serv


Table of Contents

I. The System1

II.Objective3

III.Scope and Limitation3

IV.The Causal Loop Diagram3

Building the Diagram4

V.Simulation7

VI.Results and Analysis8

2 Queues 9

3 Queues 10

4 Queues 12

5 Queues 13

6 Queues 14

Over-all Analysis 16

VIII.Recommendations 17

The System

TheManila Light Rail Transit System (LRT) is a metropolitan rail system serving millions of people every day in Metro Manila. The LRT consists of two lines: Line 1 or the Yellow line, which currently runs south-north from Baclaran in Pasay City to North Avenue station in Quezon City, and Line 2 or the Purple line, which is connected to the first line through Doroteo Jose and runs east-west from Recto in Manila to Santolan station in Marikina City. The transit system is operated and managed by theLight Rail Transit Authority(LRTA), a government-owned and controlled corporation under the authority of theDepartment of Transportation and Communications (DOTC). The LRT is part of a bigger system, the Strong Republic Transit System (SRTS) along with two other transit systems: Manila Metro Rail Transit System(known as MRT or the Blue Line), and thePhilippine National Railways(PNR), as seen in Figure 1.

According to 2009 data, the LRT serves roughly 579,000passengers each day through the two lines, 31 stations, along over 31kilometers of mostly elevated track. The original LRT Line1 was built as a no-frills means of public transport and lacks some features and comforts, but the new LRT Line2 has been built with additional standards and criteria in mind likebarrier-freeaccess. New trains have been added especially in the Line 1 to support the growing number of people that uses the trains as their first choice of mode of transportation. Security guards are positioned at each station to conduct inspections and provide assistance for the new and the old riders of the transport system. Currently, the LRTA sells reusable plastic magnetic tickets as the pass for the people to be able to ride the trains.

The LRT has been one of the modes of transportation for many passengers, mostly students, aside from road-based public transport such as jeepneys and buses. Although the system aims to reducetraffic congestionin the city as well as the travel times of its passengers, the transportation system has only been partially successful due to the rising number of motor vehicles and rapidurbanization. As time progresses, the management works on improving the system from extending its reach in the north and the south and also the level of service to the public.

Figure 1. Route Map of the Strong Republic Transit System

Objective

For this project, the group intends to find through simulation an optimal train deployment schedule that maximizes the number of passengers per ship but at the same time minimizing costs and waiting time.

Scope and Limitation

The group incorporated the lessons discussed in class to create the simulation as realistic as possible. However, due to the length of time of the course and using Microsoft Excel as the interface, some factors were not considered in the simulation such as human decisions (e.g. walking/running fast upon hearing an incoming train) and interaction between agents (e.g. frustrations during baggage check or during buying tickets.

Furthermore, the group considered the option on creating the simulation on one station, Katipunan station, rather than taking a simulation on the whole LRT system.

The Causal Loop Diagram

The Causal Loop Diagram (CLD), also known as Influence Diagram, is a representation of the cause and effect relationship of variables in the system. It reflects the overall feedback structure of the system.The important part in the CLD is determining the policy variables that will define the system. Basically the diagram is about focusing on the relationship of the variables rather than the parts.

The components or variables for the LRT system are, but not limited to, the following:

(1)weather / power – causes the system some delay in its operation

(2)frequency of train arrivals – affects the number of passengers waiting on platforms of the stations (i.e. more passengers on station platforms when a train gets delayed)

(3)number of deployed trains – affects the waiting time of passengers especially during rush hours where trains are usually jam-packed.

(4)average passengers per trip – the agents of the system

(5)operating costs – costs incurred in the operation of the whole LRT system

(6)price per trip – the amount passengers pay for riding the trains

(7)tendency to try alternative transportation – when inconvenience comes on any mode of transportation

(8)government subsidies – affects the ticket price paid by the passengers

The variables are interconnected with arrows as well as a positive and negative sign which denotes the positive or negative effect of causal variable to the target variable. In addition to that, loop polarities, determined as product of polarities, defines the overall behaviour or growth between the variables within a loop.

Building the Diagram

Looking at the variables, the following relationships were concluded:

(1)An increase in the number of deployed trains increases the frequency of train arrivals. In turn, more train arriving means that there will be fewer passengers on station platforms. Lastly, when there are fewer passengers waiting in station platforms then the number of deployed trains should be decreased to minimize operating costs. The overall polarity (product of the gray poles) of the relationship of these three variables is negative as seen in figure 2.

Figure 2. Causal Loop for three variables

(2)Increasing frequency of train arrivals means that more trains are being deployed. Moreover, more deployed trains means that there will be fewer passengers on each trip as seen in Figure 3.

Figure 3. Causal Loop between two pairs of variables

(3)In figure 4, increase in the number of deployed trains also increases the operating costs incurred.

Figure 4. Causal Loop between deployed trains and operating costs

(4)Looking at a bigger loop as in figure 5, in order to compensate for the increase in operating costs then the price per trip should also be increased. But this will cause passengers to choose alternative transport such as buses or jeepneys. In turn, this decreases the number of passengers per trip.

Figure 5. Negative polarity for five variables

(5)Adding external variables such as weather/power and government subsidies then the complete CLD is seen on figure 6. When there’s a power outage or weather disturbance, train deployment is affected. Also, the current price of train fare is low since it is subsidized by the government.

Figure 6. The complete CLD for the LRT System

Simulations

For the simulations, five Excel files are used, each with an increasing number of queues. Each of which is described in the next bullets:

  • 2 Queues – 1 human seller and 1 automatic ticket-vending machine
  • 3 Queues – 1 human seller and 2 automatic ticket-vending machine
  • 4 Queues – 1 human seller and 3 automatic ticket-vending machine
  • 5 Queues – 1 human seller and 4 automatic ticket-vending machine
  • 6 Queues – 2 human seller and 4 automatic ticket-vending machine

In contrast to the pseudo-random density for the usual simulations, since we are testing for the optimal number of queues, it has been decided by the group to choose the worst-possible density, that of 1. Having a density of 1 means that there is always a person coming into the system. This implies that people will just keep on piling-up.

What this does is a form of stress testing, wherein the system is subjected to a certain force, which in this case is represented by the constant entrance of people to the system. This stress testing can result to possible analysis on the optimal number of queues which can accommodate more people into the system at any given time.

Hence, the assumptions made by this group is as follows:

  1. People walk at a constant pace.
  2. People do not overtake each other. Hence, they form queues whenever they are walking through the system.
  3. The density is kept at 1 to subject the system to a stress test.
  4. The main variable is the number of queues. This is changed in the different number of Excel files used. The reason for not having just 1 Excel file lies on the random assignment made for each queue. This is explained in the “Splitting Queues” section of the User Documentation.
  5. People do not balk, jock or renege.
  6. There is no limit to the number of passengers per train.
  7. Time of Operations is from 05:00 to 22:00.

Results and Analysis

The results and analysis section will present the results of the queuing simulations for the 5 Excel files, subject to the constraints set by the assumptions in the previous page. There will be six sections for this part, one for each of the Excel files and one Over-all Analysis.

Ten simulations are to be done in order to minimize the bias of simulations which basically happens when only one or too few simulations are done. Hence, the group decided to do ten simulations, which due to time constraints and the amount of computer power needed, is a good enough number of simulations to generate a quite decent result.

Two tables are to be seen for each of the first five sections. The first table shows ten simulations and the number of passengers per train. The number of passengers are recorded up to the 10th train, although 12 trains are possible in the files. The last row shows the total number of passengers that were able to get on the ten trains altogether.

The second table shows the number of seconds it takes for the queues to get filled up for the very first time. The first row shows the simulation number. The second row shows the queue which gets filled up first. It is numbered 1 through n where n denotes the number of queues. A pre-paragraph explains the designation of each queue number, as to what seller they represent. The next rows show the number of counters it takes for the queues to fill-up for the very first time.

Note also that the speeds of the sellers are random integers. As explained in the User Documentation, the range for the human seller is [3, 8] while the range for the automatic ticket-selling machines is [5,7].

The main conclusion that we wish to arrive at is the optimal number of queues needed.

2 Queues

Table showing the data for ten simulations of the number of passengers for 2 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Train 1 / 29 / 31 / 33 / 31 / 30 / 32 / 31 / 32 / 30 / 38
Train 2 / 142 / 132 / 131 / 143 / 141 / 139 / 140 / 147 / 134 / 147
Train 3 / 132 / 138 / 137 / 142 / 146 / 134 / 140 / 146 / 130 / 132
Train 4 / 140 / 129 / 131 / 131 / 133 / 137 / 138 / 132 / 140 / 132
Train 5 / 141 / 139 / 133 / 132 / 131 / 142 / 126 / 143 / 137 / 140
Train 6 / 133 / 137 / 135 / 137 / 138 / 136 / 143 / 133 / 136 / 148
Train 7 / 147 / 147 / 132 / 128 / 137 / 135 / 136 / 135 / 133 / 135
Train 8 / 136 / 132 / 133 / 136 / 129 / 139 / 139 / 138 / 136 / 137
Train 9 / 142 / 132 / 138 / 130 / 146 / 141 / 139 / 141 / 141 / 143
Train 10 / 139 / 134 / 132 / 144 / 136 / 134 / 126 / 142 / 137 / 143
Total Passengers / 1281 / 1251 / 1235 / 1254 / 1267 / 1269 / 1258 / 1289 / 1254 / 1295

Table showing the data for ten simulations of the first full queue, for 2 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
First Full Queue / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
Queue 1 / 128 / 128 / 128 / 128 / 128 / 128 / 128 / 128 / 128 / 128
Queue 2 / 122 / 122 / 122 / 122 / 122 / 122 / 122 / 122 / 122 / 122

Queue 1 is the designation for the automatic ticket-selling machine while Queue 2 is the designation for the human seller.

Perhaps what’s intriguuing for the case of the 1 queues is that the result for the First Full Queues is constant. The number of times it takes tfor the human seller to be filled up is constant. The same is true for the automatic ticket-selling machine. This can be partially due to the randomization of the queues, which was explained in the User Documentation.

As for the number of passengers that got through, it is evident that an approximate of 1250 people get to ride the ten trains from 11:30 to 12:00, a span of 30 minutes with 10 trains passing-by.

3 Queues

Table showing the data for ten simulations of the number of passengers for 3 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Train 1 / 18 / 28 / 28 / 27 / 25 / 27 / 24 / 22 / 24 / 31
Train 2 / 104 / 124 / 117 / 110 / 111 / 120 / 122 / 118 / 115 / 111
Train 3 / 106 / 110 / 112 / 114 / 106 / 113 / 122 / 113 / 119 / 113
Train 4 / 129 / 112 / 116 / 114 / 119 / 110 / 120 / 110 / 119 / 117
Train 5 / 124 / 115 / 117 / 114 / 115 / 125 / 112 / 114 / 132 / 129
Train 6 / 119 / 112 / 108 / 120 / 113 / 120 / 124 / 117 / 112 / 118
Train 7 / 118 / 114 / 111 / 112 / 124 / 120 / 119 / 113 / 107 / 119
Train 8 / 117 / 109 / 128 / 119 / 116 / 121 / 109 / 110 / 116 / 117
Train 9 / 118 / 126 / 115 / 114 / 107 / 115 / 115 / 109 / 118 / 113
Train 10 / 117 / 113 / 120 / 119 / 117 / 115 / 117 / 141 / 118 / 123
Total Passengers / 1070 / 1063 / 1072 / 1063 / 1053 / 1086 / 1084 / 1067 / 1080 / 1091

Table showing the data for ten simulations of the first full queue, for 3 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
First Full Queue / 1 / 1 / 3 / 1 / 3 / 2 / 3 / 1 / 3 / 3
Queue 1 / 134 / 124 / 170 / 122 / 160 / 170 / 148 / 124 / 138 / 140
Queue 2 / 162 / 126 / 138 / 132 / 140 / 122 / 138 / 156 / 166 / 160
Queue 3 / 142 / 146 / 128 / 152 / 124 / 136 / 132 / 154 / 128 / 126

Queue 1 and Queue 2 are the designations for the automatic ticket-selling machine while Queue 3 is the designation for the human seller.

Looking at the results, half the time, human seller had the most number of full queues. Adding one automatic ticket-selling machine may have slowed down the process. People get to have an additional choice of seller, and this makes the randomization a bit more confusing as seen in the User Documentation.

Perhaps also, since the minimum time for the automatic ticket-selling machine is slower than the minimum of the human seller, compare 5 seconds of the machine to 3 seconds of the human sellerm, could have affected why not the ticket-selling machine is part of the first full queue.

As for the number of passengers, it is also evident that there are less people who were able to ride the ten trains, barelty breaching the 1000 mark. This could be the result of having more queues to choose from. People now have more opportunities to use the ticket-selling machine, and hence have to wait for a minimum of 5 seconds as compared to the human seller where the miniimum wait is only 3 minutes. As people go to the slower queues, then less people get to ride at each train, signalling that in the end, there will also be less people all-in-all who can ride the ten trains.

Note however that in reality, it should be that more queues should give the passengers a chance to hasten up. This is the anomaly in this simulation.

4 Queues

Table showing the data for ten simulations of the number of passengers for 4 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Train 1 / 30 / 28 / 30 / 26 / 29 / 32 / 27 / 27 / 29 / 28
Train 2 / 161 / 148 / 152 / 144 / 144 / 138 / 159 / 159 / 152 / 153
Train 3 / 147 / 154 / 157 / 152 / 169 / 148 / 150 / 157 / 143 / 159
Train 4 / 158 / 146 / 142 / 162 / 163 / 146 / 157 / 156 / 152 / 168
Train 5 / 127 / 152 / 173 / 165 / 138 / 164 / 160 / 154 / 133 / 163
Train 6 / 154 / 157 / 173 / 170 / 159 / 167 / 154 / 152 / 142 / 146
Train 7 / 162 / 155 / 168 / 154 / 152 / 173 / 170 / 158 / 150 / 150
Train 8 / 135 / 156 / 154 / 156 / 163 / 153 / 157 / 168 / 174 / 143
Train 9 / 150 / 146 / 156 / 156 / 149 / 142 / 162 / 161 / 171 / 165
Train 10 / 157 / 160 / 158 / 156 / 147 / 152 / 151 / 156 / 156 / 167
Total Passengers / 1381 / 1402 / 1463 / 1441 / 1413 / 1415 / 1447 / 1448 / 1402 / 1442

Table showing the data for ten simulations of the first full queue, for 4 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
First Full Queue / 1 / 2 / 2 / 4 / 2 / 4 / 2 / 2 / 1 / 4
Queue 1 / 130 / 158 / 142 / 204 / 142 / 200 / 176 / 244 / 134 / 156
Queue 2 / 182 / 126 / 122 / 292 / 122 / 128 / 134 / 130 / 156 / 162
Queue 3 / 240 / 138 / 292 / 150 / 128 / 144 / 136 / 140 / 194 / 188
Queue 4 / 140 / 166 / 160 / 132 / 226 / 124 / 140 / 160 / 146 / 130

Queue 1, Queue 2 and Queue 3 are the designations for the automatic ticket-selling machine while Queue 4 is the designation for the human seller.

As compared to 2 queues and 3 queues, the total passengers are now up to 1400 mark. This signifies that the addition of queues worked. Hence, 4 queues may be a good number of sellers, with 1 human seller and 3 automatic ticket-selling machines. In reality, this reflects the general assumption that more queues means more people are getting served at the same time and thefore more people can get on the trains at the same time.

As for the full queues, it is intriguing that even if queues 1, 2 and 3 have the same randomization of waiting time of 5, 6 or 7 seconds, queue 2 appeared the most number of times. Since there’s really not much of a distinction for queues 1, 2, and 3, then this doesn’t matter much. Notice that the appearance of human seller as first queue to fill up is reduced to a third. This signals that it the adding of an additional queue lessens the difference of the human seller with the other three automatic machines.

5 Queues

Table showing the data for ten simulations of the number of passengers for 4 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Train 1 / 22 / 30 / 30 / 24 / 27 / 32 / 30 / 35 / 16 / 29
Train 2 / 198 / 165 / 179 / 163 / 172 / 157 / 170 / 159 / 172 / 169
Train 3 / 186 / 162 / 192 / 193 / 176 / 163 / 198 / 178 / 186 / 192
Train 4 / 181 / 188 / 198 / 192 / 189 / 185 / 197 / 180 / 155 / 193
Train 5 / 193 / 186 / 185 / 169 / 185 / 191 / 188 / 157 / 179 / 184
Train 6 / 188 / 181 / 190 / 185 / 177 / 183 / 169 / 181 / 158 / 194
Train 7 / 186 / 166 / 180 / 177 / 167 / 182 / 151 / 190 / 176 / 198
Train 8 / 199 / 189 / 172 / 192 / 185 / 167 / 193 / 192 / 173 / 180
Train 9 / 188 / 195 / 187 / 187 / 186 / 165 / 173 / 194 / 197 / 175
Train 10 / 186 / 158 / 193 / 189 / 155 / 179 / 181 / 198 / 186 / 190
Total Passengers / 1727 / 1620 / 1706 / 1671 / 1619 / 1604 / 1650 / 1664 / 1598 / 1704

First FULL QUEUE count for each seller, for 5 queues. Note that Queues 1 to 4 are the Automatic ticket-selling machines while Queue 5, designated as 5 is the only humanseller.

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
First Full Queue / 1 / 5 / 5 / 1 / 4 / 5 / 5 / 4 / 3 / 2
Queue 1 / 140 / 158 / 304 / 134 / 180 / 238 / 164 / 246 / 338 / 188
Queue 2 / 174 / 130 / 136 / 200 / 428 / 230 / 280 / 360 / 124 / 126
Queue 3 / 218 / 180 / 176 / 154 / 174 / 138 / 152 / 150 / 122 / 160
Queue 4 / 170 / 150 / 166 / 324 / 122 / 192 / 268 / 128 / 162 / 144
Queue 5 / 150 / 138 / 134 / 202 / 170 / 132 / 122 / 168 / 152 / 200

This is interesting as the number of passengers have increased to 1700, which is a lot more than those with 2 queues, 3 queues and 4 queues. This suggests that with 5 queues, more people can enter the trains at the same time, given that they have more choices. The automatic ticket-selling machines are also effective as an additional seller, albeit having a larger minimum amount of time spent waiting.

For the first full queues, the presence of the human seller again increased. The issue now perhaps is with the randomization. And since we only have 10 simulations, then it is quite not enough for 5 queues to be randomized. Hence, this result is just a fluke. In the end, however, it is good to note that the human seller, with a slower maximum time of 8 seconds as compared to the 7 seconds maximum waiting time for the machines, is still appearing as the first to be filled up.

6 Queues

Table showing the data for ten simulations of the number of passengers for 6 queues

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Train 1 / 25 / 32 / 35 / 24 / 30 / 33 / 33 / 28 / 33 / 29
Train 2 / 181 / 199 / 149 / 209 / 162 / 190 / 170 / 178 / 175 / 170
Train 3 / 187 / 184 / 218 / 196 / 191 / 187 / 193 / 220 / 172 / 203
Train 4 / 200 / 199 / 199 / 181 / 211 / 190 / 220 / 209 / 201 / 190
Train 5 / 194 / 184 / 210 / 192 / 187 / 172 / 197 / 189 / 198 / 178
Train 6 / 185 / 185 / 217 / 226 / 216 / 173 / 206 / 176 / 178 / 183
Train 7 / 180 / 169 / 196 / 167 / 164 / 208 / 195 / 192 / 176 / 171
Train 8 / 189 / 208 / 207 / 197 / 180 / 175 / 160 / 193 / 174 / 195
Train 9 / 181 / 181 / 199 / 170 / 193 / 187 / 199 / 203 / 176 / 197
Train 10 / 177 / 175 / 152 / 190 / 221 / 186 / 174 / 171 / 180 / 158
Total Passengers / 1699 / 1716 / 1782 / 1752 / 1755 / 1701 / 1747 / 1759 / 1663 / 1674

First FULL QUEUE count for each seller, for 6 queues. Note that Queues 1 to 4 are the Automatic ticket-selling machines while Queues 5-6, designated as 5 and 6are the humansellers.

Simulation Number / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
First Full Queue / 5 / 3 / 2 / 6 / 5 / 1 / 5 / 6 / 6 / 5
Queue 1 / 414 / 270 / 140 / 208 / 202 / 142 / 212 / 266 / 240 / 202
Queue 2 / 214 / 212 / 138 / 192 / 310 / 206 / 276 / 364 / 192 / 276
Queue 3 / 304 / 140 / 336 / 154 / 290 / 318 / 272 / 222 / 304 / 260
Queue 4 / 232 / 164 / 338 / 396 / 272 / 266 / 258 / 240 / 232 / 188
Queue 5 / 132 / 248 / 194 / 144 / 132 / 178 / 126 / 180 / 188 / 134
Queue 6 / 180 / 250 / 280 / 126 / 200 / 202 / 192 / 138 / 134 / 144

Adding an additional human seller proved to do nothing much since now, people have to choose from 6 possible queues, which can prove to be too many. The maximum number of people is still at 1700 for the ten trains, which suggests that adding the second human seller did nothing.