Consider the Ml Eklclc model.

(a) Derive the steady-state difference equation for this model. [Hint: Let Pn;s1 ,s2, ... ,sk represent the probability of n in the system with s 1 channels in phase 1, s2 in phase 2, etc.]

(b) Show that Pn = p0 pn In!, p = V J1, is a solution to the problem. [Hint:
First show that it is a solution to the equation of (a). Then show that

by utilizing the multinomial expansion (x1 + x2 + · · · + xk)n, then setting x1 = x2 = · · · = Xk = 1.]

(c) Compare this result with the MIMiclc results of Section 2.6, Equation (2.52), and comment.

Pn = Pn;81,82,8k s1+s2++sk=n Apn n!