. Two-channel model with ordered entry with M = N = 1.

Suppose that the service rates at the two channels are different, being ui and u2 at the first and second channel, respectively. Show that the steady-state probabilities are given by Po,1 = -

C xp2 (2 + 11 + 12)

Pi,o =

C 12(2 + 12)

PI.I =

and C

MIM2 (22 + 11 + 12)

Po,0=

C where C = (2 + (1)[(+2)2+12]. Show further that the waiting time Win steady state has the distribution given by P[W < 1) = [M]M2 (2)+ +1+12)+2M /11-+-
+212 (2+u1+ M2) (1 - e +2)]/C, 1 > 0 (Disney, 1962). Obtain the corresponding results for the particular case HI = 12.