Related papers: Perfect Sampling and Gradient Simulation for Fork-…
We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…
We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…
A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management,…
Using a 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…
Compared to basic fork-join queues, a job in (n, k) fork-join queues only needs its k out of all n sub-tasks to be finished. Since (n, k) fork-join queues are prevalent in popular distributed systems, erasure coding based cloud storages,…
Networks in which the processing of jobs occurs both sequentially and in parallel are prevalent in many application domains, such as computer systems, healthcare, manufacturing, and project management. The parallel processing of jobs gives…
Fork-Join (FJ) queueing models capture the dynamics of system parallelization under synchronization constraints, for example, for applications such as MapReduce, multipath transmission and RAID systems. Arriving jobs are first split into…
In this paper we describe a perfect simulation algorithm for the stable $M/G/c$ queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build…
We introduce a new functional element (synchronizer for marked pairs) meant to join results of parallel processing in two-branch fork-join queueing network. Approximations for distribution of sojourn time at the synchronizer are derived…
We consider a large distributed service system consisting of $n$ homogeneous servers with infinite capacity FIFO queues. Jobs arrive as a Poisson process of rate $\lambda n/k_n$ (for some positive constant $\lambda$ and integer $k_n$). Each…
Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek to reap benefits of parallelization, albeit subject to a synchronization constraint at the output. Fork-Join (FJ) queuing models are used to analyze such systems.…
Multi-server systems have received increasing attention with important implementations such as Google MapReduce, Hadoop, and Spark. Common to these systems are a fork operation, where jobs are first divided into tasks that are processed in…
We introduce a model for synchronizer of marked pairs, which is a node for joining results of parallel processing in two-branch fork-join queueing network. A distribution for number of jobs in the synchronizer is obtained. Calculations are…
We provide the first algorithm that under minimal assumptions allows to simulate the stationary waiting-time sequence of a single-server queue backwards in time, jointly with the input processes of the queue (inter-arrival and service…
A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there…
Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis…
We develop exact simulation (also known as perfect sampling) algorithms for a family of assemble-to-order systems. Due to the finite capacity, and coupling in demands and replenishments, known solving techniques are inefficient for larger…
Inference for belief networks using Gibbs sampling produces a distribution for unobserved variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only…
In this paper we develop the first perfect sampling algorithm for queues with Hawkes input, i.e. single-server queues with Hawkes arrivals and i.i.d. service times of general distribution. In addition to the stability condition, we also…
We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…