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Simulació= n de la influencia de las demoras de autobuses en la operación de las paradas de= bus de Riobamba

 

Simulation of the influence of bus delays in the operation of the Riobamba bus stops

 


1=

Germán Ulises Moreno Arias                                 https://orcid.org/0000-0002-9616-6616

Escuela Superior Politécnica de Chimborazo (ESPOCH), Carrera de Gestión de Transporte, Chimborazo, Riobam= ba, Ecuador

ulises.moreno@espoch.edu.ec   

2=

Arquímedes Xa= vier Haro Velastegui                                https://orcid.org/0000-0003-3391-5082=

Escuela Superior Politécnica de Chimborazo (ESPOCH), Carrera de Gestión de Transporte, Chimborazo, Riobamba, Ecuador

 aharo@espoch.edu.ec

 

 

 

=  

 

Artículo de Investigación Científica y Tecnológica

Enviado: 11/12/2021

Revisado: 26/12/2021

Aceptado: 18/01/2022

Publicado:07/02/2022

DOI:  https://doi.org/10.33262/ap.v4i1.145  

      

 

 

 

Cítese:

 

 

Moreno Arias, G. U., & Haro Velastegui , A. = X. (2022). Simulación de la influencia de las demoras de autobuses en la operación de las paradas de bus de Riobamba. AlfaPublicaciones, 4(1), 97–= 116. https://doi.org/10.33262= /ap.v4i1.145

 

 

 

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Esta revista está protegida bajo una licencia Creative Commons AttributionNonCommercialNoDerivatives 4.0 International. Copia de la licencia: http://creativecommons.org= /licenses/by-nc-nd/4.0/

 

Palabras claves:= simulación, sistemas, demoras, entidades, locaciones.

 

Resumen

Introdu= cción. El transporte público juega un papel importante = en la mayoría de las áreas pobladas. Especialmente en las regiones urbanas, estos sistemas de transporte son ampliamente utilizados. Pero desafortunadamente, este tipo de servicio es a menudo objeto de quejas. L= os clientes están molestos por los "precios injustos", por el "mal servicio" y, en particular, se molestan en caso de retraso= s. Respecto a lo particular, este artículo presenta un modelo de simulación = por computadora desarrollado con el Software Promodel. Objetivo. El propósito es, evaluar mediante la técnica de simulación cómo influyen las demoras de los autobuses entre paradas, por dispositivos para el control = de tránsito e indisciplinas de los conductores en la operación de las parada= s de bus de la ciudad de Riobamba. Metodología. En el ámbito metodológi= co de la simulación se procede a desarrollar un modelo base. Antes de diseñar este modelo concretamos el objetivo de investigación en la forma de salid= as numéricas específicas; estas son, los promedios de pasajeros por bus, en = todo el sistema de ruta de la línea 2, por cada grupo de demoras contempladas = en la hipótesis de investigación, como también, los tiempos promedios de esp= era de los pasajeros (véase Tablas 1 y 2). Resultados. El modelo permi= te obtener resultados simulados si del escenario del sistema completo anulam= os, por ejemplo, las demoras por indisciplinas (Dpi) para obtener un nuevo escenario: Dep+Dpdis. Ahora tenemos una nueva versión del modelo que con = el soporte de ProModel nos permite observar las salidas numéricas bajo la influencia del par: Dep+Dpdis; y así, con los demás. Conclusión. El modelo de simulación por computadora permite concluir que el promedio de pasajeros y su tiempo de espera en las paradas de todo el sistema no se v= en afectados por cada tipo de demora que experimentan los autobuses.

 

 

Keywords: simulation, systems, delays, entities, locations=

 

Abstr= act

= Introduction. Public transportation plays an important role in most populated areas. Especially in urban regions, these transportation systems are widely used. But unfortunately, this type of service is often= the subject of complaints. Customers are annoyed by "unfair prices"= , by "bad service" and, in particular, they are annoyed in case of delays. Regarding the particular, this article presents a computer simula= tion model developed with the Promodel Software. Objective. The purpose= is to evaluate, through the simulation technique, how the delays of the buses between stops influence the traffic control devices and indiscipline of t= he drivers in the operation of the bus stops in the city of Riobamba. Met= hodology. In the methodological field of simulation, a base model is developed. Bef= ore designing this model, we specified the research objective in the form of specific numerical outputs; These are the average number of passengers per bus, throughout the line 2 route system, for each group of delays contemplated in the research hypothesis, as well as the average passenger waiting times (see Tables 1 and 2). Results. The model allows simulated results to be obtained if from the complete system scenario we cancel, for example, the delays due to indiscipline (Dpi) to obtain a new scenario: Dep+Dpdis. Now we have a new version of the model that with the support of ProModel allows us to observe the numerical outputs under the influence of the pair: Dep+Dpdis; and so, with the others. Conclusion.= The computer simulation model allows us to conclude that the average numb= er of passengers and their waiting time at stops throughout the system are n= ot affected by each type of delay experienced by buses.

&= nbsp;

 

 

Introducción

El estudio de la movilidad urbana implica una etapa de toma de información, destinada a la caracterización tanto de la oferta como de la demanda de transporte (Ortúzar, 2015). Este documento hace énfasis en lo segundo al “evaluar mediante un modelo de simulación por computadora cómo influyen las demoras de los autobuses entre paradas, por dispositivos para = el control de tránsito e indisciplinas de los conductores en la operación de l= as paradas de bus de la ciudad de Riobamba, Provincia de Chimborazo-Ecuador”. =

Aunque las técnicas de planificación de transporte han ido experimentando fuertes cambios en las últimas décadas, los problemas de transporte, particularment= e en el caso urbano, no han variado gran cosa a nivel local (Ortúzar, 2015). Así, cada vez= son más las quejas de las personas que utilizan el servicio de autobuses de la línea 2 en la ciudad de Riobamba. Estos clientes de las horas de mayor afluencia están cansados de esperar el autobús por la mañana. Más aun, mien= tras más demoran éstos, más se llenan las paradas. A medida que avanza el invier= no o el verano, los usuarios se incomodan cada vez más al no haber paradas cubie= rtas donde tomar asiento.

Este trabajo presenta una metodología basada en la modelación y simulación por computadora, que permite abordar la problemática antes mencionada. La complejidad en la operación de este tipo de sistemas requiere de una modela= ción cada vez más apegada a la realidad. Las estimaciones generales del modelo del rendimiento del sistema (tiempos de espera y colas) se comparan con las mediciones de campo de los tiempos de espera y de colas. Se realizan ajustes finos para permitir que el modelo coincida mejor con las mediciones de campo (Barceló, 2010). El modelo desarrollado con apoyo del Software Pr= oModel (García et al., 2013), se fundamenta en la teoría de colas. Cada locación o parada de bus se reduce a la interacción simultánea de dos entidades, a sab= er: bus y pasajero.

Para el estudio de sistemas modelados mediante modelos de colas cuya solución an= alítica se desconoce, o bien es muy difícil de obtener, se suele recurrir a técnica= s de simulación que, mediante el empleo de programas de computación, permiten obtener estimaciones de los parámetros de interés del comportamiento del sistema (Pazos et al., 2003).

En el campo de la investigación que nos concierne, la formación de colas de tráfico durante los períodos de congestionamiento es una fuente de demoras considerables y da como resultado una pérdida del rendimiento de las vías. = En condiciones extremas, la demora en las colas puede representar el 90% o más= del tiempo total de viaje del conductor. Dado esto, es esencial en el análisis = de demoras y tiempos de espera desarrollar una comprensión clara de las características de la formación y disipación de las colas junto con formulaciones matemáticas que puedan predecir los elementos relacionados con las colas. 

Metodología

Línea Piloto   

Se empieza realizando una breve descripción de la línea de buses. En este contexto, la línea 2 conocida con el nombre: 24 de mayo-Terminal- Bellavista, inicia su operación con un horario de 06h10 hasta las 22h30. Los vehículos que laboran diariamente sólo en esta línea; suman = en total doce; de ahí que, en conjunto las líneas 1,2 y 3 trabajen con un intervalo de 2 y 3 minutos en horas pico y horas valle respectivamente. Por= su parte, la frecuencia de despacho de las unidades de transporte de la línea 2 está regulada a intervalos de 8 minutos. 

La ruta de la línea 2 (véase figura 1) de transpor= te público que se utiliza para la asignación de viajes de los autobuses, tiene= una longitud de 26.8 Km. Además, se constituye por las principales vialidades d= e la ciudad, así como de sus intersecciones.

 

Tiempos de viaje y velocidad=

Otro aspecto importante que ayuda a estudiar y res= olver el problema planteado, es establecer el tiempo de viaje y velocidad promedi= o. Es así que, El Consejo de Tránsito de Chimborazo en períodos pico mediante = el método del vehículo flotante, que consiste en conducir un vehículo liviano tratando de mantener una velocidad representativa del flujo total, de acuer= do a las reglas de conducción, registra que en promedio el tiempo de recorrido p= ara cubrir todo el trayecto es de 1hora, 10minutos.

Por otra parte, los estudios de las velocidades de marcha realizados por El Departamento de Ingeniería de Tránsito de la Polic= ía de Chimborazo a lo largo de la ruta considerada de acuerdo con la técnica d= el vehículo medio, que consiste, en que el vehículo viaja de acuerdo a la apreciación que tenga el conductor de la velocidad predominante en el flujo= de tránsito, determinan diversas velocidades de marcha, donde el promedio de l= as mismas se emplea como la velocidad de recorrido en el modelo, esto es: 20.5= 86 km/h, o su equivalente registrada en la ventana entities de ProModel: 343.10 mpm.

Fi= gura 1=

Esquema general del servicio de transporte colectivo ur= bano “STCU” de la línea 2.

Nota: Esquema realizado en Software ProModel del servici= o de transporte colectivo urbano de la ciudad de Riobamba de la ruta de la línea= 2. Fuente: German Moreno

Capacidad y demoras entre paradas

También en el proceso de modelado es necesario con= tar con estas dos medidas; luego, es preciso tener en cuenta que estos concepto= s se aplican a autobuses y paradas en vías urbanas para análisis, tanto de diseño como de operación. La capacidad depende de las unidades de servicio. La raz= ón principal de su elección, es la necesidad de conocer en promedio el número = de pasajeros que transportan, tanto de pies como sentados. Otra razón por la q= ue se vincula al modelo de simulación es que, la cantidad de pasajeros en cola= que se suben al vehículo (pasajeros servidos) depende de la capacidad legal permitida. En este contexto, El Departamento de Ingeniería de Tránsito de Chimborazo establece un intervalo de pasajeros sentados; a saber: 38-40; mientras tanto que la ley, en el caso de pasajeros parados, permite un 20% = de la capacidad del autobús.

Para los especialistas de transporte, las medidas velocidad, tiempos de viaje, demoras, tiempos entre paradas, etc. son de importancia, de ahí que, el informe técnico del Consejo Provincial de Tráns= ito establece un estimado entre paradas de 1minuto ± 0.2 segundos. Estos datos registrados en los dos párrafos se utilizan para el ajuste del modelo matemático de simulación.

Tiempos de demoras entre paradas (DEP)<= /span>

La influencia de todas las demoras se mide como la diferencia, entre el tiempo que demora el bus entre una parada y la siguien= te y las demoras producidas por los dispositivos para el control del tránsito más las provocadas por indisciplinas del conductor en las paradas. Entonces:

Los tiempos por dispositivos para el control del tránsito se encuentran incluidos por declaración de variables y sus respect= ivas distribuciones de probabilidad, en la expresión:

&nbs= p;

Tiempos de demoras por dispositivos para el control del tránsito

Otra acción necesaria en el desarrollo del modelo de simulación por computadora = es programar los tiempos de demoras de los autobuses cuando estos se detienen total o parcialmente frente a cada señal de Ceda el Paso, Pare o Semáforo. = En el tiempo total de recorrido están incluidas todas aquellas demoras operacionales provocadas por los dispositivos de control. = No incluye aquellas demoras fuera de la vía, como pueden ser las correspondien= tes a detenciones en gasolineras (Cárdenas, 2018).

Enseguida= se ilustra con un ejemplo (véase figura 2) la distribución de probabilidad que mejor se ajusta a los datos de tiempos de demoras en el semáforo , dirección Norte-Sur. 

Figura 2

Tiempos de demoras en = el semáforo No 1

Nota: Distribución teórica obtenida mediante el Software= StaFit que modela los datos recolectados en el primer semáforo de la ruta, en dirección Norte – Sur. Fuente= : German Moreno

 

Una variable aleatoria continua X que tiene la distribución en forma de campana= (figura 2) se denomina variable aleatoria normal. La fórmula matemática para la distribución de probabilidad de la variable normal depende de los dos parámetros μ y σ, su media y su desviación estándar, respectivame= nte (Walpole et al., 2012).

Tiempos de demoras por indisciplinas del conductor =

En este apartado se consideran las demoras por indisciplinas del conductor (DPI); es decir, por demoras no planificadas en= las paradas.  El proceso que se realiza= es medir la diferencia entre el tiempo total que demora el bus en una parada (tiempo de servicio “DTS”) y el tiempo planificado de demoras por paradas q= ue, según el Consejo Provincial de Tránsito al considerar el sistema integral d= e la línea 2, éste, por sus características y funciones debe operar en las parad= as con una cantidad de tiempo de demora distribuido uniformemente entre 1 y 2 minutos, o sea: U (0.5, 1.5).

=

Una distribución uniforme tiene la probabilidad de ocurrencias de un valor y es igualmente posible de ocurrir en cualquier lugar entre el menor valor  y el mayor valor  (Levine, et al., 2006).

Modelo de colas

En los modelos de colas existentes, las tareas producidas por los usuarios de una población llegan al sistema en un instan= te de tiempo aleatorio. Estas tareas demandan una cantidad de tiempo de servic= io también aleatorio, y se sirven una a una o por grupos (Pazos et al., 2003).= En las primeras paradas de bus la inclusión de los tiempos aleatorios de servi= cio da lugar al conteo de la variable cantidad de pasajeros servidos CPS. En las paradas donde se producen ascensos y descensos de pasajeros este tiempo de servicio da lugar a contar la cantidad de pasajeros servidos, así como, la cantidad de pasajeros que descienden del autobús CPDsc. Finalmente, después= de completar el circuito, en las últimas paradas, el tiempo de descenso equivalente al tiempo de servicio da lugar al conteo del número de pasajeros que descienden del bus.

Fi= gura 3=

Disciplina de cola por parada

Nota: Ventana del Software ProModel que permite establec= er la disciplina de cola en las paradas de buses. Fuente: German Moreno

 

El orden en el que se sirven los usuarios, a saber, en: QUsr_Paradan y QUsr_Descenso_Paradan, lo dete= rmina una disciplina de gestión de cola de la forma FIFO en ProModel. La figura 3= que se muestra define la disciplina adoptada en los cincuenta y cuatro modelos = que componen el sistema (International Journal os Scientific Research in Science and Technology, 2018).

Proceso de tiempo entre llegadas

Otro parámetro que incide en el modelado son los tiempos entre llegadas de los usuarios del servicio de transporte colectivo urbano a las paradas. Este es un proceso estocástico continuo de tiempo (índice) discreto  (Pazos et al., 2003).  

=

Obviamente, una vez caracterizado uno de estos tiempos, queda muy bien caracterizado el otro. La distribución exponencial con tasa λ, se muestra en la Figura = 4. Esta aparece con frecuencia en muchas aplicaciones, incluidos los modelos de col= as y la teoría de la confiabilidad (Kobayashi et al., 2012). Los tiempos entre llegad= as de los pasajeros a la parada   se modelan con esta distribución obteni= das a través del programa Stat:Fit c= on un nivel de confianza del 95%. Estos tiempos están dados en minutos y está bas= ado en medición directa realizada por aforadores. El resto de ajustes de las de= más paradas de bus se encuentran registrados en el propio modelo de simulación.=

Fi= gura 4=

Distribución teórica: tiempos entre llegadas de pasajer= os a la parada No 5

Nota: Distribución teórica obtenida mediante el Software StaFit que modela los datos recolectados de los tiempos entre llegadas de l= os pasajeros a la parada 5 dirección Norte – Sur. Fuente: German Moreno

 

Cantidad de pasajeros en la parada: CPP

El incremento de esta variable depende de los tiem= pos de servicio y de las demoras producidas en el sistema. Los contadores de la variable cantidad de pasajeros se colocan en el Layout y están identificados con el letrero CPP. En el programa de la figura 7, se muestra, la condición= que debe cumplirse para que en las paradas de bus se produzca el incremento de pasajeros.  identificados con el le= trero CPP.

Fi= gura 5=

Incremento de pasajeros en la Paradan

Nota: Línea de código que calcula el incremento de cantidad de pasajeros en la n-ésima parada de la r= uta de la línea 2. Fuente: German Moreno

En la publicación de la Organización de Planificación Metropolitana del Área Urbana de Memphis (MPO), se estableció que las paradas de autobús mal diseñ= adas pueden disminuir la satisfacción del cliente, hacer que el transporte públi= co sea menos atractivo para los nuevos clientes potenciales y, potencialmente, hacer que la espera en las paradas sea insegura para los pasajeros.

Tiempo promedio de espera: Pte <= /i>

El tiempo promedio se asume como aquel en el que l= os pasajeros invierten desde su llegada hasta su salida de los sistemas de col= as que se generan en cada parada de la ruta en análisis (Osais, 2018). Una de las me= didas utilizadas para evaluar el rendimiento del sistema de colas de la ruta surg= e al formularse la siguiente pregunta: ¿Cuál es el tiempo promedio que los usuar= ios del servicio de transporte colectivo invierten en el sistema entero, incluy= endo el tiempo de espera y de servicio? La Figura 6 del siguiente programa defin= ido en la ventana processing responde la pregunta.

Entidad

Dos entidades conforman este modelo, una de ellas representa los pasajeros que se encuentran subiendo y bajando en las parada= s, y la otra representa el autobús. Puesto que las entidades se mueven, hemos asignado una velocidad de 100 metros por minuto a los pasajeros que es aproximadamente la de una caminata normal; mientras que los autobuses se mu= even con una velocidad promedio de 343.10 metros por minuto durante todo el tray= ecto de la ruta; línea 2 (Blanco & Fajardo, 2001).

Fi= gura 6=

Cálculo general de los tiempos promedio

Nota: Línea de código que calcula los tiempos promedio de espera y de servicio, en cada n- ési= ma parada. Fuente: German Moreno

Atributo

Un atributo es una característica común de todas l= as entidades (Kelton et al., 2008). Por ejemplo, la entidad bus tiene un atributo en el modelado que lo definimos como: attr_Capacidad_del_Bus =3D 40, tambi= én en el modelo se encuentran dos atributos más, a saber: attr_Cantidad_de_Pas= ajeros_en_el_Bus, y  attr_Hora_de_entrada_al_Siste= ma

Variables de entrada y salida        

La simulación de la mayoría de los sistemas de servicio es una simulación de terminación, porque tienen un evento de terminación obvio (es decir, hora de cierre) (Kyu & Kang, 2013). La terminología, “operación de las paradas = de bus” dice de la cantidad de pasajeros presentes en las paradas y de su tiem= po de espera. En este contexto, las salidas numéricas son: 1. cantidad de pasajeros en la parada “CPP”, y 2. Tiempo de espera “Pte”. Cabe recordar que las dos variables mencionadas son las que constan como variables dependient= es en la hipótesis de investigación.

Como salidas numéricas complementarias el modelo de simulación establece las siguientes: 1. El tiempo de espera forzado “Ptef” = y 2. La cantidad de pasajeros desertores “CPD”.

Con las salidas identificadas, el siguiente paso es identificar las variables de entradas. Éstas son valores numéricos que, una= vez determinados, permiten iniciar la simulación y calcular todas las salidas requeridas. Estas entradas son: 1. Arribos del bus, 2. Arribos del pasajero= a la parada, y 3. Tiempos de servicio.

Los arribos del bus en el modelo son las frecuenci= as aleatorias con las que los vehículos ingresan al recorrido desde la Coopera= tiva de vivienda 24 de mayo. Estos tiempos obtenidos por medición directa se aju= stan con una distribución uniforme: U (120,480) segundos, la cual se programa en= la ventana arrivals de ProModel, bajo la entidad bus.

El uso de un número semilla aleatorio diferente cambia el perfil del tráfico q= ue llega y, por lo tanto, los resultados también pueden cambiar. Por lo tanto,= se puede simular la variación estocástica de los tiempos de llegada del flujo = de entrada (Macioszek & = Sierpiṅski, 2016).

Cálculo del tamaño de muestra para estimar un valor de media

Para comprender cuántas veces se debe repetir una simulación cuando el objetivo consiste en estimar la media de un valor de salida, es mejor empezar por escoger un número específico de corridas de simulación y preguntarse qué tan precisa es la estimación del valor de sali= da obtenido. Para responder a esta pregunta se requiere la creación de un intervalo de confianza alrededor de la estimación (Mathur & Sol= ow, 1996).

Intervalo de confianza para la media verdadera

Supongamos que se usa   corridas de simulación para obtener un promedio estimado   para la media verdadera, . La pregunta = que nos planteamos ahora es: ¿qué tan cerca está este valor estimado  del valor verdadero de ?. Aplicando la teoría sobre estimación estadística, el objetivo es determinar un valor  , y crear un intervalo de la forma:  

      [1]

de modo que, con un cierto grado de confianza, se pueda decir que la media verdadera, , está en este intervalo. Seleccionamos el nivel de confianza en la forma de un valor de <= /span>  entre cero y uno, de manera que con un n= ivel de confianza de , podemos afir= mar que el valor verdadero de  está en el intervalo:  (Mathur & Solow, 1996).

Por ejemplo, para obtener un nivel de confianza de 95%, escogemos un valor de =3D0.05. Una v= ez elegido un valor apropiado de , calculamos el intervalo de confianza asociado mediante:

                                                   <= /span>        [2]

Donde:

el tamaño de la muestra (es decir, el número de corridas de simulación)

promedio de muestra

desviación estándar de la muestra

el valor de la distribución   con  grados de libertad

Notemos que en la expresión 3, 

=        [3]                                                                                   <= /o:p>

En consecuencia, a este valor de     se le conoce como precisión de la estimación y representa una medida de qué tan fiable es la salida de la simulación. Para un valor fijo de  , la precisión= de la estimación puede mejorarse aumentando solamente el tamaño de la muestra,= , lo cual significa aumentar el número de réplicas o corridas de simulación.

Cálculo del tamaño de muestra para lograr un nivel de confianza y una precisión dados<= /span>

Ahora se verá cómo calcular el tamaño de la muestr= a , para lograr = una precisión deseada en la estimación. Supongamos que un cierto nivel de confianza  , calculado anteriormente y asociado con un intervalo de confianza digamos de 95%, debe reducirse a un valor dado  <= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-ansi= -language: ES-EC;mso-fareast-language:EN-US'> . Este objetivo puede lograrse mediante el aumento del número de corridas de simulación de<= span style=3D'mso-spacerun:yes'>   a un nuevo valor,  , tal que:

Precisión  e=3D  

Resolviendo para   tenemos que:

=       [4]

Aunque se conoce el valor de  , el de  = depende de  . Más aún, el valor de la desviación estándar de la muestra, , no puede ser determinado hasta que se lleven a cabo las simulaciones (y todavía no se conoce el valor de ).<= /span>

Para valores grandes de , la distribuc= ión  puede ser aproximada bastante bien por la distribución normal estándar, de modo que un planteamiento para resolver el problema de que  depende de   consiste en sustituir  =  con el correspondiente valor de la normal estándar. Específicamente, =  es sustituido por  , de manera qu= e el área bajo la curva de la distribución normal que se encuentra a la derecha = de este valor es  . Esto es:

                                                         [5]                                   <= /o:p>

Donde

: el número de corridas o réplicas de simulación.

Sin embargo, para resolver el hecho de que el valo= r de  todavía no se conoce, se utiliza un enfo= que alternativo, a saber:

1. Seleccionar un valor inicial para 

2. Efectuar   corridas de simulación=

3. Sobre la base de los resultados de todas las corridas de simulación, calcular  <= /span>   , luego determinar:

=    

4. Si  detener el proceso de simulación. Pues, = ya se han efectuado suficientes corridas de simulación. En cualquier otro caso, efectuar   más corridas de simulación, antes de reg= resar al paso 3 (Mathur & Solow, 1996).

Resultados

Los resultados que se obtienen giran en torno a los escenarios objeto de investigación y análisis que se encuentran en el objetivo general; así, para evaluar cómo influyen las demoras de los autobuses entre paradas, por dispositivos de control de tránsito, e indisciplinas de los conductores en = el número de pasajeros y su tiempo de espera en las paradas de bus, determinam= os tres escenarios de análisis; a saber: Dep+Dpdis+Dpi, Dep+Dpi y Dep.

El escenario general: Dep+Dpdis+Dpi, representa al sistema modelado en su totalidad, es decir, con las demoras entre paradas (Dep), las demoras por dispositivos de tránsito (Dpdis) y las demoras por indisciplinas de los conductores (Dpi). Los resultados simulados según este escenario, son importantes en virtud de la comparación que es posible realizar con los nue= vos escenarios que se desprenden del modelo general. Las salidas numéricas obtenidas bajo simulación corresponden a las etiquetas: CPS, CPP, CPD, Pte, Tep y Ptef; do= nde: CPS, representa la cantidad de pasajeros servidos, CPP: cantidad de pasajer= os en la parada, CPD: cantidad de pasajeros desertores, Pte: promedio de tiemp= o de espera, Tep: tiempo de espera planificado y Ptef: promedio de tiempo de esp= era forzado.

El modelo permite obtener resultados simulados si del escenario del sistema completo anulamos, por ejemplo, las demoras por indisciplinas (Dpi) para obtener un nuevo escenario: Dep+Dpdis. Ahora tenemos una nueva versión del modelo que con el soporte de ProModel nos permite observar las salidas numéricas bajo la influencia del par: Dep+Dpdis. 

Si del escenario completo anulamos o retiramos todos los dispositivos para el control del tránsito, es decir, si suponemos que el sistema opera sin ningún dispositivo, obtenemos un nuevo modelo del tipo: Dep+Dpi. Ahora, la simulac= ión permite observar salidas numéricas bajo la influencia de las demoras entre paradas e indisciplinas de los conductores. El objetivo es estimar y observ= ar el efecto que bajo este tratamiento experimental se produce en el número de pasajeros y su tiempo de espera. <= o:p>

Por último, si del modelo completo retiramos las demoras por dispositivos y las provocadas por indisciplinas de los conductores, entonces estamos en capaci= dad de observar el comportamiento de las paradas de autobús bajo la influencia = de las demoras entre paradas (Dep). Es evidente que crear un escenario sin las demoras producidas entre paradas es imposible.

Variable dependiente: número de pasajeros <= /o:p>

Los promedios de pasajeros por bus, en todo el sistema de ruta de la línea 2, p= or cada grupo de demoras contempladas en la hipótesis de investigación se mues= tra en la tabla 1.  No obstante, el pri= mer grupo “Dep+Dpdis+Dpi” de las primeras columnas de las tablas 1 y 2, present= an los promedios de pasajeros y tiempos de espera, respectivamente, en todo el sistema en condiciones normales. Sin embargo, de no emplearse en la prueba = de hipótesis los registramos para compararlos con los que sí intervienen en la misma.

Ta= bla 1=
Promedios de pasajeros por bus en todo el sistema

Bus

Dep+Dpdis+Dpi

Dep+Dpdis

Dep+Dpi

Dep

1

2.310

2.380

2.314

2.166

2

1.490

1.560

1.522

1.534

3

1.251

1.283

1.231

1.272

4

1.152

1.173

1.129

1.142

5

1.129

1.139

1.084

1.089

6

1.091

1.059

1.130

1.126

7

1.127

1.092

1.106

1.085

8

1.128

1.129

1.125

1.123

9

1.159

1.107

1.125

1.129

10

1.167

1.093

1.124

1.141

11

1.114

1.133

1.136

1.110

12

1.142

1.177

1.057

1.058

Fuente: German Moreno

 

Variable dependiente: tiempo de espera

Los tiempos promedios de tiempo de espera de los pasajeros, por bus, en todo el sistema de ruta de la línea 2, por cada grup= o de demoras contempladas en la hipótesis de investigación se muestran en la tab= la 2.

Ta= bla 2=

Promedios de tiempos de espera por bus en todo el siste= ma

Bus

Dep+Dpdis+Dpi (min)

Dep+Dpdis (min)

Dep+Dpi (min)

Dep (min)

1

1.489

1.392

1.404

1.532

2

1.796

1.760

1.820

1.960

3

2.044

1.941

2.002

2.129

Ta= bla 3=

Promedios de tiempos de espera por bus en todo el siste= ma (continuación)

Bus

Dep+Dpdis+Dpi (min)

Dep+Dpdis (min)

Dep+Dpi (min)

Dep (min)

4

2.272

1.997

2.121

2.164

5

2.430

2.254

2.395

2.383

6

2.476

2.318

2.440

2.509

7

2.517

2.338

2.387

2.508

8

2.511

2.406

2.480

2.576

9

2.663

2.444

2.431

2.445

10

2.523

2.432

2.375

2.440

11

2.418

2.384

2.355

2.451

12

2.366

2.495

2.208

2.432

Fuente: German Moreno

Discusión

Los resultados simulados de la tabla 1, evidencian para los cuatro escenarios un asombroso grado de regularidad de pasajeros durante el recorrido de los doce buses. Los promedios de pasajeros obtenidos de todas las 51 paradas oficial= es por cada bus en condiciones normales del sistema y en función de su correspondiente número de réplicas, reflejan el comportamiento de las misma= s a medida que transcurre el tiempo. Esto se observa en la columna: Dep+Dpdis+D= pi, de la tabla 1 y la figura 7.

Figura 7

Gráfico de l= ínea que muestra la demanda de clientes de 6h30 a 9h30

 

 

 

 

 

 

 







 

Nota: <= /b>Distribución de los pasajeros por bus según el orden de salida a par= tir de las 6h30. Fuente: German Moreno.

Los valores promedios de pasajeros obtenidos del sistema en condiciones normales (Ver columna: Dep+Dpdis+Dpi, de la tabla 1 = y figura 7) nos muestran que hasta el recorrido del sexto bus existe un decrecimient= o de promedios progresivo leve. Por el contrario, a partir del recorrido del sép= timo bus, los valores crecen ligeramente hasta cuando el décimo bus completa su recorrido.

 

Figura 8

Gráfico de l= ínea que muestra los “Pte” de clientes de 6h30 a 9h30

 

 

 

 

 

 

 

 

 

 


}=

 

Nota: Distribución de los tiempos de espera por bus en el orden de salida a partir de las 6h30. Fuente:= German Moreno=

El análisis de datos (ver columna: Dep+Dpdis+Dpi, = de la tabla 2) de los tiempos promedios de espera que experimentan los usuario= s de la línea 2, en condiciones normales, muestra que, para los doce buses, las esperas en las paradas del sistema no exceden, peor se acercan a los cinco minutos de tiempo de espera planificado por parte de los pasajeros. Este he= cho se comprueba en el gráfico de la Figura 8, donde se observan los tiempos promedios de espera por cada bus, a partir de las 6h30.

Conclusiones<= /o:p>

·&nb= sp;        Las pruebas de simulación ejecutadas y visualizada= s en sus variables cuantitativas de salida con el apoyo de herramientas de gráfi= cos de la hoja de cálculo de Excel, evidencian que no hay largos tiempos de esp= era; como tampoco, existe aglomeración en las paradas, debido a los distintos ti= pos de demoras que experimentan los autobuses. Lo dicho, se puede corroborar co= n la realidad; es decir, los largos tiempos de espera y acumulación de usuarios = en las paradas se descartan en virtud de la presencia de otras líneas de buses= que convergen en una gran parte de la ruta modelada.

·&nb= sp;        Por otro lado, está el comportamiento probabilísti= co del sistema, el cual, permite concluir que los valores promedios del número= de pasajeros en las paradas guardan estrecha relación con los horarios de mayor demanda que se presentan en el periodo de 6h30 a 9h30.

·&nb= sp;        Al observar las salidas numéricas-por parada de bu= s- de las variables cantidad de pasajeros “CPP” y cantidad de pasajeros servid= os “CPS” concluimos que en la mayoría de paradas de bus, el número de pasajeros que esperan el vehículo, son el mismo número que reciben servicio. La experiencia confirma que esto es así. En general, los resultados muestran q= ue las quejas de los usuarios más bien pueden ser de tipo esporádicas, debido a interrupciones no periódicas que el servicio de buses pueden experimentar.<= o:p>

 

Referencias Bi= bliográficas

Barceló, J. (2010). Fundamentals of Traffic Simulation. In J. Barceló. Springer.=

Blanco River= o, L. E., & Fajardo Piedrahita, I. D. (2001). Simulación con PROMODEL. I= n Casos de producción y logística. Escuela Colombiana de Ingenieria.

Cárdenas, J. (2018). Ingeniería de Tránsito Fundamentos y Aplicaciones (Novena edición ed.). México: Alfaomega Grupo Editor, S.A.

García, E., García Reyes, H., & Cardenás, L. (2013). Simulación y Análisis de Sistemas con ProModel. Monterrey, México: Pearson.

Interna= tional Journal os Scientific Research in Science and Technology. (2018). Technoscience Academy.

Kelton,= D. W., Sadowski, R. P., & Sturrock, D. T. (2008). Simulación con software Arena. México: McGrawHil= l.

Kobayas= hi, H., Mark, B., & Turin, W. (2012). Probability. Cambridge.<= /span>

Kyu Cho= i, B., & Kang, D. (2013). Modeling and Simulation od Discrete - Event Systems. New Jersey: Wiley.

Levine , D., Krehbiel, T., & Berenson, M. (2006). Estadística para administración.= México: Pearson.

Maciosz= ek, E., & Sierpiṅski, G. (2016). Comtemporary Challenges of Transpo= rt Systems and Traffic Engineering. Poland.

Mathur, K., & Solow, D. (1996). El arte de la toma de decisiones. México: Pearson Educación.

Ortúzar, J. (2015). Modelos de Demanda de Transporte. In J. d. Ortúzar. Chile: Alfaomega.

Osais, = Y. (2018). Computer Simulation A Foundation Approach Using Python. CRC Press.

Pazos Arias,= J. J., Suaréz González, A., & Díaz Redondo, R. (2003). Teoría de Colas y Simulación de Eventos Discretos. Madrid: Pearson Educación S.A.

Walpole, R., Myers, R., Myers, S., & Ye, K. (2012). Probabilidad y estadística para ingeniería y ciencias. México: Pearson.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Alfa Publicaciones.

 


El artículo queda en propiedad d= e la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Alfa Publicaciones.

 

 

 

 


=  

 

&nb= sp;

 

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= ISSN: 2773-7330

= Vol. 4 No. 1,  pp. 97 – 116 , enero – marzo 2022

 

 

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