Abstract: | For stable FIFO GI/GI/s queues, s ≥ 2, we show that finite (k+1)st moment of service time, S, is not in general necessary for finite kth moment of steady-state customer delay, D, thus weakening some classical conditions of Kiefer and Wolfowitz (1956). Further, we demonstrate that the conditions required
for ED
k]<∞ are closely related to the magnitude of traffic intensity ρ (defined to be the ratio of the expected service time to the
expected interarrival time). In particular, if ρ is less than the integer part of s/2, then ED] < ∞ if ES3/2]<∞, and EDk]<∞ if ESk]<∞, k≥ 2. On the other hand, if s-1 < ρ < s, then EDk]<∞ if and only if ESk+1]<∞, k ≥ 1. Our method of proof involves three key elements: a novel recursion for delay which reduces the problem to that of a
reflected random walk with dependent increments, a new theorem for proving the existence of finite moments of the steady-state
distribution of reflected random walks with stationary increments, and use of the classic Kiefer and Wolfowitz conditions.
This revised version was published online in June 2006 with corrections to the Cover Date. |