TY - JOUR
T1 - Rare event asymptotics for a random walk in the quarter plane
AU - Guillemin, F.
AU - Leeuwaarden, van, J.S.H.
PY - 2011
Y1 - 2011
N2 - This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.
AB - This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.
U2 - 10.1007/s11134-010-9197-7
DO - 10.1007/s11134-010-9197-7
M3 - Article
SN - 0257-0130
VL - 67
SP - 1
EP - 32
JO - Queueing Systems
JF - Queueing Systems
IS - 1
ER -