$$G/{ GI}/N(+{ GI})$$ G / G I / N ( + G I ) queues with service interruptions in the Halfin–Whitt regime

Hongyuan Lu (), Guodong Pang () and Yuhang Zhou ()

Mathematical Methods of Operations Research, 2016, vol. 83, issue 1, 127-160

Abstract: We study $$G/GI/N(+GI)$$ G / G I / N ( + G I ) queues with alternating renewal service interruptions in the Halfin–Whitt regime. The systems experience up and down alternating periods. In the up periods, the systems operate normally as the usual $$G/GI/N(+GI)$$ G / G I / N ( + G I ) queues with non-idling first-come–first-served service discipline. In the down periods, arrivals continue entering the systems, but all servers stop functioning while the amount of service that each customer has received will be conserved and services will resume when the next up period starts. For models with abandonment, interruptions do not affect customers’ patience times. We assume that the up periods are of the same order as the service times but the down periods are asymptotically negligible compared with the service times. We establish the functional central limit theorems for the queue-length processes and the virtual-waiting time processes in these models, where the limit processes are represented as stochastic integral convolution equations driven by jump processes. The convergence in these limit theorems is proved in the space $${\mathbb D}$$ D endowed with the Skorohod $$M_1$$ M 1 topology. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: $$G/GI/N(+GI)$$ G / G I / N ( + G I ) queues; Service interruptions; Halfin–Whitt regime; Functional central limit theorems; Skorohod $$M_1$$ M 1 topology; Integral convolution mapping; 60K25; 60F17; 90B22; 60J75 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-015-0523-z (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:83:y:2016:i:1:p:127-160

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-015-0523-z

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().