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# A dynamically sequenced semaphore controlled on the queue length

IP.com Disclosure Number: IPCOM000124568D
Original Publication Date: 2005-Apr-28
Included in the Prior Art Database: 2005-Apr-28
Document File: 5 page(s) / 166K

IBM

## Abstract

The semaphore was the first device used in order to perform traffic control and actually represents an extremely valid alternative to the policeman presence. Even though in some cases the semaphore may not be enough and the policeman operation becomes needful in order to overcome to the limits that belong to a device that has been thought at the beginning of the past century and obsolete if compared to nowadays requirements.

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A dynamically sequenced semaphore controlled on the queue length

Introduction

This scenario applies to something related to everyday life, though some basic math knowledge is required in order to understand the modeling that has been used in order to both justify and plan the solution described below.

This paper uses a suitable kinematical model in order to define the motion of an average performance car under the following assumptions:

· Any delay since the semaphore green light and the effective start of the vehicle is neglected.
· The acceleration trend try to best emulate the one achieved by a car with automatic gear and is the one represented in Figure 1.
· The speed is upper limited to 50 km/h, which is supposed to be the highest speed that can be reached in the urban area without occurring in a driving ticket, though it depends by the policeman attitude and origin (if the place is close to Naples this limit may rise till 80/90 km/h).

This approach also disregards the dynamical and friction dependant terms in order to avoid any linearity in the model evaluation.

The car velocity time function is defined like

() ()dt t a t v

=

[1],

d is the time that is taken in order to change the gear ratio to the next value, the acceleration can be stated like below:

() ) 2 ( 1

)

where ()

t a stands for the acceleration. Assuming that 0

a t a

+ ∆ ⋅

( 1

a t

t

)

∆ - - ⋅

( 1

0

1

1

d t

t

+

a

∆ - ∆ - ⋅ - ⋅

0

2

t

d

t

=1 t

t

2

t

3

1

2

3

[2]

where ()

t 1 is the step function.

1

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Velocity

60

50

v(t) km/h

40

30

v(t)

20

10

00 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7 7.7 8.4 9.1 9.8 10.5 11.2 11.9 12.6 13.3 14 14.7

Figure 1: Acceleration trend.

Folding [2] in [1], the integration yields to the final velocity trend represented in Figure 2 (the integration has been performed numerically in order to overcome to the difficulties concerned with the symbolic equations)

Velocity

60

50

40

v(t) km/h

30

v(t)

20

10

00 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7 7.7 8.4 9.1 9.8 10.5 11.2 11.9 12.6 13.3 14 14.7

Figure 2: Velocity trend.

A further numeric integration of the ( )

t v brings to the car position trend ( )

t s :

2

Page 3 of 5

s(t)

200

180

160

140

s(t) [m]

120

100

s(t)

80

60

40

20

00 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7 7.7 8.4 9.1 9.8 10.5 11.2 11.9 12.6 13.3 14 14.7

Figure 3: Position trend.

Description

The semaphore controls the traffic by exposing a light with a different color accordingly with the signal that "should" be understood by the driver.

The classic and most spread model of semaphore defines a fixed signals switching period that cannot be changed without a manual operation. Hence the semaphore is programmed in order to properly handle the traffic only in certain default conditions. When the load of car affluence goes over a certain amount (that was estimated in order to achieve the default switching cycle), the device causes an overcrowding of cars in the incoming lanes.

Accordingly with the above described d...