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Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild conditions, we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval. If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed, it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous-time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.

Objective. Angiogenesis is one of the therapeutic targets of cerebral infarction. Long noncoding RNAs (lncRNAs) can regulate the pathological process of angiogenesis following ischemic stroke. Taurine-upregulated gene 1 (TUG1), an lncRNA, is correlated to ischemic stroke. We intended to determine the effect of TUG1 on angiogenesis following an ischemic stroke. Materials and Methods. Middle cerebral artery occlusion (MCAO) was adopted to build a focal ischemic model of the rat brain, and pcDNA-TUG1 and miR-26a mimics were injected into rats. Neurological function was estimated through modified neurological severity scores. The volume of focal brain infarction was calculated through 2,3,5-triphenyltetrazolium chloride staining. The level of TUG1 and miR-26a was measured by PCR. The expression of vascular endothelial growth factor (VEGF) and CD31 was checked using immunohistochemistry and western blot. The correlation between miR-26a and TUG1 was verified through a luciferase reporter assay. Results. TUG1 increased noticeably while miR-26a was markedly reduced in MCAO rats. Overexpression of miR-26a improved neurological function recovery and enhanced cerebral angiogenesis in MCAO rats. TUG1 overexpression aggravated neurological deficits and suppressed cerebral angiogenesis in MCAO rats. Bioinformatics analysis revealed that miR-26a was one of the predicted targets of TUG1. Furthermore, TUG1 combined with miR-26a to regulate angiogenesis. TUG1 overexpression antagonized the role of miR-26a in neurological recovery and angiogenesis in MCAO rats. Conclusions. TUG1/miR-26a, which may act as a regulatory axis in angiogenesis following ischemic stroke, can be considered a potential target for cerebral infarction therapy.

An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.

We study M/M/c queues (c = 1, 1 < c < ∞ and c = ∞) in a Markovian environment with impatient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

In this paper, we study the problem of a variety of nonlinear time series model Xn+1 = TZn+1(X(n), …, X(n − Zn+1), en+1(Zn+1)) in which Zn is a Markov chain with finite state space, and for every state i of the Markov chain, en(i) is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence Xn defined by the above model is investigated. Some new novel results on the underlying models are presented.

This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures. Different from standard batch arrival retrial queues with starting failures, we assume that each customer after service either immediately returns to the orbit for another service with probability θ or leaves the system forever with probability 1 − θ (0 ≤ θ < 1). On the other hand, if the server is started unsuccessfully by a customer (external or repeated), the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 − q (0 ≤ q < 1). Firstly, we introduce an embedded Markov chain and obtain the necessary and sufficient condition for ergodicity of this embedded Markov chain. Secondly, we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time. We also derive a stochastic decomposition law. In the special case of individual arrivals, we develop recursive formulae for calculating the steady-state distribution of the orbit size. Besides, we investigate the relation between our discrete-time system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on the mean orbit size.

The paper studies the dual risk model with a barrier strategy under the concept of bankruptcy, in which one has a positive probability to continue business despite temporary negative surplus. Integrodifferential equations for the expectation of the discounted dividend payments and the probability of bankruptcy are derived. Moreover, when the gain size distribution is exponential, explicit solutions for the expected dividend payments and the bankruptcy probability are obtained for constant bankruptcy rate function. It also provided some numerical examples to illustrate the applications of the explicit solutions.