140520200849
The purpose of the exercise is to indicate the general performance characteristics of the banking information processing system.
The following formulas come from the study: Hillier F.S., Lieberman G.J. Instruction of Operation Research. New York: McGrew Hill 1990 oraz Z. Jędrzejczyk, K.Kukuła, J.Skrzypek, A. Walkosz Badania operacyjne w przykładach i zadaniach, Wydawnictwo Naukowe PWN
Arrival rate: λ
These are transactions arriving within a minute. It is a stream of transaction orders sent from bank customers sent online.
import numpy as np
np.random.seed(148)
Λ1 = (np.random.random_sample(2354)*4690)
Λ2 = (np.random.random_sample(4899)*2319)
Λ3 = (np.random.random_sample(3511)*5491)
a1= sum(Λ1)
p1= len(Λ1)
λ1 = 1/(p1/a1)
a2= sum(Λ2)
p2= len(Λ2)
λ2 = 1/(p2/a2)
a3= sum(Λ3)
p3= len(Λ3)
λ3 = 1/(p3/a3)
print('Number of transactions: ', p1)
print('Sume of transactions time: print('Arrival_λ1: print('-----------------------------------------------')
print('Number of transactions: ', p2)
print('Sume of transactions time: print('Arrival_λ2: print('-----------------------------------------------')
print('Number of transactions: ', p3)
print('Sume of transactions time: print('Arrival_λ3: print('-----------------------------------------------')
Service rate: μ
This parameter represents the execution time of individual banking transactions by the banking transaction system.Each of the three data centers has a number of servers. A single server is treated as an individual information flow channel.
r1 = 5
r2 = 6
r3 = 8
np.random.seed(148)
M1 = (np.random.random_sample(2354)*959)
M2 = (np.random.random_sample(4899)*790)
M3 = (np.random.random_sample(3511)*903)
a1= sum(M1)
p1= len(M1)
μ1 = 1/(p1/a1)
a2= sum(M2)
p2= len(M2)
μ2 = 1/(p2/a2)
a3= sum(M3)
p3= len(M3)
μ3 = 1/(p3/a3)
print('Number of transactions: ', p1)
print('Sume of service time: print('Service_μ: print('-----------------------------------------------')
print('Number of transactions: ', p2)
print('Sume of service time: print('Service_μ: print('-----------------------------------------------')
print('Number of transactions: ', p3)
print('Sume of service time: print('Service_μ: print('-----------------------------------------------')
Traffic intensity: ϱ
Traffic intensity is the ratio of arrival rate to service rate.
\bbox[#f3f3f3,12px,border:1px solid black] {
{ϱ}=\frac{λ}{{μ}*r}
} \qquad (1)
$$
ϱ1 = λ1/(μ1*r1)
if ϱ1 >= 1:
print("The system is unstable, we do not carry out further calculations!")
print('Arrival rate λ1 > service rate μ1, ϱ1= else:
print("The system is stable, you can calculate the probabilities!")
print('Arrival rate λ1 > service rate μ1')
print('Arrival rate λ1: print('Service rate μ1: print('Traffic intensity ϱ1: ϱ2 = λ2/(μ2*r2)
if ϱ2 >= 1:
print("The system is unstable, we do not carry out further calculations!")
print('Arrival rate λ2 > service rate μ2 ,ϱ2= else:
print("The system is stable, you can calculate the probabilities!")
print('Arrival rate λ2 > service rate μ2')
print('Arrival rate λ2: print('Service rate μ2: print('Traffic intensity ϱ2: ϱ3 = λ3/(μ3*r3)
if ϱ3 >= 1:
print("The system is unstable, we do not carry out further calculations!")
print('Arrival rate λ3 > service rate μ3, ϱ3= else:
print("The system is stable, you can calculate the probabilities!")
print('Arrival rate λ3 > service rate μ3')
print('Arrival rate λ3: print('Service rate μ3: print('Traffic intensity ϱ3: