Little's theorem states that under very general conditions L = λW, where L is the time average number in the system, W is the expected sojourn time in the system, and λ is the mean arrival rate to the system. For certain systems it is known that relations of the form E((L)
l
) = λ lE((W)
l
) are also true, where (L)
l
= L(L – 1)· ·· (L – l + 1). It is shown in this paper that closely analogous relations hold in closed, product-form queueing networks. Similar expressions relate Nji
and Sji, where Nji
is the total number of class j jobs at center i and Sji
is the total sojourn time of a class j job at center i, when center i is a single-server, FCFS center. When center i is a c-server, FCFS center, Qji
and Wji
are related this way, where Qji
is the number of class j jobs queued, but not in service at center i and Wji
is the waiting time in queue of a class j job at center i. More remarkably, generalizations of these results to joint moments of queue lengths and sojourn times along overtake-free paths are shown to hold.
Product-Form Queueing Networks with Batches