Calculate the space mean speed

Assignment Help Basic Statistics

Reference no: EM133803156

Assignment: Traffic Flow & Statistics

I. Speed, Statistics and Traffic Flow Parameters

Spot speeds were collected on a highway for 100 vehicles during a 10 minute period, as shown in Table 1 below. Use this data to do the following:

1. Calculate the time mean speed (arithmetic mean).

2. Calculate the standard deviation.

3. Determine the median.

4. Determine the mode.

5. Calculate the space mean speed. To do this, assume that all vehicles were traveling at a constant speed.

6. Estimate the hourly flow rate. Express your answer in vehicles per hour.

7. Using your answers to the two previous parts (5 and 6), estimate the density. Express your answer in vehicles per mile.

Table 1: Spot Speeds Observed During a 10-Minute Period (mph)

61	54	67	69	58	62	57	61	63	55
60	75	58	54	57	60	71	65	57	51
69	69	59	54	60	67	58	46	53	59
62	54	58	68	66	59	57	64	58	52
61	65	61	65	58	57	65	47	64	54
68	59	59	62	57	66	67	58	64	60
59	59	63	56	62	64	59	57	61	52
58	57	64	51	65	55	63	45	65	57
73	61	67	62	48	62	57	60	73	53
58	52	65	61	67	62	76	71	71	58

II. Greenshield's Model

A section of highway is known to have a free-flow speed of 55 mph and a capacity of 4,125veh/hr. Assume the flow-density-speed relationship is described by Greenshield's model.

1. Estimate the jam density (in units of veh/mile).

2. Using your answer from the previous part (a), write out Greenshield's linear model for speed (u) and density (k). Your answer should be in the form of an equation including variables u and k.

3. Using your answers from the previous two parts (a,b), write out Greenshield's model relating flow (q) and density (k). Your answer should again be in the form of an equation including variables q andk.

4. Using your answers from the previous parts (a,b,c), write out Greenshield's model relating flow (q) and speed (u) Your answer should again be in the form of an equation including variables q and u.

5. You conduct traffic counts for 1 hour on this road and observe 2,200 vehicles at a specified point on the highway during that time. Using your answers to the previous question, estimate the space mean speed of these 2,200 vehicles. Note: there is more than one answer.

III. Traffic Flow Regression

Table 2 summarizes observations conducted through time-lapse photography on a highway.

Table 2: Speed and Density data

Speed (MPH)	56	59	48	58	38	52	39	35	28	36	36	28
Density (Veh/mi)	28	28	36	30	40	33	42	55	64	45	44	69

1. In Excel (or another software program of your choice), plot speed vs. density and estimate a best-fit line. Please put speed on the y-axis. Include your density-speed plot in the PDF of your homework (you can simply cut-and-paste the graph). Also, please write out your final best fit line equation.

From the equation developed using software, calculate the following:

2. Free flow speed

3. Jam density

4. Capacity (i.e., maximum flow)

IV. Deterministic Queuing

Vehicles arrive at a single toll booth beginning at 8:00 A.M. They arrive and depart according to a uniform deterministic distribution. The toll booth does not open until 8:10 A.M. The arrival rate is 6veh/min, and the departure rate is 8veh/min. Answer the following questions:

1. Sketch the queuing diagram showing the number of arrivals and the number of departures. Plot time (in minutes) on the x-axis and vehicles on the y-axis.

Note: you only need to show the morning period when a queue forms.

2. When does the initial queue clear?

3. What is the total delay? Express your answer in vehicle-minutes.

4. What is the average delay per vehicle (in minutes)?

5. What is the longest queue length (in vehicles)?

6. What is the wait time (in minutes) of the 100th vehicle to arrive (assuming first-in-first-out)?

V. Poisson

Vehicles arrive at an intersection at a rate of 300 veh/h according to a Poisson distribution. What is the probability that more than five vehicles will arrive in a 1-minute interval?

Reference no: EM133803156

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