. M / M/c (Kabak, 1968) queue with rates and / = 1 Consider (i) the delay system M' / M/c/00, where customers are

. M / M/c (Kabak, 1968) queue with rates À and / = 1 Consider (i) the delay system M' / M/c/00, where customers are al-

lowed to wait, and (ii) the loss system M / M/c/c, where customers are lost when all the channels are busy. If { p;} is the steady-state proba-

bility distribution of the system size, show that p; satisfies the following equations.

For the delay system, THE 2

Isise-1, Pi = 7 i

J=max(0.i-r)

=

Pj, i ≥c, and J=max(0,i-r)

CP = 1.

For the loss system, Pi == > Pp, Igisc, ist j=0 1-
Pp, Isise, ian, and j=i-r C. P = 1.
i=0