Jackson network problem: (The mathematical modeling by Amine Moulay Ramdane)
Description:
From:
http://www.perfdynamics.com/Tools/PDQpython.html
http://simpy.sourceforge.net/examples/Jackson%20network.htm
Messages arrive randomly at rate 0.5 per unit time at a communication network with 3 nodes (computers). Each computer can queue messages and service-times are exponential with mean m[i] at node i. These values are given in the column headed m[i] in the table below. On service at a node a message transfers to one of the other nodes or leaves the system. The probability of a transfer from node i to node j is p[i,j]. Node 4 means "outside the system" so a message will transfer out of the system from node i with probability p[i,4].
Your task is to estimate the average time taken for jobs going through the system and the average number of jobs in the system.
You can download my tutorial and the solution from here:
You can go to download the zip files by clicking on the following web link:
https://drive.google.com/drive/folders/11l8QkKSTr3j3h_NsgtGu45kcOzY_Fkt1?usp=sharing