2.2.1 The mean arrival rate of the number of users in a particular cell making a call in the busy hour and the time interval of those calls is calculated. Every user makes a call in an interval by using the uniform random number. If this number exceeds 1-mean arrival rate or is equal to the mean arrival rate, then a call is generated which is referred as poisson threshold. 2.2.2
In this case the green line indicated the poisson threshold. When the customer uniform random number exceeds this value, a call is generated. The blue dot indicates the number of calls made. In this case the number of blue dots are around are 1000. Here the mean arrival rate is 1000/3600=0.277
Hence the poisson threshold= 1- 0.277=0.7222
Here the value of the poisson threshold is very high. No customers uniform random number exceeds this value hence no call is initiated. 2.2.1 Exercise
Here The mean arrival time= 25/1800=0.01388
Therefore the poisson distribution threshold = 1-0.01388=0.9688. The customer random number should exceed this high value to make a call. This is the difference between the threshold limit in the previous case which was lower than this particular one and hence it is easy to make a call in the previous case than this one. 2.2.4
Comparison of simulated call arrival and reference Poisson distribution. Call arrival in a cellular system are assumed to be poisson distributed. In this case the simulation period of 1 hour and the mean arrival is equal to 100 calls per hour. The graph above shows that the number of calls arrivals in multiple simulations follows poisson distribution along with a comparison with the theoretical poisson distribution.
2.3 Call Holding time Simulation
Graph shows the reference Poisson distribution function and the distributed call holding time.