Consider a structure consisting of two M/M/1 QSs working in parallel, with service ratesµ1 andµ2, respectively. The overall arrival rate is Poisson with parameter λ. Each arriving customer, independently of the others, is dispatched to QS one with probability p1 and to QS two with probability p2 = 1 − p1:
a) What is the stability condition for the whole structure?
b) Find p1 such that the mean time a customer remains in the structure is minimized.