Reconstructing arrival processes to discrete queueing systems by inverse load transformation

293 Return Rates for Opioid Versus Non-Opioid Management of Abdominal Pain in the Emergency Department

We use the concept of burstiness to propose new descriptors of arrival processes or, more generally, point or traffic processes. We say that the arrival process is in aburst when its interarrival times are less than or equal to some threshold value; during periods in which interarrival times are greater than the threshold value, the process is in agap. We propose to describe the arrival process in terms of the number of arrivals during a burst (gap) and the duration of a burst (gap). For the case of discrete-time Markovian arrival processes we derive the distribution of the number of arrivals during a burst (gap) and the mean duration of a burst (gap). We present numerical results to illustrate how our descriptors can be used to understand the behavior of an arrival process and the congestion it induces in a queueing system. We also report the results of an experiment which shows a statistical relationship between two of our descriptors and a measure of queueing congestion.

Abstract. Infant mortality is one of the main concerns for governments in programs of public health. It is also an important measure used to evaluate the quality of life in several countries. The aim of this paper is twofold: first, study the spatial distribution of infant mortality in a Brazilian city using spatial lattice methods. Secondly, propose a new method based on the square root transformation in the response variable of the spatial regression models in order to reach residuals with constant variance or normality. The response variable is “the number of deaths of infants under one-year-old”, while the independent variables are “the number of women in fertile age”, “the number of women in gestational risk age”, “the number of illiterate women”, “the monthly income of the woman and the men”, “the number of residences with more than six inhabitants” and “the demographic density”. All these variables are available for each census sector of a Brazilian city. The spatial dependence of the number of deaths of infants under one-year-old has been assessed through the global and local Moran indexes. Furthermore, three models have been fitted, namely, the classic regression model, the spatial autoregressive model (SAR) and the conditional autoregressive model (CAR). The Akaike information criterion (AIC) has indicated SAR model as best goodness of fit. The variables “number of women in fertile age” and “monthly income of the women” have been shown to be statistically significant to predict the number of deaths of infants under one-year-old inside the census sectors.

Analysis of queueing model with processor sharing discipline and customers impatience

Heavy traffic limit theorems are established for a class of single server queueing models including those with heavy-tailed or long-range dependent arrivals and time-varying service rates. The models are motivated by wireless queueing systems for which there is an increasing evidence of the presence of heavy-tailed or long-range dependent arrivals, and where the service rates vary with the changes in the wireless medium. The main focus of the paper is to obtain the different possible limit processes that can arise depending on the relationship between scalings for both the arrival and departure processes. The limit processes obtained here are driven by either Brownian motion (when the contribution from the departure process dominates the limit) or the limits of properly scaled arrivals (when the contribution from the arrival process dominates the limit), typical examples being stable Lévy motion or fractional Brownian motion. In particular, for the case where arrival process is given by the infinite source Poisson process, this relationship, which determines the type of the limiting queue-length process, is a simple condition involving the heavy tail exponent, arrival rate and channel variation parameter in the wireless medium model. To establish these limit results, two approaches are studied. In one approach, when the limit is driven by Brownian motion, the perturbed test function method is extended to incorporate reflection. In contrast, the second approach allows for non-Markovian and/or non-Gaussian driving processes in the limit. Both approaches involve averaging in the drift term arising from random service rates at the departures. In the second approach, this averaging is carried out directly and pathwise, thus sidestepping the assumption of driving Brownian motion used in the perturbed test function method.

Although there is a growing literature that uses national and international data to investigate health outcomes and their link to the determinants of health, empirical studies on whether or not there is a causal relationship between health outcomes and the determinants of health, to our knowledge, has not been generally done previously. To fill this gap, the main focus of this dissertation is to empirically analyze the relationship existing between health determinants and health outcomes among the least healthy state (Mississippi), the middle ranked state (Virginia) and the healthiest state (Hawaii) as measured by American Health Ranking (AHR). This study uses multiple regression models in order to measure the impact of independent variables on health outcomes. For more in depth study of the casual relations between health outcomes and our independent variables, Vector Auto Regression Model (VAR) with embedded Granger causality is used. The data for this analysis are chiefly obtained from the American Health Rankings Organization. Premature death, cancer death, cardiovascular death, and infant mortality are used as proxy for health outcomes. Our independent variables, to measure what factors influence health outcomes, are divided into four categories: behavioral factors, environmental factor, socioeconomic factors, and policy factors. The measures of our independent variables for health behavior are smoking, excessive drinking, obesity and physical inactivity. The measure of environmental factor is air pollution. Education, change in personal income, unemployment rate and income disparity are included in this study as the measure of socioeconomic independent variables. The measures of policy factors are health insurance and public health funding. The results reveal that obesity, air pollution, income disparity, high school graduation rate, public health funding and health insurance influence health outcomes and are the main factors that affect the health outcomes of Mississippi, Virginia and Hawaii. The finding of this study may provide the useful information for researchers, health professionals and policymakers in assessing the conditions and possible improvements, which can be made within each determinants of health that have been identified as a leading cause of death to reduce health disparities.

Loss performance model for wireless channels with autocorrelated arrivals and losses

This paper reviews recent developments in the use of practical queueing­ based tools, particularly queueing network models, to study the performance of computer systems. We emphasize those research results that have been responsible for the successful transfer of this technology-the widespread use of these tools in computer system design, sizing, and capacity planning by people whose expertise lies in these application areas, rather than in modeling or mathematics. Queueing theory as a discipline dates from the 1920s. Almost without exception, the results of the early decades concern models of single conges­ tion points. These results encompass a wide variety of specific assumptions about the arrival process, the service process, the scheduling discipline, the queue size limitation, etc. Applications of these single resource models are found in many areas, particularly operations research, management science, and industrial engineering. In computer system engineering, these models have met with great success when used by skilled practitioners for the one-time analysis of subsystems, e.g. a specific communication network

Sleep modes are important for user equipment to reduce power consumption or to reduce battery reloading. To keep the user equipment connected, it has to be activated for uplink or downlink data transfer which causes overhead and additional delay. Wireless or mobile equipment has to be monitored repeatedly for location updates. These classes of problems can be modeled by queuing systems with modified busy and idle periods. In this paper, we consider a generalized infinite-buffer, single-server queuing systems with activation overhead and under various types of sleep modes during inactive periods. For the special assumption of Markovian arrival processes of data units and generally distributed activation times and vacation (sleep) periods, the models can be analyzed exactly by a mean value analysis method which is based on regenerative stochastic processes, renewal theory and classical queuing theorems. The method allows also for dynamic sleep periods which are dependent on each other as in the case of the standard IEEE 802.16m for wireless equipment. Explicit results are derived for average values of data unit delays, resource utilization and power- saving margins dependent on given parameters for activation times and wakeup signaling frequencies. The models include the special cases of M/G/1 queuing systems with a modified service time of the first arrival initiating a busy period and M/G/1 queuing systems with vacation periods, respectively, which are well known from literature providing general solutions for the state and delay distributions. Finally, all models are extended to the exact analysis of Batch Poisson arrival processes.

This paper proposes a unified matrix-analytic approach to characterize the output processes of general discrete-time lossless/lossy queueing systems in which time is synchronized/slotted into fixed length intervals called slots. The arrival process can be continuous- or discrete-time Markovian processes. It can be either renewal or non-renewal. The service of a customer commences at the beginning of a slot, consumes a random number of slots, and completes at the end of a later slot. The service times are independent and follow a common and general distribution. Systems with and without server vacations are both treated in this paper. These queueing systems have potential applications in asynchronous transfer mode (ATM) networks, packet radio networks, etc. Since the output process of a node in a queueing network becomes an input process to some node at the next stage, the results of this paper can be used to facilitate end-to-end performance analysis which has attracted more and more attention in the literature.

Many researchers have studied variants of queueing systems with vacations. Most of them have dealt with M/G/1 systems and have explicitly analyzed some of their performance measures, such as queue length, waiting time, and so on. Recently, studies on queueing systems whose arrival processes are not Poissonian have appeared. We consider a single server queueing system with multiple vacations and E-limited service discipline, where messages arrive to the system according to a switched Poisson process. First, we consider the joint probability density functions of the queue length and the elapsed service time or the elapsed vacation time. We derive the equations for these pdf's, which include a finite number of unknown values. Using Rouche's theorem, we determine the values from boundary conditions. Finally, we derive the transform of the stationary queue length distribution explicitly.

Performance-oriented studies typically rely on the assumption that the stochastic process modeling the phenomenon of interest is already in steady state. This assumption is, however, not valid if the life cycle of the phenomenon under study is not large enough, since usually a stochastic process cannot reach steady state unless time evolves towards infinity. Therefore, it is important to address performance issues in transient state.Previous work in transient analysis of queueing systems usually focuses on Markov models. This paper, in contrast, presents an analysis of transient loss performance for a class of finite buffer queueing systems that are not necessarily Markovian. We obtain closed-form transient loss performance measures. Based on the loss measures, we compare transient loss performance against steady-state loss performance and examine how different assumptions on the arrival process will affect transient loss behavior of the queueing system. We also discuss how to guarantee transient loss performance. The analysis is illustrated with numerical results.

Markov modulated periodic arrival process offered to an ATM multiplexer

Speaker and language recognition in noisy and degraded channel conditions continue to be a challenging problem mainly due to the mismatch between clean training and noisy test conditions. In the presence of noise, the most reliable portions of the signal are the high energy regions which can be used for robust feature extraction. In this paper, we propose a front end processing scheme based on autoregressive (AR) models that represent the high energy regions with good accuracy followed by a modulation filtering process. The AR model of the spectrogram is derived using two separable time and frequency AR transforms. The first AR model (temporal AR model) of the sub-band Hilbert envelopes is derived using frequency domain linear prediction (FDLP). This is followed by a spectral AR model applied on the FDLP envelopes. The output 2-D AR model represents a low-pass modulation filtered spectrogram of the speech signal. The band-pass modulation filtered spectrograms can further be derived by dividing two AR models with different model orders (cut-off frequencies). The modulation filtered spectrograms are converted to cepstral coefficients and are used for a speaker recognition task in noisy and reverberant conditions. Various speaker recognition experiments are performed with clean and noisy versions of the NIST-2010 speaker recognition evaluation (SRE) database using the state-of-the-art speaker recognition system. In these experiments, the proposed front-end analysis provides substantial improvements (relative improvements of up to 25%) compared to baseline techniques. Furthermore, we also illustrate the generalizability of the proposed methods using language identification (LID) experiments on highly degraded high-frequency (HF) radio channels and speech recognition experiments on noisy data.

In an opportunistic spectrum sharing (OSS) wireless network there are two types of users: primary users and secondary users. The primary users own the license for the system bandwidth, while the secondary users opportunistically share the spectrum resources with the primary users. When a secondary user detects a call arrival from a primary user in its current channel, the secondary user leaves the channel immediately and switches to an idle channel, if one is available, to continue the call. Otherwise, the secondary user is preempted. Call arrivals from primary users and secondary users in the OSS system are modeled by a Markovian arrival process (MAP) which captures correlation in the aggregate arrival process consisting of the two types of call arrivals. We derive the stationary probability vector using matrix-analytic methods and obtain expressions for a set of key performance measures. We present numerical results for a sample scenario.