We consider a single GI/G/1 queueing system in which customer number 0 arrives at time t
0 = 0, finds a free server, and experiences a service time v
0. The nth customer arrives at time t
n
and experiences a service time v
n
. Let the interarrival times t
n
- t
n-1 = u
n
, n ≧ 1, and define the random vectors X
n
= (v
n-1, u
n
), n ≧ 1. We assume the sequence of random vectors {X
n
: n ≧ 1} is independent and identically distributed (i.i.d.). Let E{u
n
} = λ-1 and E{v
n
} = μ-1, where 0 < λ, μ < ∞. In addition, we shall always assume that E{v
0
2} < ∞ and that the deterministic system in which both v
n
and u
n
are degenerate is excluded. The natural measure of congestion for this system is the traffic intensity ρ = λ/μ. In this paper we shall restrict our attention to systems in which ρ < 1. Under this condition, which we shall refer to as light traffic, our system is of course stable.
Limit theorems arising from sequences of multinomial random vectors
