Replace the state m = (m, z 1 , . . . , z m ) in Section 6.6 with an expanded state m = (m, z 1 , w 1 , z 2 , w 2 , . . . , z m , w m ) where m and {z i ; 1 ≤ i ≤ m} are as before and w 1 , w 2 , . ....

Replace the state m = (m, z₁, . . . , z_m) in Section 6.6 with an expanded state m = (m, z₁, w₁, z₂, w₂, . . . , z_m, w_m) where m and {z_i; 1 ≤ i ≤ m} are as before and w₁, w₂, . . . , wm are the original service requirements of the m customers.

a) Hypothesizing the same backward round-robin system as hypothesized in Section 6.6, find the backward transition probabilities and give the corresponding equations to (6.51- 6.54) for the expanded state description.

b) Solve the resulting equations to show that