TY - JOUR
T1 - Diffusion-level universality of many-server systems with concurrent service
AU - Storm, Pieter Jacob
AU - Borst, Sem
N1 - Publisher Copyright:
© 2023 The Authors
PY - 2023/5
Y1 - 2023/5
N2 - We present diffusion limits for a queuing system with n parallel servers with concurrent service capabilities. The diffusion limits are established in the many-server heavy-traffic regime where (1−ρn)nα→β as n→∞, for α∈(0,∞)∖{1/2} and ρn a notion of normalized system load. This encompasses the so-called sub-Halfin-Whitt, super-Halfin-Whitt, non-degenerate slowdown, and super-slowdown regimes. The diffusion limits are universal in that they depend only on whether α<1/2 or α>1/2 and do not depend on specific values of α and β in both cases.
AB - We present diffusion limits for a queuing system with n parallel servers with concurrent service capabilities. The diffusion limits are established in the many-server heavy-traffic regime where (1−ρn)nα→β as n→∞, for α∈(0,∞)∖{1/2} and ρn a notion of normalized system load. This encompasses the so-called sub-Halfin-Whitt, super-Halfin-Whitt, non-degenerate slowdown, and super-slowdown regimes. The diffusion limits are universal in that they depend only on whether α<1/2 or α>1/2 and do not depend on specific values of α and β in both cases.
KW - Concurrent service capabilities
KW - Customer abandonments
KW - Diffusion limits
KW - Many-server asymptotics
KW - Sub-Halfin-Whitt regime
KW - Super-Halfin-Whitt regime
UR - http://www.scopus.com/inward/record.url?scp=85149739405&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2023.02.012
DO - 10.1016/j.orl.2023.02.012
M3 - Article
AN - SCOPUS:85149739405
SN - 0167-6377
VL - 51
SP - 212
EP - 219
JO - Operations Research Letters
JF - Operations Research Letters
IS - 3
ER -