A semidefinite optimization approach to the steady-state analysis of queueing systems

Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discrete-time priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most ‘traditional’ queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.     

Representation Formulas for Analytic Function Non－exponential in a Half Plane

ＲｅｐｒｅｓｅｎｔａｔｉｏｎＦｏｒｍｕｌａｓｆｏｒＡｎａｌｙｔｉｃＦｕｎｃｔｉｏｎＮｏｎ－ｅｘｐｏｎｅｎｔｉａｌｉｎａＨａｌｆＰｌａｎｅＤｅｎｇＧｕａｎｔｉｅ（邓冠铁）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕａｚｈｏｎｇＵｎｉｖｅｒｓｉ...     

Ordered field property for stochastic games when the player who controls transitions changes from state to state

In this paper, we consider a zero-sum stochastic game with finitely many states restricted by the assumption that the probability transitions from a given state are functions of the actions of only one of the players. However, the player who thus controls the transitions in the given state will not be the same in every state. Further, we assume that all payoffs and all transition probabilities specifying the law of motion are rational numbers. We then show that the values of both a -discounted game, for rational , and of a Cesaro-average game are in the field of rational numbers. In addition, both games possess optimal stationary strategies which have only rational components. Our results and their proofs form an extension of the results and techniques which were recently developed by Parthasarathy and Raghavan (Ref. 1).The author wishes to thank Professor T. E. S. Raghavan for introducing him to this problem and for discussing stochastic games with him on many occasions. This research was supported in part by AFOSR Grant No. 78–3495B.     

An anticipative hyperbolic discount utility on intertemporal decision making

Discount utility is facilitated to scrutinize human decision behaviors for different points in time under the consideration of time preference. Recent studies are extended from two basic models, which are the exponential and the hyperbolic discount models, and the more popular hyperbolic discount model is well recognized for resolving the effects of preference reversal and is less steeply discounting than the exponential discount model. However, to enhance the capability of explaining intertemporal decision making behavior, an anticipative hyperbolic discount utility model was proposed which revised the conventional hyperbolic discount utility by introducing the anticipative parameters under the consideration of anticipation of future gains or losses. An empirical investigation was employed to validate the effectiveness of the proposed anticipative hyperbolic discounting utility model, which was able to empirically go beyond the traditional hyperbolic discounting utility model. Also, the proposed anticipative hyperbolic model is capable of dealing with the anomalies of preference reverse and framing effects.     

Coordinating ordering and pricing decisions in a two-stage distribution system with price-sensitive demand through short-term discounting

We consider a short-term discounting model in which the distributor offers a discounted price for the retailers’ orders placed at the beginning of its replenishment cycle, in a non-cooperative distribution system with one distributor and multiple retailers, each facing price-sensitive demand. We examine the value of the price discount strategy as a mechanism for the distributor to coordinate the retailers’ ordering and pricing decisions under two common types of demand, linear demand in price and constant elasticity demand in price. Our numerical study reveals that, in the presence of homogeneous retailers (namely, retailers with identical demand rates), the distributor’s profit improvement due to coordination generally decreases as the number of retailers or the inventory holding cost rate increases, but increases as price elasticity increases. Although an increase in the inventory holding cost rate has a negative effect on the distributor’s profit, it may have a positive effect on the retailers’ profits. We further find that with heterogeneous retailers (namely, retailers with different demand rates), offering a discounted price under linear demand benefits the distributor when both the inventory holding cost rate and the variation in demand are either small or large. This cross effect, however, is absent under constant elasticity demand.     

Motional narrowing under diffusion of two spin sub-lattices in LiNaSO4

An expression for the dipolar correlation function characterizing the fluctuations of the Hamiltonian under uncorrelated diffusion of two cationic sub-lattices in a solid has been obtained. A corresponding formula, which can be used for fitting the two-step temperature dependencies of the NMR line width, has been deduced. We also considered the case of a distribution of correlation times and deduced a corresponding analytical fitting function. Elaborated expressions have been applied to the NMR line width analysis of LiNaSO₄ in the temperature range 295–788 K.     

DEGREE OF ECONOMIC UNSUSTAINABILITY IN THE MANAGEMENT OF RENEWABLE RESOURCES

A criterion commonly used to determine economic sustainability posits that the discounted welfare should not decrease over time. Resource management problems involving fluctuating stocks may be exacerbated by a lack of sustainable policies unless some violations of this condition are accepted. Moreover, sustainable policies may lead to the minimal welfare levels. To alleviate these problems, a new notion of sustainability is suggested. In this new form of sustainability, violations of nondecreasing welfare are accepted to a certain degree. The policies that maximize the discounted welfare under the constraint for the largest accepted violation for sustainability satisfy a dynamic programming type of fixed‐point condition that can be effectively utilized for finding optimal policies. The new notion of sustainability can also be utilized in defining an index for measuring the degree of overall unsustainability of resource management problems and different harvesting policies.     

Robust Markov perfect equilibria

In this paper we study a Markov decision model with quasi-hyperbolic discounting and transition probability function depending on an unknown parameter. Assuming that the set of parameters is finite, the sets of states and actions are Borel and the transition probabilities satisfy some additivity conditions and are atomless, we prove the existence of a non-randomised robust Markov perfect equilibrium.     

Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations

We survey research on radiation propagation or ballistic particle motion through media with randomly variable material density, and we investigate the topic with an emphasis on very high spatial frequencies. Our new results are based on a specific variability model consisting of a zero-mean Gaussian scaling noise riding on a constant value that is large enough with respect to the amplitude of the noise to yield overwhelmingly non-negative density. We first generalize known results about sub-exponential transmission from regular functions, which are almost everywhere continuous, to merely “measurable” ones, which are almost everywhere discontinuous (akin to statistically stationary noises), with positively correlated fluctuations. We then use the generalized measure-theoretic formulation to address negatively correlated stochastic media without leaving the framework of conventional (continuum-limit) transport theory. We thus resolve a controversy about recent claims that only discrete-point process approaches can accommodate negative correlations, i.e., anti-clustering of the material particles. We obtain in this case the predicted super-exponential behavior, but it is rather weak. Physically, and much like the alternative discrete-point process approach, the new model applies most naturally to scales commensurate with the inter-particle distance in the material, i.e., when the notion of particle density breaks down due to Poissonian—or maybe not-so-Poissonian—number-count fluctuations occur in the sample volume. At the same time, the noisy structure must prevail up to scales commensurate with the mean-free-path to be of practical significance. Possible applications are discussed.