Perfect Sampling for Infinite Server and Loss Systems
نویسندگان
چکیده
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 stationary infinite server queue backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We use the infinite server queue as an upper bound process to simulate loss systems. The running time analysis of our perfect sampling algorithm for loss systems is performed in the Quality-Driven (QD) and the Quality-and-Efficiency-Driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of convergence.
منابع مشابه
Applied Probability Trust PERFECT SAMPLING FOR INFINITE SERVER AND LOSS SYSTEMS
We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of Dominated Coupling From The Past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked p...
متن کاملStudies in Stochastic Networks: Efficient Monte-Carlo Methods, Modeling and Asymptotic Analysis
Studies in Stochastic Networks: Efficient Monte-Carlo Methods, Modeling and Asymptotic Analysis Jing Dong This dissertation contains two parts. The first part develops a series of bias reduction techniques for: point processes on stable unbounded regions, steady-state distribution of infinite server queues, steady-state distribution of multi-server loss queues and loss networks and sample path ...
متن کاملUnreliable Server Mx/G/1 Queue with Loss-delay, Balking and Second Optional Service
This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers m...
متن کاملCoupled perfect simulation of infinite range Gibbs measures and their finite range approximations
In this paper we address the question of perfectly sampling together a Gibbs measure with infinite range pairwise interactions and its finite range approximations. We solve this question by introducing a perfect simulation algorithm for the coupled measures. As a consequence we obtain an upper bound for the error we make when sampling from a finite range approximation instead of the true infini...
متن کاملImportance sampling algorithms for first passage time probabilities in the infinite server queue
This paper applies importance sampling simulation for estimating rare-event probabilities of the first passage time in the infinite server queue with renewal arrivals and general service time distributions. We consider importance sampling algorithms which are based on large deviations results of the infinite server queue, and we consider an algorithm based on the cross-entropy method, where we ...
متن کامل