Exact asymptotics for a large deviations problem for the GI/G/1 queue
Sören Asmussen and Jeffrey F. Collamore
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
1999
ISSN 14039338
1999:7

Abstract:

Let V be the steadystate workload and Q the steadystate queue length in
the GI/G/1 queue. We obtain the exact asymptotics of probabilities of the
form P(V > a(t), Q > b(t)) as t tends to infinity. In the lighttailed
case, there are three regimes according to the limiting value of a(t)/b(t),
and our analysis extends and simplifies recent work of Aspandiiarov and Pechersky
(1997). In the heavytailed subexponential case, a lower asymptotic bound
is derived and shown to be the exact asymptotics in a regime where a(t),
b(t) vary in a certain way determined by the service time distribution.


Key words:

change of measure, conditioned limit theorems, saddlepoint approximations,
subexponential distribution, workload