The busload on the route is modeled, the main statistical characteristics of the process on route number 10 were calculated, and the optimal number of buses on the route is calculated, which would maximize the total number of passengers per flight. The developed program allows us to calculate the optimal number of buses on the route according to the previously defined criteria in a certain period of the day on weekdays and weekends (including holidays). Diagrams of distribution of passengers and their dependence on the number of buses and their schedules are given in the work.
A promising direction for improving urban transport systems is to determine the
optimal number of vehicles on the route. The solution to this problem involves bringing
to the route so many large or medium-sized buses that can provide comfortable
conditions for passengers and fully meet the demand during rush hour [
To develop the system and understand the essence of the task, a plan of its work was
drawn up [
The use case diagram was built for the designed system (Fig. 1). It was singled out
two main actors: the program creator and the bus driver. The main goal of the
program creator is to optimize the number of buses on the flight along a certain route.
To do this, the program creator needs to collect data on the number of passengers on
different days, as well as different hours during these days, to statistically present this
data. This will allow the program creator to determine the optimal number of buses
for a given day and time.
To build a class diagram of this system (fig.2), you should add the rest of the classes
and associations, as well as clarify the stereotypes, attributes and operations of these
classes [
Fig. 3 presents a cooperation diagram, which shows not only the sequence of
interaction but also all the structural relationships between the objects involved in this
interaction. In contrast to a sequence diagram, a cooperation diagram shows only the
relationship between objects that play certain roles in the interaction [
The code snippet allows you to calculate all of the above characteristics. # basic statistical characteristics of the process print("Min amount of people in bus:",min(dataset.inbus)) print("Max amount of people in bus:",max(dataset.inbus)) print("Mean:",np.mean(dataset.inbus)) print("Median:",np.median(dataset.inbus)) print("Variation:",np.var(list(dataset.inbus))) print("Standart deviation:",np.std(dataset.inbus)) The results obtained in Fig. 6 allow us to conclude that the minimum of passenger number in the bus = 0, the maximum is 100 people. The average number of passengers in the bus is 60 passengers, the median is 73 passengers, the variation = 780.63 and the standard deviation = 27.9..
Travel time along the entire route by one bus was determined. The distribution of time between stops was carried out in proportion to the length of the path between stops. # time of passing the route by one bus # time to overcome the route between stops by one bus dataset['time'] = dataset['next_stop[km]']/40+2/60 time = np.ceil(sum(dataset.time)*60) dataset['time_min'] = dataset['time']*60 print("Full time of bus on its way:",time) col=['name', 'time_min'] print("Time interval between bus-stop for one bus:\n", dataset[col]) For a predetermined λ and bus capacity, we calculate the number of buses on the route that would maximize the total number of passengers carried per flight.
The following code snippet performs the above task:
dataset['queue'][i]=np.ceil(abs(random.expovariate(alpha*(i)/n)))
dataset.inbus[i]=dataset.inbus[i-1]dataset.comeout[i]+dataset['queue'][i] if(dataset.inbus[i]>m): dataset.comein[i] = m-dataset.inbus[i-1] dataset['queue'][i] = dataset['queue'][i]-(mdataset.inbus[i-1])
dataset.inbus[i] = m else: dataset['comein'][i]=dataset['queue'][i] dataset['queue'][i]=0 S+= dataset.comein.sum() dataset['comeout'][n-1]=dataset['inbus'][n-2] dataset['inbus'][n-1] = 0 f = 0 if(dataset[dataset['queue']>60].empty):
break
The next step in working with this route will be to work on weekdays and weekends,
as the number of passengers varies. That is, it was necessary to set the dependence of
λ on the hour of the day for weekdays and weekends (including holidays). And
calculate the optimal number of buses on the route for working days and for weekends
(holidays). Fragment of the program:
# number of passengers depending on the day of the week
and the time of day
# optimal number of buses
dataset_time = pd.DataFrame([[0.6,0.4],
[1,0.4],
[1,0.6],
[0.4,0.6],
[0.4,1],
[
da
Finally, we find the estimate for the mathematical expectation and construct a confidence interval that will correspond to a confidence probability = 0.8 for all flights per day. Fragment of the program: # score for mathematical expectation # confidence interval for mathematical expectation mat_spod = np.mean(count_of_people_in_run) F= 1.282 #при значенні довірчої імовірності 0.8 D = np.var(count_of_people_in_run) sigma = pow(D/len(count_of_people_in_run),1/2) d1 = mat_spod - F * sigma d2 = mat_spod + F * sigma print("Math expectation:", mat_spod) print("Сonfidence interval: (", d1,";", d2, ")") Fig.13 shows the result of the execution of the above fragment of the program code for calculation of a point estimation of mathematical expectation and trust probability. Because of work on optimizing the number of buses on the route, the theory of the queuing system is introduced. The main characteristics of QMS are considered. In addition, the end result is a program for analysis and processing of data on one of the routes of the city bus of the city of Lviv, namely: route number 10, which runs daily from six o'clock in the morning to ten o'clock in the evening every working day, and on weekends and holidays. Because of the analysis, the busload on the route is modeled, the main statistical characteristics of the process on route number 10 were calculated, and the optimal number of buses on the route is calculated, which would maximize the total number of passengers per flight. In particular, the developed program allows you to calculate the optimal number of buses on the route according to the previously specified criteria for specific hours of the day on weekdays (weekends) and weekends (including holidays). The work is illustrated by a sufficient number of schedules of passenger distribution, their dependence on the number of buses, schedule, etc.