Question: 1. Consider an M/M/2 system with arrival rate λ and service rate µ, where λ < 2µ.="">
a) Find the differential equation that govern the time-dependent probabilities pj(t).
b) Find the asymptotic probabilities πj.
2. Consider a call center with two phone lines for service. Assume that calls arrive according to a Poisson process with rate λ. During some measurements it was observed that both the lines are busy 50% of the time, whereas the mean call-holding time was 1 min. Calculate the call queueing probability in the case that the mean call holding time increases from 1 min to 2 min.