Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Dimensioning Large Call Centers
Operations Research
Heavy Traffic Limits for Queues with Many Deterministic Servers
Queueing Systems: Theory and Applications
Heavy-Traffic Limits for the G/H2*/n/m Queue
Mathematics of Operations Research
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Refining Square-Root Safety Staffing by Expanding Erlang C
Operations Research
A simple solution for the M/D/c waiting time distribution
Operations Research Letters
Sharp and simple bounds for the Erlang delay and loss formulae
Queueing Systems: Theory and Applications
Heavy-traffic limits for nearly deterministic queues: stationary distributions
Queueing Systems: Theory and Applications
Refining Square-Root Safety Staffing by Expanding Erlang C
Operations Research
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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驴驴. 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.