Exact Monte Carlo simulation for fork-join networks

Dai, Hongsheng

doi:10.1017/s000186780000495x

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…In fact when c ≥ 3, only bounds and approximations are available. As for exact simulation, there is a paper by Hongsheng Dai [10], in which Poisson arrivals and independent exponential service times are assumed. Because of the continuous-time Markov chain (CTMC) model structure, the author is able to construct (simulate) the time-reversed CTMC to use in a coupling from the past algorithm.…”

Section: Fork-join Modelsmentioning

confidence: 99%

Exact sampling for some multi-dimensional queueing models with renewal input

2019

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Using a recent result of Blanchet and Wallwater (2015: Exact sampling of stationary and time-reversed queues. ACM TOMACS, 25, 26) for exactly simulating the maximum of a negative drift random walk queue endowed with independent and identically distributed (iid) 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 iid; the FIFO GI/GI/c queue with 2 ≤ c < ∞. 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: Perfect simulation of M/G/c queues. Advances in Applied Probability, 47, 4). 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/∞ model. Finally, we even show how to handle Fork-Join queues, in which each arriving customer brings c jobs, one for each server.Keywords exact sampling; multi-server queue; random walks; random assignment; dominated coupling from the past.

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Section: Fork-join Modelsmentioning

confidence: 99%

Exact sampling for some multi-dimensional queueing models with renewal input

2019

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“…The CFTP algorithm is only practical for small discrete sample spaces or for a target distribution having a probability space equipped with a partial order preserved by an appropriate Markov chain construction. Although in recent decades, there have been many theoretical developments and applications in this area 1350-7265 © 2017 ISI/BS such as [4,8,15,16,20,24,28] and [9], the CFTP algorithm is still not practical for complex statistical models.…”

Section: Background Of Exact Monte Carlo Simulationmentioning

confidence: 99%

“…Simulate the Brownian bridgeB = {ω t , t ∈ (0, T )} given (ω 0 = x l , ω T = y); 9 Simulate I l = 1 with probability given by (10), with α(x) = ∇A(x) and A(x) = log g l (x); Simulate the Brownian bridgeB = {ω t , t ∈ (0, T )} given (ω 0 = x l , ω T = y); 11 Simulate I l = 1 with probability given by (10), with α(x) = ∇A(x) and A(x) = log g (l) (x); …”

Section: Rejection Sampling For the General Case F = ι L=1 G Lmentioning

confidence: 99%

A new rejection sampling method without using hat function

Dai¹

2017

Bernoulli

Self Cite

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This paper proposes a new exact simulation method, which simulates a realisation from a proposal density and then uses exact simulation of a Langevin diffusion to check whether the proposal should be accepted or rejected. Comparing to the existing coupling from the past method, the new method does not require constructing fast coalescence Markov chains. Comparing to the existing rejection sampling method, the new method does not require the proposal density function to bound the target density function. The new method is much more efficient than existing methods for certain problems. An application on exact simulation of the posterior of finite mixture models is presented.

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“…Ko and Serfozo [27] studied a single-class multi-server fork-join model with NES as depicted in Figure 1, where the arrival process is Poisson and service times are independent exponential, but their focus is on obtaining approximations for the steadystate system response time. In [10] an exact simulation algorithm is provided for the same Markovian model. Recently, in [8], an exact sampling algorithm is developed to simulate the stationary distribution for a multi-server forkjoin model with NES that has renewal arrivals and i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Heavy-traffic limits for a fork-join networkin the Halfin-Whitt regime

Lu¹,

Pang²

2016

Stoch. Syst.

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We study a fork-join network with a single class of jobs, which are forked into a fixed number of parallel tasks upon arrival to be processed at the corresponding multi-server stations. After service completion, each task will join a buffer associated with the service station waiting for synchronization, called "unsynchronized queue". The synchronization rule requires that all tasks from the same job must be completed, referred to as "non-exchangeable synchronization". Once synchronized, jobs will leave the system immediately. Service times of the parallel tasks of each job can be correlated and form a sequence of i.i.d. random vectors with a general continuous joint distribution function. We study the joint dynamics of the queueing and service processes at all stations and the associated unsynchronized queueing processes.The main mathematical challenge lies in the "resequencing" of arrival orders after service completion at each station. As in Lu and Pang (2015) for the infinite-server fork-join network model, the dynamics of all the aforementioned processes can be represented via a multiparameter sequential empirical process driven by the service vectors for the parallel tasks of each job. We consider the system in the Halfin-Whitt regime, and prove a functional law of large number and a functional central limit theorem for queueing and synchronization processes. In this regime, although the delay for service at each station is asymptotically negligible, the delay for synchronization is of the same order as the service times.

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Exact Monte Carlo simulation for fork-join networks

Cited by 5 publications

References 18 publications

Exact sampling for some multi-dimensional queueing models with renewal input

Exact sampling for some multi-dimensional queueing models with renewal input

A new rejection sampling method without using hat function

Heavy-traffic limits for a fork-join networkin the Halfin-Whitt regime

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