Heavy-traffic extreme value limits for Erlang delay models

Authors:
Guodong Pang;Ward Whitt
Affiliations:
IEOR Department, Columbia University, New York, USA;IEOR Department, Columbia University, New York, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2009

Citing 6
Cited 0

Modelling extremal events: for insurance and finance

Modelling extremal events: for insurance and finance
Designing a Call Center with Impatient Customers

Manufacturing & Service Operations Management
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects

Manufacturing & Service Operations Management
Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments

Management Science
Algorithmic Analysis of the Maximum Queue Length in a Busy Period for the M/M/c Retrial Queue

INFORMS Journal on Computing
Heavy-traffic extreme-value limits for queues

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment--the M/M/n+M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0,t] in the delay models converge jointly to independent random variables with the Gumbel extreme value distribution in the quality-and-efficiency-driven (QED) and ED many-server heavy-traffic limiting regimes as n and t increase to infinity together appropriately; we require that t n 驴驴 and t n =o(n 1/2驴驴 ) as n驴驴 for some 驴0.