This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi...This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.展开更多
In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model c...In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion 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.展开更多
This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponen...This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponential time instances.At a monitoring instant,if the number of customers in main queue reaches L(>K),a batch of L−K customers is transferred from the main queue to the auxiliary queue,and if the number of customers in main queue is less than or equal to K,the transfers will not happen.For this system,by using a Foster-Lyapunov type condition,we establish a sufficient stability condition.Then,we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue,the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity.Finally,we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.展开更多
Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stati...Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.展开更多
This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectiv...This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.展开更多
In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0...In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).展开更多
In this paper,we consider a non-standard renewal risk model with dependent claim sizes,where an insurance company is allowed to invest his/her wealth in financial assets,leading to some stochastic investment log-retur...In this paper,we consider a non-standard renewal risk model with dependent claim sizes,where an insurance company is allowed to invest his/her wealth in financial assets,leading to some stochastic investment log-returns described as a general adapted càdlàg process.Under the assumptions that the claim sizes are heavy-tailed and the stochastic log-return process on investments is bounded from below almost surely,we derive some asymptotic formulas for the finite-time ruin probability holding uniformly in any finite time horizon.展开更多
Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asympto...Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1).展开更多
In this paper,we consider the(L,1) state-dependent reflecting random walk(RW) on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(pos...In this paper,we consider the(L,1) state-dependent reflecting random walk(RW) on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive) recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the(L,1)-random walk.展开更多
文摘This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11271373 and 11361007the Guangxi Natural Science Foundation under Grant No.2014GXNSFCA118001 and 2012GXNSFBA053010
文摘In this paper, we consider a discrete-time preemptive priority queue with different service com- pletion 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.
文摘This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponential time instances.At a monitoring instant,if the number of customers in main queue reaches L(>K),a batch of L−K customers is transferred from the main queue to the auxiliary queue,and if the number of customers in main queue is less than or equal to K,the transfers will not happen.For this system,by using a Foster-Lyapunov type condition,we establish a sufficient stability condition.Then,we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue,the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity.Finally,we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.
基金supported by the Shandong Provincial Natural Science Foundation of China(Grtant No.ZR2019MA035)the Natural Sciences and Engineering Research Council(NSERC)of Canadasupported by the China Scholarship Council(Grant No.201708370006)。
文摘Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.20YJA910006)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201396)+2 种基金supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX211939)supported by the Research Grants Council of Hong KongChina(Grant No.HKU17329216)。
文摘This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.
基金partially supported by National Natural Science Foundation of China(11701070,71871046)Ronglian Scholarship Fund.
文摘In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).
基金his paper is supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(No.20YJA910006)Natural Science Foundation of Jiangsu Province(No.BK20201396)+2 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions(No.19KJA180003)the Grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.HKU17329216)the CAE 2013 Research Grant from the Society of Actuaries.
文摘In this paper,we consider a non-standard renewal risk model with dependent claim sizes,where an insurance company is allowed to invest his/her wealth in financial assets,leading to some stochastic investment log-returns described as a general adapted càdlàg process.Under the assumptions that the claim sizes are heavy-tailed and the stochastic log-return process on investments is bounded from below almost surely,we derive some asymptotic formulas for the finite-time ruin probability holding uniformly in any finite time horizon.
基金Supported by the National Natural Science Foundation of China(No.11071045,No.11171179,No.11201080,No.11301391)the Research Fund for the Doctoral Program of Higher Education of China(No.20133705110002)
文摘Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1).
基金Supported by National Natural Science Foundation of China(Grant No.11131003)the Natural Sciences and Engineering Research Council of Canada(Grant No.315660)
文摘In this paper,we consider the(L,1) state-dependent reflecting random walk(RW) on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for(positive) recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the(L,1)-random walk.