. Two-channel model with ordered entry and with M = 1, N = 3.

Let P ;,; denote the probability that the number in channel 1 is i and that the number in channel 2 is j (i, j include those in service, if any).

Show that 4(p+1)(p+2)

p(p2+8p+8)

Po.o =

Pro =

A A

p (3p + 4)

p(p+1)(p+4)

Po.1 =

Pr. =

A A

2p3 (p+1)

p'(p + 1)(p +2)

Po.2 =

Pi2 =

A A

p+(p+1)

p4(p + 1)2 Po.3 =

P13 =

A A

where A = p + 4p5 + 8p4 + 13p3 + 20p2 + 20p + 8, p =

(Disney, 1962).