So on Substituting into (14), One Can Conclude Lim N!1

E e tC N=2 = 1 1 ? t ; t < 0: But 1=(1 ? t) is the Laplace transform of the exponential distribution 1 ? e ?x ; x 0, so the L evy continuity theorem 5, p. 191] completes the proof of the limit law for C. 2 In general, an exponential approximation P(W EX] > x) e ?x to the waiting time distribution can be expected whenever N is large and each individual cell serves a given processor only rarely. Feller 4, pp. 355{356] outlined an argument for a similar result, but some care is needed to justify the approximations. The next theorem supplies these details when X is uniformly distributed. Proof: The argument examines P(W > t) with t = cN + a = xN=2, and hence c = b x 2 c. Let = x 2 ? b x 2 c, so that = a N. Since 1 ? R c = r 1 + + r c = P(C c), Theorem 5 shows that R c ! 1 for any xed c. From (13),