Is there a causal relationship between oil prices and tourist arrivals?

This application note investigates the causal relationship between oil price and tourist arrivals to further explain the impact of oil price volatility on tourism-related economic activities. The analysis itself considers the time domain, frequency domain and information theory domain perspectives. Data relating to US and nine European countries are exploited in this paper with causality tests which include time domain, frequency domain, and Convergent Cross Mapping (CCM). The CCM approach is nonparametric and therefore not restricted by assumptions. We contribute to existing research through the successful and introductory application of an advanced method, and via the uncovering of significant causal links from oil prices to tourist arrivals.     

A queueing model to study the occurrence and duration of ozone exceedances in Mexico City

It is well known that long-term exposure to high levels of pollution is hazardous to human health. Therefore, it is important to study and understand the behavior of pollutants in general. In this work, we study the occurrence of a pollutant concentration's surpassing a given threshold (an exceedance) as well as the length of time that the concentration stays above it. A general N(t)/D/1 queueing model is considered to jointly analyze those problems. A non-homogeneous Poisson process is used to model the arrivals of clusters of exceedances. Geometric and generalized negative binomial distributions are used to model the amount of time (cluster size) that the pollutant concentration stays above the threshold. A mixture model is also used for the cluster size distribution. The rate function of the non-homogeneous Poisson process is assumed to be of either the Weibull or the Musa–Okumoto type. The selection of the model that best fits the data is performed using the Bayes discrimination method and the sum of absolute differences as well as using a graphical criterion. Results are applied to the daily maximum ozone measurements provided by the monitoring network of the Metropolitan Area of Mexico City.     

Busy period in batch queues

in a recent paper Takacs [1] generalized the classical ballot problem and used the results of the classical ballot problem to analyze the busy period in queues involving arrivals in batches or departures in batches. In this paper the generalized ballot problem is used to analyze the busy period in queues having both batch arrivals and batch departures.     

Costing Mixed Coxian Phase-type Systems with Poisson Arrivals

Previously, we developed a modeling framework which classifies individuals with respect to their length of stay (LOS) in the transient states of a continuous-time Markov model with a single absorbing state; phase-type models are used for each class of the Markov model. We here add costs and obtain results for moments of total costs in (0, t], for an individual, a cohort arriving at time zero and when arrivals are Poisson. Based on stroke patient data from the Belfast City Hospital we use the overall modelling framework to obtain results for total cost in a given time interval.     

Long-Range Dependence of Markov Renewal Processes

This paper examines long‐range dependence (LRD) and asymptotic properties of Markov renewal processes generalizing results of Daley for renewal processes. The Hurst index and discrepancy function, which is the difference between the expected number of arrivals in (0, t] given a point at 0 and the number of arrivals in (0, t] in the time stationary version, are examined in terms of the moment index. The moment index is the supremum of the set of r > 0 such that the rth moment of the first return time to a state is finite, employing the solidarity results of Sgibnev. The results are derived for irreducible, regular Markov renewal processes on countable state spaces. The paper also derives conditions to determine the moment index of the first return times in terms of the Markov renewal kernel distribution functions of the process.     

Cultural tourism and temporary art exhibitions in Italy: a panel data analysis

The main aim of this work is to study the relationship between cultural tourism and temporary art exhibitions by means of a panel data analysis. In literature, the capability of cultural attractions, e.g. art exhibitions, of increasing the tourist flow has not been investigated yet and we start to fill this gap. Our data set consists of monthly observed variables on 52 Italian provinces over the period 2003–2007. Our response variable is the amount of hotel arrivals and the set of covariates includes the amount of visitors of temporary exhibitions of ancient, modern and contemporary art plus a set of variables that contribute to tourist arrivals, like the kind of destination, the attraction capability of each province and so on. Of particular interest is to discover the art sector that has the strongest influence on the tourist flow towards Italy by keeping into account both the temporal dynamic and the heterogeneity of the Italian provinces. To this aim, we discuss the static and dynamic error component regression models from both the theoretical and practical point of view. The estimated two-way fixed effects regression models suggest that all the three sectors contribute to the tourist flow but in a quite different fashion. On the basis of our analysis we derive some indications for the policy maker in the field of cultural tourism.     

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling

We study the workload processes of two M/G/1 queueing systems with restricted capacity: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait more than a fixed threshold time in line. For Model 1 we obtain several results concerning the rate of convergence to equilibrium. In particular, we derive uniform bounds for geometric ergodicity with respect to certain subclasses. For Model 2 geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution. We derive bounds for the convergence rates in special cases. The proofs use the coupling method.     

Functionals of Markovian Branching D-BMAPS

Abstract

We consider a stochastic system in which Markovian customer attribute processes are initiated at customer arrivals in a discrete batch Markovian arrival process (D-BMAP). We call the aggregate a Markovian branching D-BMAP. Each customer attribute process is an absorbing discrete time Markov chain whose parameters depend both on the phase transition, of the driving D-BMAP, and the number of arrivals taking place at the customer's arrival instant. We investigate functionals of Markovian branching D-BMAPs that may be interpreted as cumulative rewards collected over time for the various customers that arrive to the system, in the transient and asymptotic cases. This is achieved through the derivation of recurrence relations for expected values and Laplace transforms in the former case, and Little's law in the latter case.     

Confidence sets for the maximizers of intensity functions

Identifying times or time intervals when the intensity function of a Poisson process is maximal is important in a variety of practical problems, for instance in traffic control or with planning issues involving customer arrivals or accident occurrences. For this purpose, we propose confidence sets that are intuitive and easy to obtain, which makes them practicable for a quick exploratory data analysis. They may also be used in the context of mode estimation for probability densities. In the current literature, confidence sets for the mode are based on the assumption of an—at least locally—unique mode. In contrast, our approach retains the coverage probability even if the underlying intensity or density has a flat top. We even allow the intensity to be constant in the extreme.     

A surplus process involving a compound Poisson counting process and applications

Abstract

In this paper, we introduce a surplus process involving a compound Poisson counting process, which is a generalization of the classical ruin model where the claim-counting process is a homogeneous Poisson process. The incentive is to model batch arrival of claims using a counting process that is based on a compound distribution. This reduces the difficulty of modeling claim amounts and is consistent with industrial data. Recursive formula, some properties and relevant main ruin theory results are provided. Further, we consider applications involving zero-truncated negative binomial and zero-truncated binomial batch arrivals when the claim amounts follow exponential or Erlang distribution.     

AN INFINITE-PHASE QUASI-BIRTH-AND-DEATH MODEL FOR THE NON-PREEMPTIVE PRIORITY M/PH/1 QUEUE

This paper considers a single server queue that handles arrivals from N classes of customers on a non-preemptive priority basis. Each of the N classes of customers features arrivals from a Poisson process at rate λ _i and class-dependent phase type service. To analyze the queue length and waiting time processes of this queue, we derive a matrix geometric solution for the stationary distribution of the underlying Markov chain. A defining characteristic of the paper is the fact that the number of distinct states represented within the sub-level is countably infinite, rather than finite as is usually assumed. Among the results we obtain in the two-priority case are tractable algorithms for the computation of both the joint distribution for the number of customers present and the marginal distribution of low-priority customers, and an explicit solution for the marginal distribution of the number of high-priority customers. This explicit solution can be expressed completely in terms of the arrival rates and parameters of the two service time distributions. These results are followed by algorithms for the stationary waiting time distributions for high- and low-priority customers. We then address the case of an arbitrary number of priority classes, which we solve by relating it to an equivalent three-priority queue. Numerical examples are also presented.     

Analysis of a discrete-time queue with load dependent service under discrete-time Markovian arrival process

In the study of normal queueing systems, the server’s average service times are generally assumed to be constant. However, in numerous applications this assumption may not be valid. To prevent congestion in overload control telecommunication networks, the transmission rates vary depending on the number of packets waiting in the queue. As traffics in telecommunication networks are of bursty nature and correlated, we assume that arrivals follow the discrete-time Markovian arrival process. This paper analyzes a queueing model in which the server changes its service times (rates) only at the beginning of service depending on the number of customers waiting in the queue. We obtain the steady-state probabilities at various epochs and some performance measures. In addition, varieties of numerical results are discussed to display the effect of the system parameters on the performance measures.     

Comparison of confidence intervals of traffic intensity forM/E k/1 queueing systems

This paper compares the width of confidence intervals for the traffic intensity inM/E _k/1 queueing systems with three methods-Lilliefors' method, a second method based on the number of arrivals during the service period, and a third method using censored observations, in which only those service periods with no arrivals are observed. It is shown that the width of confidence intervals, based on the number of arrivals during the service period, is narrower than for other methods.     

Information geodesics for gamma models of communication clustering

Recently, Akyildiz called for further work on non-Poisson models for communication arrivals in distributed networks such as cellular phone systems. The basic ‘random’ model for stochastic events is the Poisson process; for events on a line this resuits in an exponential disiribuuon of intervals between events. Network designers and managers need too monotor and quantify call clustering in order to optimize resaurce usage; the natural reference state from which to measure departures is that arising from a Poisson, process of calls. Here we consider gamma distributions, which contain exponential distributions as a special case. The surface representing gamma models has a natural Riemannian information metric and we obtain some geodesic sprays for this metric. The exponential distributions form a 1-dimensional subspace of the 2-dimensional space of all gamma distributions, so we have an isometric embedding of the random model as a subspace of the gamma models. This geometry may provide an appropriate structure on which to represent clustering as quantifiable departures from randomness and on which to impose dynamic control algorithms to optimize traffic at receiving nodes in distributed communication networks. In practice, we may expect correlation between call arrival times and call duration, reflecting for example peaks of different users of internet services. This would give rise to a twisted product of two surfaces with the twisting controlled by the correlation. Though bivariate gamma models do exist, such as Kibble's, none has tractabie information geometry nor sufficiently general marginal gammas,but a simulation method of approach is suggested.     

Approximated Transient Queue Length and Waiting Time Distributions via Steady State Analysis

Abstract

We propose a method to approximate the transient performance measures of a discrete time queueing system via a steady state analysis. The main idea is to approximate the system state at time slot t or on the n-th arrival–-depending on whether we are studying the transient queue length or waiting time distribution–-by the system state after a negative binomially distributed number of slots or arrivals. By increasing the number of phases k of the negative binomial distribution, an accurate approximation of the transient distribution of interest can be obtained.

In order to efficiently obtain the system state after a negative binomially distributed number of slots or arrivals, we introduce so-called reset Markov chains, by inserting reset events into the evolution of the queueing system under consideration. When computing the steady state vector of such a reset Markov chain, we exploit the block triangular block Toeplitz structure of the transition matrices involved and we directly obtain the approximation from its steady state vector. The concept of the reset Markov chains can be applied to a broad class of queueing systems and is demonstrated in full detail on a discrete-time queue with Markovian arrivals and phase-type services (i.e., the D-MAP/PH/1 queue). We focus on the queue length distribution at time t and the waiting time distribution of the n-th customer. Other distributions, e.g., the amount of work left behind by the n-th customer, that can be acquired in a similar way, are briefly touched upon.

Using various numerical examples, it is shown that the method provides good to excellent approximations at low computational costs–-as opposed to a recursive algorithm or a numerical inversion of the Laplace transform or generating function involved–-offering new perspectives to the transient analysis of practical queueing systems.     

BMAP/G/1 Queue Under D-Policy: Queue Length Analysis

ABSTRACT

We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented.     

Flexible Modeling in the Koziol-Green Model by a Copula Function

In survival analysis, the classical Koziol-Green random censorship model is commonly used to describe informative censoring. Hereby, it is assumed that the distribution of the censoring time is a power of the distribution of the survival time. In this article, we extend this model by assuming a general function between these distributions. We determine this function from a relationship between the observable random variables which is described by a copula family that depends on an unknown parameter θ. For this setting, we develop a semi-parametric estimator for the distribution of the survival time in which we propose a pseudo-likelihood estimator for the copula parameter θ. As results, we show first the consistency and asymptotic normality of the estimator for θ. Afterwards, we prove the weak convergence of the process associated to the semi-parametric distribution estimator. Furthermore, we investigate the finite sample performance of these estimators through a simulation study and finally apply it to a practical data set on survival with malignant melanoma.     

Estimation in the Cox proportional hazards model with doubly censored and truncated data

In longitudinal studies, the proportional hazard model is often used to analyse covariate effects on the duration time, defined as the elapsed time between the first and second event. In this article, we consider the situation when the first event suffers partly interval-censoring and the second event suffers left-truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the proportional model. A simulation study is conducted to investigate the performance of the proposed estimator.     

Gaussian models for degradation processes-part I: Methods for the analysis of biomarker data

We present two stochastic models that describe the relationship between biomarker process values at random time points, event times, and a vector of covariates. In both models the biomarker processes are degradation processes that represent the decay of systems over time. In the first model the biomarker process is a Wiener process whose drift is a function of the covariate vector. In the second model the biomarker process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the infection until the time the presence of the infection is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals.     

Queue Length Analysis of MAP/G/1 Queue Under D-Policy

Abstract

We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided.