scholarly journals A product form for the general stochastic matching model

2021 ◽  
Vol 58 (2) ◽  
pp. 449-468
Author(s):  
Pascal Moyal ◽  
Ana Bušić ◽  
Jean Mairesse
Keyword(s):  
Stationary Distribution ◽  
Product Form ◽  
Necessary Condition ◽  
Matching Model ◽  
Bipartite Matching ◽  
Compatibility Graph ◽  
Stochastic Matching ◽  
Dynamic Reversibility ◽  
Original Dynamic ◽  
Do So

AbstractWe consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.

scholarly journals An Objective Algorithm for Detecting and Tracking Tropical Cloud Clusters: Implications for Tropical Cyclogenesis Prediction

2011 ◽  
Vol 28 (8) ◽  
pp. 1007-1018 ◽  
Author(s):  
Christopher C. Hennon ◽  
Charles N. Helms ◽  
Kenneth R. Knapp ◽  
Amanda R. Bowen
Keyword(s):  
Tropical Cyclone ◽  
Numerical Models ◽  
Global Analysis ◽  
Ocean Basin ◽  
Necessary Condition ◽  
Tropical Cyclogenesis ◽  
Movement Vector ◽  
Cloud Clusters ◽  
Real Time Tracking ◽  
Do So

Abstract An algorithm to detect and track global tropical cloud clusters (TCCs) is presented. TCCs are organized large areas of convection that form over warm tropical waters. TCCs are important because they are the “seedlings” that can evolve into tropical cyclones. A TCC satisfies the necessary condition of a “preexisting disturbance,” which provides the required latent heat release to drive the development of tropical cyclone circulations. The operational prediction of tropical cyclogenesis is poor because of weaknesses in the observational network and numerical models; thus, past studies have focused on identifying differences between “developing” (evolving into a tropical cyclone) and “nondeveloping” (failing to do so) TCCs in the global analysis fields to produce statistical forecasts of these events. The algorithm presented here has been used to create a global dataset of all TCCs that formed from 1980 to 2008. Capitalizing on a global, Gridded Satellite (GridSat) infrared (IR) dataset, areas of persistent, intense convection are identified by analyzing characteristics of the IR brightness temperature (Tb) fields. Identified TCCs are tracked as they move around their ocean basin (or cross into others); variables such as TCC size, location, convective intensity, cloud-top height, development status (i.e., developing or nondeveloping), and a movement vector are recorded in Network Common Data Form (NetCDF). The algorithm can be adapted to near-real-time tracking of TCCs, which could be of great benefit to the tropical cyclone forecast community.

scholarly journals A general stochastic matching model on multigraphs

2021 ◽  
Vol 18 (1) ◽  
pp. 1325
Author(s):  
Jocelyn Begeot ◽  
Irène Marcovici ◽  
Pascal Moyal ◽  
Youssef Rahme
Keyword(s):  
Matching Model ◽  
Stochastic Matching ◽  
General Stochastic

Bipartite matching model with dynamic arrivals and departures

2018 ◽  
Vol 09 (04) ◽  
pp. 1850031 ◽  
Author(s):  
Weiwei Jiang
Keyword(s):  
Time Horizon ◽  
Strategic Behavior ◽  
Matching Markets ◽  
Matching Model ◽  
Bipartite Matching ◽  
Long Time ◽  
Classical Models ◽  
Matching Mechanism ◽  
Finite Time Horizon ◽  
Dynamic Arrivals

In this paper, we introduce a bipartite matching model for matching markets with dynamic arrivals and departures. Different from classical models with a finite-time horizon, our model has a long-time horizon with infinite vertices. In our model, the matching goal is to maximize the ratio of matched vertices, i.e., matched ratio. We define two types of online algorithms, i.e., Greedy and Patient, analyze their performance with evaluation metrics of both upper bounds and competitive ratios, and conduct extensive simulations to validate our analysis. To further simulate the real situation, we extend our model with the user’s strategic behavior and prove the existence of a specific Nash equilibrium under a differentiated matching mechanism.

scholarly journals Stability of the Bipartite Matching Model

2013 ◽  
Vol 45 (2) ◽  
pp. 351-378 ◽  
Author(s):  
Ana Bušić ◽  
Varun Gupta ◽  
Jean Mairesse
Keyword(s):  
Bipartite Graph ◽  
Stability Region ◽  
Joint Probability ◽  
Matching Model ◽  
Time Step ◽  
Random Match ◽  
Bipartite Matching ◽  
Discrete Time Markov Chain ◽  
The Stability ◽  
Maximal Stability

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan and Weiss (2009). Customers and servers play symmetrical roles. There are finite sets C and S of customer and server classes, respectively. Time is discrete and at each time step one customer and one server arrive in the system according to a joint probability measure μ on C× S, independently of the past. Also, at each time step, pairs of matched customers and servers, if they exist, depart from the system. Authorized matchings are given by a fixed bipartite graph (C, S, E⊂ C × S). A matching policy is chosen, which decides how to match when there are several possibilities. Customers/servers that cannot be matched are stored in a buffer. The evolution of the model can be described by a discrete-time Markov chain. We study its stability under various admissible matching policies, including ML (match the longest), MS (match the shortest), FIFO (match the oldest), RANDOM (match uniformly), and PRIORITY. There exist natural necessary conditions for stability (independent of the matching policy) defining the maximal possible stability region. For some bipartite graphs, we prove that the stability region is indeed maximal for any admissible matching policy. For the ML policy, we prove that the stability region is maximal for any bipartite graph. For the MS and PRIORITY policies, we exhibit a bipartite graph with a non-maximal stability region.

Kurt Baier on Reason and Morality

Dialogue ◽  
1997 ◽  
Vol 36 (4) ◽  
pp. 813-818
Author(s):  
Ishtiyaque Haji
Keyword(s):  
Moral Order ◽  
Necessary Condition ◽  
Moral Conduct ◽  
Rationality Problem ◽  
Do So

The Rational and the Moral Order, a work of sweeping scope and depth, opens with three problems: the Rationality Problem, briefly, is that the following set is inconsistent, although each of its elements seems true: our conduct cannot be rationally justified unless it promotes our own good; moral conduct is rationally justified; but morality often requires that we do things that do not promote our own good. The Motivation Problem distills to this: can something be a reason for someone to do something without its actually motivating him to do so (the so-called “externalist” position), or is being a motivator a necessary condition of being a reason for that person (the “internalist position”)? Finally, the Sanction Problem notes that, although it seems plausible and generally accepted that immorality should be sanctioned, it seems neither plausible, nor is it generally accepted, that irrationality should be. Why this asymmetry? I restrict my attention, in what follows, to aspects of Baier's fascinating discussion on the Rationality Problem and the Motivation Problem.

Insensitivity and product-form decomposability of reallocatable GSMP

1993 ◽  
Vol 25 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Stationary Distribution ◽  
Jump Process ◽  
Product Form ◽  
Balance Equations ◽  
Independent Components ◽  
Extended Sense ◽  
Wide Range ◽  
Standard Models

A stochastic process, called reallocatable GSMP (RGSMP for short), is introduced in order to study insensitivity of its stationary distribution. RGSMP extends GSMP with interruptions, and is applicable to a wide range of queues, from the standard models such as BCMP and Kelly's network queues to new ones such as their modifications with interruptions and Serfozo's (1989) non-product form network queues, and can be used to study their insensitivity in a unified way. We prove that RGSMP supplemented by the remaining lifetimes is product-form decomposable, i.e. its stationary distribution splits into independent components if and only if a version of the local balance equations hold, which implies insensitivity of the RGSMP scheme in a certain extended sense. Various examples of insensitive queues are given, which include new results. Our proofs are based on the characterization of a stationary distribution for SCJP (self-clocking jump process) of Miyazawa (1991).

ON THE TIME-DEPENDENT BEHAVIOR OF A MARKOVIAN REENTRANT-LINE MODEL

2018 ◽  
Vol 33 (3) ◽  
pp. 367-386
Author(s):  
Brian Fralix
Keyword(s):  
Stationary Distribution ◽  
Time Dependent ◽  
Product Form ◽  
Line Model ◽  
Transition Functions ◽  
Geometric Product ◽  
Dependent Behavior ◽  
Product Technique ◽  
Form Representation ◽  
Similar Product

We use the random-product technique from [5] to study both the steady-state and time-dependent behavior of a Markovian reentrant-line model, which is a generalization of the preemptive reentrant-line model studied in the work of Adan and Weiss [2]. Our results/observations yield additional insight into why the stationary distribution of the reentrant-line model from [2] exhibits an almost-geometric product-form structure: indeed, our generalized reentrant-line model, when stable, admits a stationary distribution with a similar product-form representation as well. Not only that, the Laplace transforms of the transition functions of our reentrant-line model also have a product-form structure if it is further assumed that both Buffers 2 and 3 are empty at time zero.

Domination and Assertion Towards a theory of educational change

1968 ◽  
Vol 9 (1) ◽  
pp. 1-11
Author(s):  
Margaret Scotford Archer ◽  
Michalina Vaughan
Keyword(s):  
Educational Change ◽  
Max Weber ◽  
Social Institutions ◽  
Social Institution ◽  
Necessary Condition ◽  
The Social ◽  
Social Domination ◽  
History Of ◽  
Do So

In the sociology of Max Weber, the history of any social institution corresponds to the constant interplay of a dominant and an assertive group and their supportive ideologies. While Weber himself posited the relevance of such interaction for the study of educational change, he limited himself to the description of historical stages in this process without attempting to account for their sequence. To do so requires a specification of the necessary condition for successful educational domination or assertion by any group. The factors of such domination over the social institution of education may at times coincide with those required for social domination–defined as domination over the main institutions of a society. This coincidence will depend on the degree to which education is integrated with other social institutions. When education is largely unintegrated with such institutions, the group dominating it will tend to be distinct from the ruling group in society. A corresponding statement can be made about assertion. However, as education is never completely autonomous, a theory of educational change (1) necessarily goes beyond this institution to the extent to which it is integrated with others.

A stochastic lower bound for assemble-transfer batch service queueing networks

2000 ◽  
Vol 37 (3) ◽  
pp. 881-889 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Lower Bound ◽  
Stationary Distribution ◽  
Upper Bound ◽  
Queueing Networks ◽  
Product Form ◽  
Arrival Process ◽  
Batch Service ◽  
Original Network ◽  
Departure Process ◽  
Geometric Product

Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch service queueing networks which do not have tractable stationary distribution. However by assuming a certain additional arrival process at each node when it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the original network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each node which tends to remove all the customers present in it. This model in combination with the aforementioned upper bound model gives a better sense for the properties of the original network.

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