Heavy traffic limits for queues with many deterministic servers

abstract

• Consider a sequence of stationary GI/D/N queues indexed by N , with servers' utilization 1 - /N, > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift -. This further implies a corresponding limit for the number of customers in the system, an easily computable non-degenerate limiting delay probability in terms of Spitzer's random-walk identities, and N rate of convergence for the latter limit. Our asymptotic regime is important for rational dimensioning of large-scale service systems, for example telephone- or internet-based, since it achieves, simultaneously, arbitrarily high service-quality and utilization-efficiency.

authors

• Momcilovic, Petar

published proceedings

• QUEUEING SYSTEMS

author list (cited authors)

• Jelenkovic, P., Mandelbaum, A., & Momcilovic, P.

citation count

• 60

complete list of authors

• Jelenkovic, P||Mandelbaum, A||Momcilovic, P

publication date

• May 2004

publisher

• Springer Nature  Publisher

published in

• Queueing Systems  Journal

keywords

• Deterministic Service Time
• Economies Of Scale
• Gaussian Random Walk
• Gi/d/n
• Heavy-traffic
• Multi-server Queue
• Quality And Efficiency Driven (qed) Or Halfin-whitt Regime
• Spitzer's Identities
• Telephone Call Or Contact Centers

Digital Object Identifier (DOI)

• 10.1023/B:QUES.0000032800.52494.51

start page

• 53

end page

• 69

volume

• 47

issue

• 1-2

URL

• http://dx.doi.org/10.1023/b:ques.0000032800.52494.51