Ability Forecast For a Transit Traffic Signal System

by Ruchi Tyagi*,

- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659

Volume 3, Issue No. 4, Feb 2012, Pages 0 - 0 (0)

Published by: Ignited Minds Journals

ABSTRACT

The paper has considered a traffic signal system for itsability forecast. This traffic signal system is based on three colour signals,namely red, green and yellow. The red colour signal is used to stop the trafficand the green colour signal is used to moving of stopped traffic. The yellowcolour signal indicates ready to move and it works prior to green signal.Therefore, on failure of red or green colour signal the whole system goes tofailed state while on failure of yellow colour signal the system works inreduced efficiency state.

KEYWORD

ability forecast, transit traffic signal system, colour signals, red signal, green signal, yellow signal, failed state, reduced efficiency state

INTRODUCTION

The whole system can also fail due to environmental reasons like storm, heavy raining etc. The system has to wait for repair in case of environmental failure otherwise; the repair facilities are always available. All the failures follow exponential time distribution whereas all repairs follow general time distribution. Pre-emptive resume policy has been adopted for repair purpose. Repair of red or green signals pre-empts the yellow colour signal. Since, the system under consideration is of Non-Markovian nature, the supplementary variable technique has been used to mathematical formulation of system. State-transition diagram has shown in fig -1. Difference-differential equations for all the transition-states have been obtained. Laplace transform has been used to solve these mathematical equations. Availability and profit function of considered system have computed. Ergodic behaviour of the system and a particular case have been obtained to improve practical utility of the model.

FORMULATION OF MATHEMATICAL MODEL

Probability considerations and limiting procedure yield the following set of difference-differential equations governing the behaviour of considered signal system:

…(1) …(2) …(3) …(4) …(5) …(6) …(7)

…(8)

Boundary conditions are:

…(9) …(10)

…(11)

…(13) …(14)

Initial conditions are:

…(15)

Fig-1 (State-Transition Diagram)

Fig-2

Fig-3

In this study, the author deals with the transit traffic signal system for evaluation of its ability measures. Failures due to environmental reasons have also taken into account to obtain better results. Laplace transform of various transition state probabilities, shown in fig-1, have been obtained. Availability function and profit function for considered system have computed. Long run transition state probabilities and a particular case, when all repairs follow exponential time distribution, have been also determined to improve practical utility of the model. A numerical computation has mentioned to highlight important results of the study. By using this numerical computation. The corresponding graphs have been shown in fig-2 and 3, respectively. Fig-2 shows the way in which availability of system decreases as we increase in the value of time ‘t’. Fig-3 gives the variation in cost function with the time t.

REFERENCES :

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