Plots

[miguelrizzog96]

[miguelrizzog96]

[miguelrizzog96]

[miguelrizzog96]

[sandrosvan]

Hi Miguel! when I directly copy and paste your code (pls see below), the program runs (though shows some errors) and gives output: all plots except service utilization and probabilities' plots. so tell me please why?

##single server

#Importing Libraries
import pandas as pd
import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

import warnings
warnings.filterwarnings('ignore')

#Single server, single queue simulation
l = 1 # average number of arrivals per minute
µ =1.5 # average number of people served per minute
ncust =1000# number of customers
c=1 # number of servers

#generating inter arrival times using exponential distribution

inter_arrival_times = list(np.random.exponential(scale=1/l,size=ncust))

arrival_times= []# list of arrival times of a person joining the queue
service_times = [] # list of service times once they reach the front
finish_times = [] # list of finish times after waiting and being served

arrival_times = [0 for i in range(ncust)]
finish_times = [0 for i in range(ncust)]

arrival_times[0]=round(inter_arrival_times[0],2)#arrival of first customer

#Generate arrival times

for i in range(1,ncust):
arrival_times[i]=round((arrival_times[i-1]+inter_arrival_times[i]),2)

# Generate random service times for each customer 

service_times = list(np.random.exponential(scale=1/µ,size=ncust))

#finish time for first customer

finish_times[0]=round((arrival_times[0]+service_times[0]),2)

#generating finish times

for i in range(1,ncust):
finish_times[i] = round((max(arrival_times[i], finish_times[i-1]) + service_times[i]),2)

    # Total time spent in the system by each customer

total_times =[abs(round((finish_times[i]-arrival_times[i]),2)) for i in range(ncust)]

 # Time spent@waiting before being served (time spent in the queue)

wait_times = [abs(round((total_times[i] - service_times[i]),2)) for i in range(ncust)]

#creating a dataframe with all the data of the model

data = pd.DataFrame(list(zip(arrival_times,service_times,total_times,finish_times,wait_times,inter_arrival_times)),
columns =['arrival_times', 'service_times','total_times','finish_times','wait_times','inter_arrival_times'])

#generating time between events , and their description (arrivals, departures)

tbe=list([0])
timeline=['simulation starts']
for i in range(1,ncust):
tbe.append(data['arrival_times'][i])
tbe.append(data['finish_times'][i])
timeline.append('customer ' +str(i)+' arrived')
timeline.append('customer ' +str(i)+' left')

#Creating a dataframe to summarize the time between events
timeline = pd.DataFrame(list(zip(tbe,timeline)),
columns =['time','Timeline']).sort_values(by='time').reset_index()
timeline=timeline.drop(columns='index')

#generating the number of customers inside the system at any given time of the simulation

timeline['n']=0
x=0
idletime=0
workingtime=0
for i in range(1,(2*ncust)-2):
if len(((timeline.Timeline[i]).split()))>2:
z=str(timeline['Timeline'][i]).split()[2]
else:
continue
if z =='arrived':
x = x+1
timeline['n'][i]=x
else:
x=x-1
if x==-1:
x=0
timeline['n'][i]=x

if timeline['n'][i]==0:
    idletime=idletime+ timeline['time'][i+1]-timeline['time'][i]
else:
    workingtime= workingtime+ timeline['time'][i+1]-timeline['time'][i]

workingtime=workingtime+timeline['time'][2ncust-3]-timeline['time'][2ncust-2]

timeline.time.max()
workingtime+idletime

data['occupied']=[0 for i in range(ncust)]
for i in range(1,ncust):

if data.arrival_times[i]>data.finish_times[i-1]:
    data['occupied'][i]=1
else:
    data['occupied'][i]=0

t= list()
for i in timeline.index:
if i == (2*ncust) -2 :
continue
x=timeline.time[i+1]
y=timeline.time[i]
t.append(round((x-y),3))

t.append(0)
timeline['tbe']=t
Pn=timeline.groupby('n').tbe.agg(sum)/sum(t)

#checking central tendency measures and dispersion of the data
timeline.n.describe()
data.occupied.value_counts()

timeline['Lq']=0
for i in timeline.index:
if timeline.n[i]>1:
timeline.Lq[i]= timeline['n'][i]-c

ocupation= pd.Series(name='ocupation',data=[idletime/data.finish_times.max(),
workingtime/data.finish_times.max()],index=['Idle','Ocuppied'])
#plots

plt.figure(figsize=(12,4))
sns.lineplot(x=data.index,y=wait_times,color='black')
plt.xlabel('Customer number')
plt.ylabel('minutes')
plt.title('Wait time of customers')
sns.despine()
plt.show()

plt.figure(figsize=(7,7))
sns.distplot(inter_arrival_times,kde=False,color='r')
plt.title('Time between Arrivals')
plt.xlabel('Minutes')
plt.ylabel('Frequency')
sns.despine()
plt.show()

plt.figure(figsize=(8,8))
sns.distplot(service_times,kde=False)
plt.title('Service Times')
plt.xlabel('Minutes')
plt.ylabel('Frequency')
sns.despine()
plt.show()

plt.figure(figsize=(8,8))
sns.barplot(x=Pn.index,y=Pn,color='g')
plt.title('Probability of n customers in the system')
plt.xlabel('number of customers')
plt.ylabel('Probability')
sns.despine()
plt.show()

plt.figure(figsize=(7,7))
sns.barplot(ocupation.index,ocupation,color='mediumpurple')
plt.title('Utilization %')
plt.xlabel('System state')
plt.ylabel('Probability')
sns.despine()
plt.show()

Ls=(sum(PnPn.index))
Lq=sum((Pn.index[c+1:]-1)(Pn[c+1:]))

print('Output:','\n',
'Time Between Arrivals : ',str(data.inter_arrival_times.mean()),'\n',
'Service Time: (1/µ)',str(data.service_times.mean()),'\n'
' Utilization (c): ',str(workingtime/timeline.time.max()),'\n',
'Expected wait time in line (Wq):',str(data['wait_times'].mean()),'\n',
'Expected time spent on the system (Ws):',str(data.total_times.mean()),'\n',
'Expected number of customers in line (Lq):',str(Lq),'\n',
'Expected number of clients in the system (Ls):',str(Ls),'\n')