how can I simulate a single realization of the Poisson counting process as described above. Such that the discrete-amplitude random process X(t) counts the number of packets arriving in the time interval [0,t). Take your simulation total time to be 10 hours, time sampling step size to be 1 sec.
Assume that the average number of packets arriving per minute in a certain cell equal 10
I tried to simulate the poisson but I can't understand how to simulate it and how to compute the interval times between the arrival of each two successive packets
The chance of an event in $1$ second is $\frac 1{6}$ because you have $10$ events per minute. Throw a random number with that probability for whether an event happens. You have an error because you can't have two events in one second, but the chance is rather small. I would have taken a shorter interval to reduce that, but $1$ second is specified in the problem.