Schedule Analysis and Optimization for Dinky Service

Table 9: New Schedule for Dinky and the corresponding waiting time

The new schedule reduces not only the waiting time but also its variance. Here is the statistical result of the new waiting time of four different routes. All the means have been reduced by at least 4 minutes compared with the original schedule.

	from New York to Princeton	from Princeton to Trenton	from Trenton to Princeton	from Princeton to New York
Mean(unit: min)	7.96	8.59	11.38	9.69
Median(unit:min)	5	6	12	8.5
var(unit:min^2)	36.54	58.41	73.23	38.99

Table 10: Statistical result of the new waiting time

Fig 32: Scatter plot of Wait time for trains from NY to Princeton	Fig 33: Scatter plot of Wait time for trains from Princeton to Trenton
Fig 34: Scatter plot of Wait time for trains from Trenton to Princeton	Fig 35: Scatter plot of Wait time for trains from Princeton to NY
The following figures show the improvements of the new schedule.

• 
  The Second Scenario: Cases of cancellation and delay.
  

The demand responsive schedule can perform much better than a fixed time schedule when the corresponding trains are cancelled or delayed since the demand responsive schedule can change the time Dinky departures so that even the train has some problem Dinky can still make passengers catch the train without waiting a long time. Dinky can operate under the information about the NEC trains given by Trenton Station and New Brunswick Station. From the observation during the data collection period, generally, the station can be informed of the information about cancellation and delay around 5 minutes behind the schedule time, which can make Dinky operators have more than 15 minutes to decide whether to send a Dinky or not.

There are several operating rules suggested for Dinky operation:

• 
  For general delay of NEC trains, operate Dinky under the fixed time schedule and make minor changes with the help of trains information given by the two stations.
  
• 
  If the delay time is known:
  

1. 
   If the time duration between two trains from different direction is shorter than 10 minutes, send the Dinky before the arrival of the first train and get back after the arrival of the other train.
   
2. 
   If the time duration between the two trains of are longer than 30 minutes.
   

1. 
   If the first train is from Trenton to New York, send the Dinky for both trains.
   
2. 
   If the first train is from New York to Trenton, send the Dinky for the second train only.
   

• 
  If the delay time is unknown:
  

1. 
   Since most passengers from Princeton is to New York, so make sure all the Dinkys arrive earlier than the arrival of trains from Trenton to New York. Send a Dinky from Princeton to Princeton Junction when the delayed train has stopped at the NB station and Trenton station, which can leave around 5 minutes for passengers on Dinky to catch the train.
   
2. 
   The trains at night receive passengers go back from New York, so let the Dinky wait for the trains from New York at Princeton Junction during the night time.
   

• 
  If trains has been cancelled:
  

1. 
   Do not send Dinky to Princeton Junction if trains from both directions have been cancelled.
   
2. 
   Operate under the fixed time schedule if only trains from one direction have been cancelled.
   

Future Work

1. 
   Function of Wait time
   

Passengers have different reactions and feelings to different ranges of wait time. Generally speaking, passengers are more anxious if they have to wait for more than 30 minutes but they do not feel much difference between a 2-minute-wait-time and a 5-minute-wait-time. So it is more important to reduce the long wait time in the schedule. In order to reflect the feelings into the analysis of the performance of the schedule and the improvements, it is suggested to build a function of wait time which is the multiplication of wait time and the scale of anxiety related to the wait time. The scale may be a step function or a exponential function, which needs more survey about passengers.

2. 
   Simulation of different type of operating policy
   

There are many different kinds of operating policies for Dinky, for example, to use a fixed schedule or to follow a demand responsive schedule or to combine the two schedules together. In order to test the performance of these policies, a simulation model may be built and use the probability of cancellation or delay, travel time, arrival reliability and train schedule as input. The simulation model can help to find out which policy is the best.

Appendix 1: Waiting time of each type

Dinky			NEC	Wait Time		NEC	Wait Time
Depart Princeton	Arrive PJCT (fr Princeton)	Depart PJCT (to Princeton)	Arrive PJCT (fr NY/New Brnwk)	For next Dinky: fr NY to Princeton	Fr Previous Dinky To Trenton	Arrival PJCT (Fr Trenton )	For next Dinky: fr Trenton to Princeton	Fr Previous Dinky To NY/New Brnwk
		4:50				4:45	5
5:00	5:05	5:12
5:25	5:30	5:39	5:32	7	2	5:10	2	5
						5:19	20	14
5:55	6:00	6:09	6:03	6	3	5:37	2	7
						6:05	4	5
6:25	6:30	6:42	6:39	3	9	6:15	27	15
						6:27	15	27
						6:39	3	9
6:52	6:57	7:07				7:01	6	4
7:17	7:22	7:27	7:12	15	15	7:14	13	17
7:47	7:52	7:57	7:36	21	14	7:27	0	5
						7:32	25	10
						7:42	15	20
8:12	8:17	8:30	8:24	6	7	8:02	28	10
						8:12	18	20
						8:23	7	6
8:53	8:58	9:09	9:02	7	4	8:41	28	24
						9:04	5	6
9:19	9:24	9:32	9:25	7	1	9:17	15	19
						9:29	3	5
9:52	9:57	10:04	9:39	25	15	10:03	1	6
			9:48	16	24
			9:57	7	0
10:17	10:22	11:04	10:23	41	1
			10:51	13	29	10:29	35	7
11:15	11:20	11:27	11:20	7	0	11:07	20	45
11:50	11:55	12:00	11:46	14	26	11:30	30	10
12:17	12:22	12:27	12:17	10	22	12:05	22	10
12:46	12:51	12:59	12:51	8	0	12:32	27	10
13:14	13:19	13:26	13:19	7	0	13:01	25	10
13:47	13:52	14:02	13:52	10	0	13:28	34	9
14:16	14:21	14:26	14:17	9	25	14:03	23	11
14:45	14:50	14:56	14:51	5	1	14:27	29	6
15:18	15:23	15:28	15:21	7	31	14:58	30	8
15:44	15:49	16:00	15:55	5	6	15:31	29	8
						15:55	5	6
16:13	16:18	16:25	16:20	5	2	16:16	9	27
16:37	16:42	16:47	16:39	8	21	16:40	7	22
17:05	17:10	17:16	16:58	18	16	16:47	0	5
			17:07	9	25	17:00	16	18
17:42	17:47	17:57	17:43	14	33	17:16	0	6
			17:52	5	5
18:09	18:14	18:19	18:10	9	23	18:02	17	15
18:31	18:36	18:41	18:27	14	13	18:29	12	15
			18:36	5	0
18:51	18:56	19:03	18:48	15	12	18:51	12	15
			18:56	7	0
19:13	19:18	19:23	19:13	10	17	19:21	2	3
19:34	19:39	19:44	19:38	6	20
19:56	20:01	20:15	19:57	18	18	19:58	17	19
			20:07	8	6
20:25	20:30	20:40	20:35	5	5
20:52	20:57	21:15	20:58	17	1	20:45	30	15
			21:08	7	11
			21:26	19	29	21:22	23	25
			21:42	3	45
21:55	22:00	22:20	22:15	5	15	22:04	16	4
22:35	22:40	22:52	22:47	5	7
23:05	23:10	23:28	23:23	5	13	23:16	12	6
23:50	23:55	0:06	23:48	18	38	0:01	5	6
0:16	0:21	0:32	0:27	5	6
0:58	1:03	1:17	1:12	5	9	1:12	5	9
1:27	1:32
1:27