Explicit Formulae for the Characteristics of the M/H2/1 Retrial Queue

In this paper we study the M/H2/1 queue with returning customers. We obtain explicit formulae for the steady-state distribution and the expected quality characteristics of the system. In addition, a simple recursion scheme for computing the 'orbit' busy period is proposed

The M/G/1 retrial queue: an information theoretic approach

In this paper, we give a survey of the use of information theoretic techniques for the estimation of the main performance characteristics of the M/G/1 retrial queue. We focus on the limiting distribution of the system state, the length of a busy period and the waiting time. Numerical examples are given to illustrate the accuracy of the maximum entropy estimations when they are compared versus the classical solutions.Peer Reviewe

Markovian arrivals in stochastic modelling: a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.Peer Reviewe

Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system

Optimal control and performance analysis of an M-X/M/1 queue with batches of negative customers

We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived

Markovian arrivals in stochastic modelling : a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension

Entropy maximization and the busy period of some single-server vacation models

In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T- and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable M/G/1 queueing models provides a parallel numerical study of the solution obtained via the maximum entropy approach versus “classical” solutions. The maximum entropy analysis of a continuous system descriptor (like the busy period) enriches the current body of literature which, in most cases, reduces to discrete queueing measures (such as the number of customers in the system)

The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group

We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed

Low Rates of Both Lipid-Lowering Therapy Use and Achievement of Low-Density Lipoprotein Cholesterol Targets in Individuals at High-Risk for Cardiovascular Disease across Europe

Aims To analyse the treatment and control of dyslipidaemia in patients at high and very high cardiovascular risk being treated for the primary prevention of cardiovascular disease (CVD) in Europe. Methods and Results Data were assessed from the European Study on Cardiovascular Risk Prevention and Management in Usual Daily Practice (EURIKA, ClinicalTrials.gov identifier: NCT00882336), which included a randomly sampled population of primary CVD prevention patients from 12 European countries (n = 7641). Patients’ 10-year risk of CVD-related mortality was calculated using the Systematic Coronary Risk Evaluation (SCORE) algorithm, identifying 5019 patients at high cardiovascular risk (SCORE 5% and/or receiving lipid-lowering therapy), and 2970 patients at very high cardiovascular risk (SCORE 10% or with diabetes mellitus). Among high-risk individuals, 65.3% were receiving lipid-lowering therapy, and 61.3% of treated patients had uncontrolled low-density lipoprotein cholesterol (LDL-C) levels ( 2.5 mmol/L). For very-high-risk patients (uncontrolled LDL-C levels defined as 1.8 mmol/L) these figures were 49.5% and 82.9%, respectively. Excess 10-year risk of CVD-related mortality (according to SCORE) attributable to lack of control of dyslipidaemia was estimated to be 0.72%and 1.61% among high-risk and very-high-risk patients, respectively. Among high-risk individuals with uncontrolled LDL-C levels, only 8.7% were receiving a high-intensity statin (atorvastatin 40 mg/day or rosuvastatin 20 mg/day). Among veryhigh- risk patients, this figure was 8.4%. Conclusions There is a considerable opportunity for improvement in rates of lipid-lowering therapy use and achievement of lipid-level targets in high-risk and very-high-risk patients being treated for primary CVD prevention in EuropeWriting support was provided by Oxford PharmaGenesis Ltd, Oxford, UK, and was funded by AstraZenec

The association between blood pressure and lipid levels in Europe

Objectives: Several studies have suggested a positive association between serum lipid levels and blood pressure (BP). This study investigated this association in a large population from 12 European countries. Methods: Data were taken from the European Study on Cardiovascular Risk Prevention and Management in Usual Daily Practice (ClinicalTrials.gov identifier: NCT00882336). Associations between BP and lipid levels in patients free from cardiovascular disease and with at least one major cardiovascular disease risk factor (N=7641) were assessed using linear regression analyses. Results: Overall, 72.8 and 64.8% of patients had hypertension and dyslipidaemia, respectively; 47.0% had both conditions. Regression coefficients (95% confidence interval) for the associations of LDL cholesterol, non-HDL cholesterol, total cholesterol and apolipoprotein B levels with SBP, adjusted for age, sex and BMI, were 0.93 mmHg/mmol per l (0.54-1.31), 1.07 mmHg/mmol per l (0.73-1.40), 1.02 mmHg/mmol per l (0.69-1.35) and 4.94 mmHg/g per l (3.43-6.46), respectively. The corresponding values (95% confidence interval) for the associations with DBP were 0.96 mmHg/mmol per l (0.73-1.19), 0.95 mmHg/mmol per l (0.75-1.15), 0.87 mmHg/mmol per l (0.67-1.07) and 4.33 mmHg/g per l (3.42-5.23), respectively. Most of these associations remained significant whether patients were treated with statins or not. Conclusion: Small but statistically significant associations between lipid levels and BP were observed in a large, multinational European population. Further research is warranted to assess the causality of this association and its implications on the management of patients with both hypertension and dyslipidaemia