Stationary analysis of a single queue with remaining service time dependent arrivals

We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$ of the current customer being served. We derive a natural stability condition and provide a stationary analysis under it both at service completion times (of the queue length process) and in continuous time (of the queue length and the residual service time). In particular, we show that the stationary measure of queue length at service completion times is equal to that of a corresponding $M/G/1$ system. For $f > 0$ we show that the continuous time stationary measure of the $rM/G/1$ system is linked to the $M/G/1$ system via a time change. As opposed to the $M/G/1$ queue, the stationary measure of queue length of the $rM/G/1$ system at service completions differs from its marginal distribution under the continuous time stationary measure. Thus, in general, arrivals of the $rM/G/1$ system do not see time averages. We derive formulas for the average queue length, probability of an empty system and average waiting time under the continuous time stationary measure. We provide examples showing the effect of changing the reshaping function on the average waiting time.Comment: 31 pages, 3 Figure

Tourism and Empirical Applications of International Trade Theory: A Multi-Country Analysis

This paper examines the application of quantitative techniques to further our understanding of international trade theory with respect to tourism flows. The analyses are based on the construction of Balassa and Grubel-Lloyd Indices, as well as the construction of dynamic indices. The results of the analyses suggest that international trade theory has much to offer the study of international tourism flows. Many countries seem to specialize as both exporters and importers of tourism services. The analyses also explore the theoretical assertion that intra-industry trade is likely to be of importance in understanding international tourism flows

Tourism and Empirical Applications of International Trade Theory: A Multi-Country Analysis

This paper examines the application of quantitative techniques to further our understanding of international trade theory with respect to tourism flows. The analyses are based on the construction of Balassa and Grubel-Lloyd Indices, as well as the construction of dynamic indices. The results of the analyses suggest that international trade theory has much to offer the study of international tourism flows. Many countries seem to specialize as both exporters and importers of tourism services. The analyses also explore the theoretical assertion that intra-industry trade is likely to be of importance in understanding international tourism flows

Low Power Dynamic Scheduling for Computing Systems

This paper considers energy-aware control for a computing system with two states: "active" and "idle." In the active state, the controller chooses to perform a single task using one of multiple task processing modes. The controller then saves energy by choosing an amount of time for the system to be idle. These decisions affect processing time, energy expenditure, and an abstract attribute vector that can be used to model other criteria of interest (such as processing quality or distortion). The goal is to optimize time average system performance. Applications of this model include a smart phone that makes energy-efficient computation and transmission decisions, a computer that processes tasks subject to rate, quality, and power constraints, and a smart grid energy manager that allocates resources in reaction to a time varying energy price. The solution methodology of this paper uses the theory of optimization for renewal systems developed in our previous work. This paper is written in tutorial form and develops the main concepts of the theory using several detailed examples. It also highlights the relationship between online dynamic optimization and linear fractional programming. Finally, it provides exercises to help the reader learn the main concepts and apply them to their own optimizations. This paper is an arxiv technical report, and is a preliminary version of material that will appear as a book chapter in an upcoming book on green communications and networking.Comment: 26 pages, 10 figures, single spac

Mexican Immigrants: How Many Come? How Many Leave?

Based on U.S. and Mexican government data, analyzes 2001-09 trends in the flow of Mexican immigrants into the United States and that of Mexican-born migrants returning from the U.S. Examines claims that migrants are leaving due to the 2008-09 recession

Conditional PASTA

Let Y be a stochastic process representing the state of a system and N a doubly stochastic Poisson process whose intensity varies with the state of a random environment represented by a stochastic process X. In this context a generalization of “PASTA” (Poisson Arrivals See Time Averages) is shown to be valid. Various applications of the result are given