Answer the following questions for a host where the arrival times and service ti

Question

Answer the following questions for a host where the arrival times and service times follow Poisson distributions. The average arrival rate is 2000 packets per second.
a) How many packets do we expect to be stored in the host if the average service rate is 3000 packets per second?
b) What average service rate do we need if we want a packet to be in queue (not the whole system) for an average of 1 millisecond?
c) What is the smallest average service rate that can still allow the host's queue to be in equilibrium, assuming that the host has infinite memory? Why?

Explanation / Answer

=2000

=3000

a) E[N]=(/)/(1-/)=2;

b) average waiting time in queue =1 ms

E(W) =1MS

=/2/(1-/)

=5464 packets/sec

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