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


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


FundersFunder number
Belgian government
Dutch government1462/13
Israel Science Foundation


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


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