Abstract
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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
11 articles.
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