy. So the westbound trips are going to the base period divided by headway have to move to accommodate the smaller layover we have planned. This is part of the process in the base period. Also referred we call slipping and sliding. to as "base period vehicle require- Effectively we are revisiting the schedule pattern to decide how the peak will work. This raises ment." an important consideration in developing schedules--that the peak schedule pattern may be different from the off-peak schedule pattern. Why? There may be several reasons, including: Different frequencies, a regular occurrence since the bulk of travel is during peak times. Different running times during the day. Running times may change several times dur- ing the day to take into account different operating speeds due to congestion, loads, or other factors. In this example, we continue to assume constant running times all day. The need to have specific departure times at specific times of day, i.e., to connect with other service or modes whose schedules change at a certain time. To adjust the blocking, perhaps to schedule with less layover during the peaks (to mini- mize peak vehicles), but to allow more time in the off peak where resources aren't at such a premium. 3-22

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Level . Intermediate Schedule Building Chapter 3. Schedule Building Some agencies com- In this case we have decided that our preference would be to give three minutes at "D" as the Tip bine operator rest time "away" terminal and the remaining six at "A." Three provides the buffer we are looking for. Re- ("layover") with time to get back on member that we have done a bang-up job of calculating the running time for accuracy, so we schedule ("recovery") and others are only concerned with providing that extra buffer for conditions beyond the ordinary. The six have separate standards and con- minutes at "A" provide a more reasonable time for the operator to get off the bus and stretch tract rules for each. Know the rules his/her legs. of your agency before you begin to schedule! We have also decided that we want to keep our existing : and : eastbound departure times (assuming in this case we have a connection we want to make at "A"). Following this strategy means we will have to slide our existing westbound trips earlier by nine minutes, so that the : trip arriving at : will now leave at : instead of the present : . All of this can be looked at as we develop our schedule patterns sheet, which for the AM peak now looks like the following: A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 Eastbound Westbound 5 Block # Pull Out A B C D D C B A Next Trip 8 3 5:50 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 During the peaks this becomes a -minute repeating schedule pattern. So again our first bus gets back to make the : departure, giving a -minute cycle. Or to prove the theory, we will need buses for the : , : , : , : and : eastbound departures ( in all). Some of the above could have been carried out a little differently in some computerized sched- uling systems. For example the ability to drag trips along a time distance graph can visually represent the process of creating or altering schedule patterns. It's pretty simple--move the trip until you see it "fit" into the linkup. Typically this should be done with one round-trip, effec- tively recreating the schedule pattern procedure anyway, before rebuilding the schedule. 3-23

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Chapter 3. Schedule Building Level . Intermediate Schedule Building Refining the Schedule Now we fill out the rest of the trips to meet the intended schedule pattern--departures from "A" at : , : , : & : ; departures from "D" at : , : , : & : in the peaks, but keeping midday the same: A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 Eastbound Westbound 5 Block # Pull Out A B C D D C B A Next Trip 6 6:06 6:17 6:31 6:39 6:45 7 6:21 6:32 6:46 6:54 7:00 8 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 9 6:15 6:23 6:37 6:48 6:51 7:02 7:16 7:24 7:30 10 6:30 6:38 6:52 7:03 7:06 7:17 7:31 7:39 7:45 11 6:45 6:53 7:07 7:18 7:21 7:32 7:46 7:54 8:00 12 7:00 7:08 7:22 7:33 7:36 7:47 8:01 8:09 8:15 13 7:15 7:23 7:37 7:48 7:51 8:02 8:16 8:24 8:30 14 7:30 7:38 7:52 8:03 8:06 8:17 8:31 8:39 8:45 15 7:45 7:53 8:07 8:18 8:21 8:32 8:46 8:54 9:00 16 8:00 8:08 8:22 8:33 8:36 8:47 9:01 9:09 17 8:15 8:23 8:37 8:48 8:51 9:02 9:16 9:24 9:30 18 8:30 8:38 8:52 9:03 9:06 9:17 9:31 9:39 10:00 19 8:45 8:53 9:07 9:18 20 9:00 9:08 9:22 9:33 9:45 9:56 10:10 10:18 10:30 21 9:30 9:38 9:52 10:03 10:15 10:26 10:40 10:48 11:00 22 10:00 10:08 10:22 10:33 10:45 10:56 11:10 11:18 11:30 23 10:30 10:38 10:52 11:03 11:15 11:26 11:40 11:48 12:00 24 11:00 11:08 11:22 11:33 11:45 11:56 12:10 12:18 12:30 25 11:30 11:38 11:52 12:03 12:15 12:26 12:40 12:48 13:00 26 12:00 12:08 12:22 12:33 12:45 12:56 13:10 13:18 13:30 Transitioning Besides round trip cycles (and accuracy, of course), the most interesting concept to introduce to a new scheduler is transitioning. Transitioning involves the smoothing of the change in head- way, running time, or both. On our first schedule we had the same running time and headway all day, so transitioning was not a factor. This second schedule adds the complication of chang- ing from a -minute during the AM peak to a -minute in the midday, back to a -minute in the PM Peak and finally back to a -minute headway during the course of an operating day. The next section will introduce a schedule with variable running time. Learning to smooth these changes is an integral part of being able to develop quality schedules. 3-24

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Level . Intermediate Schedule Building Chapter 3. Schedule Building Transitioning allows For our current schedule, we want to review how well we have handled these headway transi- Tip service to ease into a tions. First, look at the end of the AM peak. Notice that eastbound, we abruptly stop providing new schedule pattern as demand a -minute service and go directly into a . On a smaller or lighter route, one where policy changes gradually over the service headways are driving the service strategy, this is perfectly acceptable. If we were driven by day. demand, there might be a period where the headways would widen (service would reduce) maybe to a , then a -minute headway. However, the service policy is the deciding factor in this case, so we go to the base as soon as our service plan tells us to do so. The westbound side is not so cut and dried, because the leaving times changed to accommo- date the five-bus round trip cycle layover scheme. As the schedule shows, we shift back to the : /: leave times as we transition out of the peak. Notice that we go from : to : , which is a -minute headway. That headway is a combination of the - and a nine-minute adjust- ment in order to get the westbound trips onto our three-bus base cycle. It would have been easy to make the next trip : , continuing the -minute headway. But the next trip at : would have been minutes later, which is not acceptable when a -minute headway is called for. A similar shift is made going into the PM peak westbound. We move what normally would have been the : trip up (forward) by nine minutes to become the : and the start of our : , : , : and : leaving strategy which puts layover times where we decided earlier we wanted them. You can make these transitions work for you or against you; it is a matter of learning how to do the former. There is no one rule that works every time, because every transition is dif- ferent. But a good scheduler always studies a headway (or running time) transition to see the result. If the result yields a wider headway than you are planning to operate after the change, then you need to look at shifting an earlier trip. In this example, we didn't want to go from a to a . We could go from a , to a , to a , which is progressively widening the headway. The same situation in reverse is true for shortening the headway going into the PM peak. This is a simple example of transitioning, but its principles hold true even in the most complex schedule. A slightly different approach to the transition from peak to off-peak (and again back to peak) would be to provide a consistent set of departure times westbound throughout the day. This leaves us with a decision--at a -minute headway do we choose : /: or : /: eastbound, and : /: or : /: westbound? Which to choose may depend on any other connections, at what time you transition to the off peak, or just a general preference. Either would work. In our case we choose : /: eastbound and : /: westbound. This maintains the minutes 3-25

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Chapter 3. Schedule Building Level . Intermediate Schedule Building of layover per round-trip, and the three off-peak buses. In effect we have revisited the off-peak schedule entirely to keep consistent departure times with the peaks. The off-peak schedule pattern now looks like this: A B C D E F G H I J K L M 1 Example Headway Sheet #2 2 ROUTE 97 Broad Street 3 DAY Weekday 4 Eastbound Westbound 5 Block # Pull Out A B C D D C B A Next Trip 20 9:00 9:08 9:22 9:33 9:36 9:47 10:01 10:09 10:30 Note that one disadvantage of this approach is that the layover time at point A is now min- utes. Many schedulers would be uncomfortable with this amount of layover, and might choose the first approach to avoid a long layover at one point. Others might tolerate it for the sake of consistent departure times. Now we simply build the schedule according to the schedule pattern. If your formulas are correct (and of course they are!), all intermediate end times will simply adjust. And departure times can be calculated simply by changing the multiplier (or the minutes, if you are using the time function) to (i.e., the trip start time is the previous time plus minutes) during the peaks. For the PM peak begin the -minute schedule at : eastbound and : westbound and continue until the : / : trip. Look at your next trips. They should be six minutes after the arrival time at Point A. Go ahead and add in your Next Trip times for the whole sheet. The final schedule for -minute peak service on Route under this approach is shown on the next page. As for our simple schedule, the use of a computerized scheduling package will make the re- generation of the schedule much simpler and less prone to error. In this case you could simply delete the westbound trips all at once, keep the existing eastbound, add the new eastbound peak trips, and regenerate the entire westbound schedule, all with relative ease. Use of time/distance and other graphics contained in computerized systems allows a good visual representation of transitioning. Computerized systems also allow the impacts of altered transitioning approaches to be seen immediately (e.g., breaking planned hooks or increasing the number of buses). 3-26

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Level . Intermediate Schedule Building Chapter 3. Schedule Building Transitioning allows Tip service to ease into a 1 Example Headway Sheet #2 new pattern, generally matching 2 ROUTE 97 Broad Street service to demand which often 3 DAY Weekday 4 Eastbound Westbound changes more gradually over the 5 Block # Pull Out A B C D D C B A Next Trip Block Pull In service day. 6 6:06 6:17 6:31 6:39 6:45 7 6:21 6:32 6:46 6:54 7:00 8 6:00 6:08 6:22 6:33 6:36 6:47 7:01 7:09 7:15 9 6:15 6:23 6:37 6:48 6:51 7:02 7:16 7:24 7:30 10 6:30 6:38 6:52 7:03 7:06 7:17 7:31 7:39 7:45 11 6:45 6:53 7:07 7:18 7:21 7:32 7:46 7:54 8:00 12 7:00 7:08 7:22 7:33 7:36 7:47 8:01 8:09 8:15 13 7:15 7:23 7:37 7:48 7:51 8:02 8:16 8:24 8:30 14 7:30 7:38 7:52 8:03 8:06 8:17 8:31 8:39 8:45 15 7:45 7:53 8:07 8:18 8:21 8:32 8:46 8:54 9:00 16 8:00 8:08 8:22 8:33 8:36 8:47 9:01 9:09 17 8:15 8:23 8:37 8:48 8:51 9:02 9:16 9:24 9:30 18 8:30 8:38 8:52 9:03 9:06 9:17 9:31 9:39 10:00 19 8:45 8:53 9:07 9:18 20 9:00 9:08 9:22 9:33 9:36 9:47 10:01 10:09 10:30 21 9:30 9:38 9:52 10:03 10:06 10:17 10:31 10:39 11:00 22 10:00 10:08 10:22 10:33 10:36 10:47 11:01 11:09 11:30 23 10:30 10:38 10:52 11:03 11:06 11:17 11:31 11:39 12:00 24 11:00 11:08 11:22 11:33 11:36 11:47 12:01 12:09 12:30 25 11:30 11:38 11:52 12:03 12:06 12:17 12:31 12:39 13:00 26 12:00 12:08 12:22 12:33 12:36 12:47 13:01 13:09 13:30 27 12:30 12:38 12:52 13:03 13:06 13:17 13:31 13:39 14:00 28 13:00 13:08 13:22 13:33 13:36 13:47 14:01 14:09 14:30 29 13:30 13:38 13:52 14:03 14:06 14:17 14:31 14:39 15:00 30 14:00 14:08 14:22 14:33 14:36 14:47 15:01 15:09 15:15 31 14:30 14:38 14:52 15:03 15:06 15:17 15:31 15:39 15:45 32 15:21 15:32 15:46 15:54 16:00 33 15:00 15:08 15:22 15:33 15:36 15:47 16:01 16:09 16:15 34 15:15 15:23 15:37 15:48 15:51 16:02 16:16 16:24 16:30 35 15:30 15:38 15:52 16:03 16:06 16:17 16:31 16:39 16:45 36 15:45 15:53 16:07 16:18 16:21 16:32 16:46 16:54 17:00 37 16:00 16:08 16:22 16:33 16:36 16:47 17:01 17:09 17:15 38 16:15 16:23 16:37 16:48 16:51 17:02 17:16 17:24 17:30 39 16:30 16:38 16:52 17:03 17:06 17:17 17:31 17:39 17:45 40 16:45 16:53 17:07 17:18 17:21 17:32 17:46 17:54 18:00 41 17:00 17:08 17:22 17:33 17:36 17:47 18:01 18:09 42 17:15 17:23 17:37 17:48 17:51 18:02 18:16 18:24 18:30 43 17:30 17:38 17:52 18:03 18:06 18:17 18:31 18:39 19:00 44 17:45 17:53 18:07 18:18 45 18:00 18:08 18:22 18:33 18:36 18:47 19:01 19:09 3-27

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Chapter 3. Schedule Building Level . Intermediate Schedule Building Finishing Up Now review your schedule. Does this give us -minute service for the whole of the peak period as defined earlier? Is the transition from peak to off-peak and back again the way we want it? If so, we have achieved the results we planned for in our schedule pattern-building exercise. As with the first schedule, take time to look over all aspects of the schedule for completeness and to catch any obvious errors--those things that have changed (or maybe you have failed to change) as the result of the adjustments introduced from the original schedule. That should do it. We now have another schedule ready for the blocking process. 3-28

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Level . Intermediate Schedule Building Chapter 3. Schedule Building LEVEL End of Intermediate Schedule Building, Part A 2A Intermediate Schedule Building, Part B continues on the next page. To jump to Schedule Blocking, go to page - . 3-29