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Abstract We present the first algorithm that samples max n ≥0 { S n − n α }, where S n is a mean zero random walk, and n α with $$\alpha \in ({1 \over 2},1)$$ defines a nonlinear boundary. We show that our algorithm has finite expected running time. We also apply this algorithm to construct the first exact simulation method for the steady-state departure process of a GI/GI/∞ queue where the service time distribution has infinite mean.
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Exact sampling for some multi-dimensional queueing models with renewal input
Abstract Using a result of Blanchet and Wallwater (2015) for exactly simulating the maximum of a negative drift random walk queue endowed with independent and identically distributed (i.i.d.) increments, we extend it to a multi-dimensional setting and then we give a new algorithm for simulating exactly the stationary distribution of a first-in–first-out (FIFO) multi-server queue in which the arrival process is a general renewal process and the service times are i.i.d.: the FIFO GI/GI/ c queue with $$ 2 \leq c \lt \infty$$ . Our method utilizes dominated coupling from the past (DCFP) as well as the random assignment (RA) discipline, and complements the earlier work in which Poisson arrivals were assumed, such as the recent work of Connor and Kendall (2015). We also consider the models in continuous time, and show that with mild further assumptions, the exact simulation of those stationary distributions can also be achieved. We also give, using our FIFO algorithm, a new exact simulation algorithm for the stationary distribution of the infinite server case, the GI/GI/ $$\infty$$ model. Finally, we even show how to handle fork–join queues, in which each arriving customer brings c jobs, one for each server.
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- PAR ID:
- 10132114
- Date Published:
- Journal Name:
- Advances in Applied Probability
- Volume:
- 51
- Issue:
- 4
- ISSN:
- 0001-8678
- Page Range / eLocation ID:
- 1179 to 1208
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/apr.2019.45
