On many-server queues in heavy traffic

By Anatolii A. Puhalskii, Josh E. Reed. 2010

60 citations recorded by the source corpus.

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit process does not have trajectories in the Skorohod space. We give conditions for the convergence to hold in the topology of compact convergence. Some new results for an infinite server are also provided.

Subfields: Management Information Systems, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa88652e1e98294dbf40f1cd4dbb96ceae8cc929

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In Management Information Systems

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Many-server diffusion limits for G/Ph/n+GI queues (2010, methodology): “This terminology is consistent with the usage in conventional heavy traffic, where the limit process is often a constrained diffusion process; see, for example, Reiman (1984). In the critically-loaded regime, Halfin and Whitt (1981) is the first paper to establish a diffusion limit for the GI/M/n mo”
SPDE Limits of Many Server Queues (2010, background): “To date, the most general results on process level convergence in the Halfin–Whitt regime were obtained in a nice pair of papers by Reed [27] and Puhalskii and Reed [25].”