Basic probability involving a poisson distribution Packets a

Basic probability involving a poisson distribution..

Packets arrive at a network with a Poisson distribution with rate lambda = 10 per second They are directed independently to two different routers with a probability of p = 0.5. 1) what is the distribution of the arrival streams at each router? What is the rate for the incoming stream for each individual router? 2) Assume now that algorithm of distributing the packets at the two routers change as follows: odd packets go to router 1, even packets gp to router 2. Comment on the distribution of arrivals for each router in this case. Does the arrival rate for individual routers change? 3) For the previous case (case 2) what is the distribution of the inter-arrival times for each incoming stream into the routers?

Solution

distribution of arrival of steamers is exponential.

Prob for each individual =0.5

2) Arrival rate does not change as prob for odd or even is equally likely and each has prob 0.5

3) Distribution will be again exponential.