. The system M/ Ek/ 1: transient behavior. Define 00 00 P(s, t) => Pm(1)s", P*(s,a) = > pt(a)s",

₪=0 where p*(@) is the LT of p,(t). Assume that po(0) = 1. Show that s - ku(1-s) po(@)

P* (s,a) =

s(c+ +kp) - kj - Ask+1) |s| <1, and that c

lim po

(a) =

0-0 ku(1-c)'

where c = c(s,

a) is the only zero of (a + + ku)s - ku - Ask+1 inside the unit circle |s| = 1. Noting that lim @ p"

(a) = lim p ,, (t) = P, and a >0

,00 lim @ P*(s,a) = lim P(s, t) = P(s) => pms",

₾-+0 1-00

*= 0 derive the expression for the PGF P(s) [in the form given in (4.1.6)].