An ASIP model with general gate opening intervals

Onno Boxma (), Offer Kella () and Uri Yechiali ()
Additional contact information
Onno Boxma: Eindhoven University of Technology
Offer Kella: The Hebrew University of Jerusalem
Uri Yechiali: Tel Aviv University

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 1, No 1, 20 pages

Abstract: Abstract We consider an asymmetric inclusion process, which can also be viewed as a model of n queues in series. Each queue has a gate behind it, which can be seen as a server. When a gate opens, all customers in the corresponding queue instantaneously move to the next queue and form a cluster with the customers there. When the nth gate opens, all customers in the nth site leave the system. For the case where the gate openings are determined by a Markov renewal process, and for a quite general arrival process of customers at the various queues during intervals between successive gate openings, we obtain the following results: (i) steady-state distribution of the total number of customers in the first k queues, $$k=1,\dots ,n$$ k = 1 , ⋯ , n ; (ii) steady-state joint queue length distributions for the two-queue case. In addition to the case that the numbers of arrivals in successive gate opening intervals are independent, we also obtain explicit results for a two-queue model with renewal arrivals.

Keywords: Asymmetric inclusion process; Tandem network; Synchronized service; Queue length distribution; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s11134-016-9492-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:queues:v:84:y:2016:i:1:d:10.1007_s11134-016-9492-z

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/11134/

DOI: 10.1007/s11134-016-9492-z

Access Statistics for this article

Queueing Systems: Theory and Applications is currently edited by Sergey Foss

More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().