TY - JOUR

T1 - Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

AU - Janssen, A.J.E.M.

AU - Leeuwaarden, van, J.S.H.

AU - Zwart, B.

PY - 2008

Y1 - 2008

N2 - To investigate the quality of heavy-traffic approximations for queues with
many servers, we consider the steady-state number of waiting customers in an M/D/s
queue as s¿8. In the Halfin-Whitt regime, it is well known that this random variable
converges to the supremum of a Gaussian random walk. This paper develops
methods that yield more accurate results in terms of series expansions and inequalities
for the probability of an empty queue, and the mean and variance of the queue
length distribution. This quantifies the relationship between the limiting system and
the queue with a small or moderate number of servers. The main idea is to view the
M/D/s queue through the prism of the Gaussian random walk: as for the standard
Gaussian random walk, we provide scalable series expansions involving terms that
include the Riemann zeta function.

AB - To investigate the quality of heavy-traffic approximations for queues with
many servers, we consider the steady-state number of waiting customers in an M/D/s
queue as s¿8. In the Halfin-Whitt regime, it is well known that this random variable
converges to the supremum of a Gaussian random walk. This paper develops
methods that yield more accurate results in terms of series expansions and inequalities
for the probability of an empty queue, and the mean and variance of the queue
length distribution. This quantifies the relationship between the limiting system and
the queue with a small or moderate number of servers. The main idea is to view the
M/D/s queue through the prism of the Gaussian random walk: as for the standard
Gaussian random walk, we provide scalable series expansions involving terms that
include the Riemann zeta function.

U2 - 10.1007/s11134-008-9070-0

DO - 10.1007/s11134-008-9070-0

M3 - Article

VL - 58

SP - 261

EP - 301

JO - Queueing Systems: Theory and Applications

JF - Queueing Systems: Theory and Applications

SN - 0257-0130

IS - 4

ER -