import pandas as pd

import seaborn as sns

import numpy as np

import matplotlib.pyplot as plt

import warnings

warnings.filterwarnings('ignore')

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'])

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')

timeline = pd.DataFrame(list(zip(tbe,timeline)),

columns =['time','Timeline']).sort_values(by='time').reset_index()

timeline=timeline.drop(columns='index')

timeline['n']=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'][2*ncust-3]-timeline['time'][2*ncust-2]

timeline.time.max()

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)

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'])

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(Pn*Pn.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')