You are required to simulate simple worm propagation in a medium-scale network by using discrete-time simulation technique.
Assume that in an isolated network with IP address space (i.e., the network is assigned with /n IP prefix space), there are N vulnerable computers to a particular worm in this network. These vulnerable computers occupy the even number of IP addresses starting from the lower end of the address space of the network. For example, if the network has an IP space of 192.168.0.0/16 and there are 100 vulnerable computers, then the IP addresses of these vulnerable computers are: 192.168.0.0, 192.168.0.2, 192.168.0.4, ....., until 192.168.0.200.
Now the worm starts its infection within this network from 1 initially infected machine (randomly picked from those vulnerable computers). At each discrete time unit, a worm-infected computer can scan randomly picked IP addresses within this network (the network has IP addresses). If it finds a vulnerable computer, it infects the vulnerable computer and this newly infected computer can start infecting others from the next discrete time (no delay is considered).
For such a worm propagation, we have introduced that it can be modeled by:
Where I(t) is the number of infected computers at time t.
Your assignments are:
1). Simulate a worm propagation considering no delay.
Simulate a worm propagation with parameters n=18, N=400, =2. You need to simulate the worm propagation for 100 runs in order to get the average values for I(t) for each discrete time t. Each of your simulation run should end when all vulnerable machines have been infected.
a). Draw a figure to compare the I(t) derived from the simulations (averaged value or called sample mean) and the above differential equation (i.e., the figure contains two I(t) curves). They should be matched with each other (with some statistical errors). The numerical result of the differential equation above can be derived by Matlab Simulink.
b). Draw a figure shows the I(t) from the first 3 simulation runs. This figure will exhibit the statistical variance in worm propagation process (each simulation run the worm's propagation dynamic is slightly different).