An ASIP model with general gate opening intervals

Onno Boxma*, Offer Kella, Uri Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 , ⋯ , 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.

Original languageAmerican English
Pages (from-to)1-20
Number of pages20
JournalQueueing Systems
Issue number1-2
StatePublished - 1 Oct 2016

Bibliographical note

Funding Information:
Onno Boxma: research done in the framework of the IAP BESTCOM project, funded by the Belgian government and by the Gravity program NETWORKS of the Dutch government.

Funding Information:
Offer Kella: supported in part by Grant 1462/13 from the Israel Science Foundation and the Vigevani Chair in Statistics.

Publisher Copyright:
© 2016, The Author(s).


  • Asymmetric inclusion process
  • Queue length distribution
  • Synchronized service
  • Tandem network


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