Regenerative rare events simulation via likelihood ratios

1994 ◽  
Vol 31 (03) ◽  
pp. 797-815 ◽  
Author(s):  
Søren Asmussen ◽  
Reuven Y. Rubinstein ◽  
Chia-Li Wang
Keyword(s):  
Queueing Networks ◽  
Score Function ◽  
Gradient Estimates ◽  
Queueing Models ◽  
Service Time Distribution ◽  
Ratio Score ◽  
Likelihood Ratios ◽  
The Given ◽  
Suitable Change ◽  
Steady State Probabilities

In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ 0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.

Regenerative rare events simulation via likelihood ratios

1994 ◽  
Vol 31 (3) ◽  
pp. 797-815 ◽  
Author(s):  
Søren Asmussen ◽  
Reuven Y. Rubinstein ◽  
Chia-Li Wang
Keyword(s):  
Queueing Networks ◽  
Score Function ◽  
Gradient Estimates ◽  
Queueing Models ◽  
Service Time Distribution ◽  
Ratio Score ◽  
Likelihood Ratios ◽  
The Given ◽  
Suitable Change ◽  
Steady State Probabilities

In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.

On First-Come First-Served Versus Random Service Discipline in Multiclass Closed Queueing Networks

1997 ◽  
Vol 11 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Ronald Buitenhek ◽  
Geert-Jan van Houtum ◽  
Jan-Kees van Ommeren
Keyword(s):  
Steady State ◽  
Queueing Networks ◽  
Form Solution ◽  
Product Form ◽  
Service Discipline ◽  
Single Server ◽  
Service Time Distribution ◽  
Closed Queueing Networks ◽  
Steady State Probabilities ◽  
Closed Network

We consider multiclass closed queueing networks. For these networks, a lot of work has been devoted to characterizing and weakening the conditions under which a product-form solution is obtained for the steady-state distribution. From this work, it is known that, under certain conditions, all networks in which each of the stations has either the first-come first-served or the random service discipline lead to the same (product-form expressions for the) steady-state probabilities of the (aggregated) states that for each station and each job class denote the number of jobs in service and the number of jobs in the queue. As a consequence, all these situations also lead to the same throughputs for the different job classes. One of the conditions under which these equivalence results hold states that at each station all job classes must have the same exponential service time distribution. In this paper, it is shown that these equivalence results can be extended to the case with different exponential service times for jobs of different classes, if the network consists of only one single-server or multiserver station. This extension can be made despite of the fact that the network is not a product-form network anymore in that case. The proof is based on the reversibility of the Markov process that is obtained under the random service discipline. By means of a counterexample, it is shown that the extension cannot be made for closed network with two or more stations.

scholarly journals Symmetric double bubbles in the Grushin plane

2019 ◽  
Vol 25 ◽  
pp. 77
Author(s):  
Valentina Franceschi ◽  
Giorgio Stefani
Keyword(s):  
Direct Method ◽  
Regularity Theory ◽  
Contact Interface ◽  
Double Bubble ◽  
Grushin Plane ◽  
Existence Of Minimizers ◽  
Double Bubbles ◽  
The Given ◽  
Suitable Change ◽  
Horizontal Interface

We address the double bubble problem for the anisotropic Grushin perimeter Pα, α ≥ 0, and the Lebesgue measure in ℝ2, in the case of two equal volumes. We assume that the contact interface between the bubbles lies on either the vertical or the horizontal axis. We first prove existence of minimizers via the direct method by symmetrization arguments and then characterize them in terms of the given area by first variation techniques. Even though no regularity theory is available in this setting, we prove that angles at which minimal boundaries intersect satisfy the standard 120-degree rule up to a suitable change of coordinates. While for α = 0 the Grushin perimeter reduces to the Euclidean one and both minimizers coincide with the symmetric double bubble found in Foisy et al. [Pacific J. Math. 159 (1993) 47–59], for α = 1 vertical interface minimizers have Grushin perimeter strictly greater than horizontal interface minimizers. As the latter ones are obtained by translating and dilating the Grushin isoperimetric set found in Monti and Morbidelli [J. Geom. Anal. 14 (2004) 355–368], we conjecture that they solve the double bubble problem with no assumptions on the contact interface.

scholarly journals Cyclic queueing networks with subexponential service times

2004 ◽  
Vol 41 (03) ◽  
pp. 791-801
Author(s):  
H. Ayhan ◽  
Z. Palmowski ◽  
S. Schlegel
Keyword(s):  
Queueing Networks ◽  
Time Distribution ◽  
Waiting Times ◽  
Queueing Network ◽  
Service Time Distribution ◽  
Tail Behavior ◽  
Cycle Times ◽  
General Service Times ◽  
Service Times ◽  
General Service

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

A Probability Scoring Rule for Simultaneous Events

2019 ◽  
Vol 16 (4) ◽  
pp. 301-313
Author(s):  
Andrew Grant ◽  
David Johnstone ◽  
Oh Kang Kwon
Keyword(s):  
Economic Benefit ◽  
Score Function ◽  
Interesting Property ◽  
Usual Sense ◽  
Power Utility ◽  
Scoring Rule ◽  
The Individual ◽  
Individual Scores ◽  
The Given ◽  
Special Case

We develop a scoring rule tailored to a decision maker who makes simultaneous bets on events that occur at times that require bets to be placed together. The rule proposed captures the economic benefit to a well-defined bettor who acts on one set of probabilities p against a baseline or rival set q. To allow for simultaneous bets, we assume a myopic power utility function with a risk aversion parameter tailored to suit the given user or application. Our score function is “proper” in the usual sense of motivating honesty. Apart from a special case of power utility, namely, log utility, the score is not “local,” which we excuse because a local scoring rule cannot capture the economic result that our score reflects. An interesting property of our rule is that the individual scores from individual events are multiplicative, rather than additive. Probability scores are often added to give a measure of aggregate performance over a set of trials. Our rule is unique in that scores must be multiplied to reach a meaningful aggregate.

MODELING TRAFFIC FLOWS WITH QUEUEING MODELS: A REVIEW

2007 ◽  
Vol 24 (04) ◽  
pp. 435-461 ◽  
Author(s):  
TOM VAN WOENSEL ◽  
NICO VANDAELE
Keyword(s):  
Queueing Networks ◽  
Road Networks ◽  
Queueing Network ◽  
Analytical Application ◽  
Buffer Size ◽  
Queueing Models ◽  
Finite Buffer ◽  
Traffic Flows ◽  
Single Node ◽  
The Impact

In this paper, an overview of different analytic queueing models for traffic on road networks is presented. In the literature, it has been shown that queueing models can be used to adequately model uninterrupted traffic flows. This paper gives a broad review on this literature. Moreover, it is shown that the developed published methodologies (which are mainly single node oriented) can be extended towards queueing networks. First, an extension towards queueing networks with infinite buffer sizes is evaluated. Secondly, the assumption of infinite buffer sizes is dropped leading to queueing networks with finite buffer sizes. The impact of the buffer size when comparing the different queueing network methodologies is studied in detail. The paper ends with an analytical application tool to facilitate the optimal positioning of the counting points on a highway.

The ELECTRE I Multi-Criteria Decision-Making Method Based on Hesitant Fuzzy Sets

2015 ◽  
Vol 14 (03) ◽  
pp. 621-657 ◽  
Author(s):  
Na Chen ◽  
Zeshui Xu ◽  
Meimei Xia
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Uncertain Information ◽  
Deviation Function ◽  
Outranking Relations ◽  
Electre I ◽  
Parameter Interval ◽  
The Given

Hesitant fuzzy set (HFS), which allows the membership degree of an element to a set represented by several possible values, is considered as a powerful tool to express uncertain information in the process of multi-criteria decision making (MCDM) problems. In this paper, we develop a hesitant fuzzy ELECTRE I (HF-ELECTRE I) method and apply it to solve the MCDM problem under hesitant fuzzy environments. The new method is formulated using the concepts of hesitant fuzzy concordance and hesitant fuzzy discordance which are based on the given score function and deviation function, and employed to determine the preferable alternative. Numerical examples are provided to demonstrate the application of the proposed method, and the influence of different numbers of alternatives on outranking relations is analyzed based on a derived sensitive parameter interval in which a change in the parameters has no effects on the set of the nonoutranked alternatives. The randomly generated numerical cases are also investigated in the framework of the HF-ELECTRE I method. Furthermore, the outranking relations obtained in the HF-ELECTRE I method with those derived from the aggregation operator-based approach and the ELECTRE III and ELECTRE IV methods are discussed.

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