The GI/M/1 queue with start-up period and single working vacation and Bernoulli vacation interruption

Consider a GI/M/1 queue with start-up period and single working vacation. When the system is in a closed state, an arriving customer leading to a start-up period, after the start-up period, the system becomes a normal service state. And during the working vacation period, if there are customers at a service completion instant, the vacation can be interrupted and the server will come back to the normal working level with probability p (0 ? p ? 1) or continue the vacation with probability 1 − p. Meanwhile, if there is no customer when a vacation ends, the system is closed. Using the matrix-analytic method, we obtain the steady-state distributions for the queue length at both arrival epochs and arbitrary epochs, the waiting time and sojourn time.     

Long-term optimization model of tree water networks

This paper describes an optimization method to design, over a period of time, a radial water network consisting of pipes, pumps and pressure reducing valves. The network structure can be modified during the planning period by the addition or removal of certain nodes and elements. The evolution of the consumption at the nodes is known. The hydraulic constraints of pressure and flow velocity are respected throughout the studied period.The investment decisions are determined in such a manner as to minimize the sum of the present worth values of the investment costs and operation costs over the planning period.The choice of pipe lengths to be invested in each branch as variables allows one to formulate the dynamic investment problem as a multi-stage linear program. Each stage corresponds to the state of the network at a time of the planning period. Such a formulation of a combinatorial problem of investments allows one to design networks of large dimensions in the long term whilst maintaining acceptable times of computation.An application of the model to a real problem is presented.     

A hidden Markov model for informative dropout in longitudinal response data with crisis states

We adopt a hidden state approach for the analysis of longitudinal data subject to dropout. Motivated by two applied studies, we assume that subjects can move between three states: stable, crisis, dropout. Dropout is observed but the other two states are not. During a possibly transient crisis state both the longitudinal response distribution and the probability of dropout can differ from those for the stable state. We adopt a linear mixed effects model with subject-specific trajectories during stable periods and additional random jumps during crises. We place the model in the context of Rubin’s taxonomy and develop the associated likelihood. The methods are illustrated using the two motivating examples.     

Minimum-fuel rocket trajectories involving intermediate-thrust arcs

The optimal trajectories in the neighborhood of an optimal intermediate-thrust arc are investigated for the minimumfuel orbit rendezvous problem with fixed specific impulse. Since such an arc is singular, the thrust acceleration magnitude being the singular control component, a second-variation analysis leads to the identification of a field of neighboring, singular arcs in a state space of dimension four rather than six, provided that a suitable Jacobi condition is met. A given neighboring initial six-dimensional state vector does not generally lie on a neighboring singular arc, and junction onto the appropriate singular arc must be accomplished by a short period of strong variations in the acceleration. This contributes an addition to the fuel expenditure which is of order 5/2 rather than 2 in the initial state displacement. The minimization of this higher-order cost, in the case of bounded acceleration, leads to an unsymmetrical version of Fuller's problem, whose solution requires an infinite number of switches between maximum and zero thrust during the short period. For unbounded thrust, the junction simplifies to either coast-impulse-singular trajectories or impulse-coast-impulse-singular trajectories. The neighboring singular arc meets the final condition in 4 dimensions, rather than 6 dimensions, and rendezvous must be completed by another, terminal short period of strong variations in the acceleration. Implications for midcourse guidance near a singular arc are discussed.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

A mixed priority retrial queue with negative arrivals,unreliable server and multiple vacations

A retrial queue accepting two types of positive customers and negative arrivals, mixed priorities, unreliable server and multiple vacations is considered. In case of blocking the first type customers can be queued whereas the second type customers leave the system and try their luck again after a random time period. When a first type customer arrives during the service of a second type customer, he either pushes the customer in service in orbit (preemptive) or he joins the queue waiting to be served (non-preemptive). Moreover negative arrivals eliminate the customer in service and cause server’s abnormal breakdown, while in addition normal breakdowns may also occur. In both cases the server is sent immediately for repair. When, upon a service or repair completion, the server finds no first type customers waiting in queue remains idle and activates a timer. If timer expires before an arrival of a positive customer the server departs for multiple vacations. For such a system the stability conditions and the system state probabilities are investigated both in a transient and in a steady state. A stochastic decomposition result is also presented. Interesting applications are also discussed. Numerical results are finally obtained and used to investigate system performance.     

Complex dynamics in an OLG model of neoclassical growth with endogenous retirement age and public pensions

This study analyses the dynamics of a general equilibrium, overlapping-generations (closed) economy with pay-as-you-go public pensions and tax-financed health investments that affect the retirement time when old. Life of the typical agent is divided between youth (firth period) and old age (second period). The latter period of life is, in turn, divided between work time and retirement time in a proportion contingent on an individual’s state of health. We show that: (i) a unique non-trivial steady state exists, and (ii) when the labour income tax rates used to finance health expenditure or public pensions are included in an intermediate range of values, complex dynamics occur when individuals have perfect foresight. This holds because the increase either in the fraction of time spent working when old or disability pensions reduces savings and capital accumulation. In addition, dynamic phenomena such as multiple bubbling structures related to the bifurcation diagram can be observed. Under some general assumptions, we show that the rise in health care expenditure and/or public pensions initially destabilises the steady-state equilibrium and causes complex dynamics but eventually acts as a stabilising device.     

An infinite horizon mathematical programming model of a multicohort single species fishery

Fishery policy evaluation should take account of the initial state of the fishery and the population dynamics of the fish stock. Although multicohort bioeconomic fishery policy evaluation models have been developed, the results from these models depend on the choice of planning period and the desired state of the stock at the end of this period. In this paper it is noted that these limitations can be overcome by evaluating fishery policy over an infinite time horizon, and a mixed integer programming (MIP) model is developed for carrying out this form of analysis in a multicohort single species fishery. This new MIP model allows policies to be evaluated over an infinite horizon by incorporating results from a steady state fishery model into a multiperiod framework. The use of this MIP model in determining policies for reaching and maintaining a steady state is illustrated.     

不同价格水平下排队策略研究

在M/M/1排队中引入了不同的服务价格,基于"收益-成本"结构,以顾客和企业均追求利益最大化为出发点,在两种不可见情形下,研究了顾客均衡策略行为和企业最优服务定价决策,通过数值模拟,描述了休假期服务价格对顾客均衡策略的影响,以及几乎不可见情况下休假期服务价格对企业收益的作用和完全不可见情况下休假期服务价格随潜在到达率的变化情况,以及当企业获得最大收益时,正常工作期和休假期服务价格的关系.     

Rejection rules in theM/G/1 queue

We consider aM/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) describing his impatience and on the state of the system. Three main variants of this scheme are studied. The steady-state distribution is expressed in terms of Volterra equations and the relation to storage processes, dams and queues with state-dependent Poisson arrival rate is discussed. For exponential service times, we further find the busy period Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associated birth-death process.     

The use of state space relaxation for the dynamic facility location problem

Dynamic facility location is concerned with developing a location decision plan over a given planning horizon during which changes in the market and in costs are expected to occur. The objective is to select from a list of predetermined possible facility sites the locations of the facilities to use in each period of the planning horizon to minimise the total costs of operating the system. The costs considered here include not only transport and operation/maintenance charges but also relocation costs arising from the opening and closing of facilities as required by the plan.The problem is formulated in terms of dynamic programming but for simplicity with restrictions on the numbers of facilities that can be opened in a given period. The problem was solved using both dynamic programming and a branch and bound approach using state space relaxation. These two approaches are contrasted with different data and with different assumptions to compare the influence of alternative factors on the computational efficiency of both solution methods.     

Estudio probabilista del daño por choque según la metodología PEER. Aplicación a un paso superior sísmicamente aislado

Bridges with deck supported either on sliding or elastomeric bearings are common in mid-seismicity regions. Pounding between deck and abutments is linked with their main seismic vulnerabilities, which can be assessed by estimating the probability of a given state of damage being reached in a given time period. This paper presents a state of the art methodology used to solve that problem, as well as its application to the assessment of the vulnerability of an overpass placed in Granada area (South-east of Spain), belonging to the previously mentioned typology.The Pacific Earthquake Engineering Research Center methodology will be adapted and applied. Their main steps will be briefly presented, although the identification and characterization of damage likely to occur will be described in more detail. The model of the structure, and specially pounding modeling, will also be detailed.Results are interesting since this bridge can be considered as a representative of a widespread class. The adapted methodology may be applied to similar structures. Also, probability values obtained may serve as benchmarks.     

Stochastic analysis of a n-unit repairable system with slow switch

This paper deals with the costn–benefit analysis of a cold standby system composed of n identical repairable units, subject to slow switch. Two models of system functioning are studied in this paper. In model 1, the repair time of a unit is assumed to follow exponential distribution and the other time distributions as arbitrary, while in model 2, the repair time of a unit is assumed to be arbitrarily distributed and the other time distributions follow exponential law. For both the models, the system characteristics, namely

(i) the expected upn–time of the system during the period (O,t]

(ii) the expected busyn–period of the repair facility during the period (0,t] and

(iii) the expected time the units spend in the switchover/installation state during the period (O,t]

are studied by identifying the system a t suitable regeneration epochs. The cost-benefit analysis is carried out using these characteristics     

Using kalman filter and finite difference techniques in default free bond pricing models

A model to price default free bonds, similar to ones developed by Cox, Ingersoll and Ross, Langetieg, and Richard, is empirically examined. Calculation of model prices involves three disjoint tasks: (1) estimation of the values of the real interest rate and the inflation rate (which we will refer to as state variables or sources of uncertainty) as well as the parameters of the state stochastic differential equations, (2) estimation of the market prices of risk associated with the two state variables, and (3) the solution of the valuation partial differential equation. Task 1 is accomplished by using a Kalman Filter algorithm, task 2 uses a Fama/MacBeth approach, and task 3 utilizes an Alternating Direction Implicit finite difference technique. Model prices are compared to actual prices. The model performs better during a period of relatively stable economic conditions compared to a period associated with more volatile conditions. Pricing errors are smaller at short maturities, and increase as time to maturity increases.     

Discrete NT-policy single server queue with Markovian arrival process and phase type service

We consider a discrete time single server queueing system in which arrivals are governed by the Markovian arrival process. During a service period, all customers are served exhaustively. The server goes on vacation as soon as he/she completes service and the system is empty. Termination of the vacation period is controlled by two threshold parameters N and T, i.e. the server terminates his/her vacation as soon as the number waiting reaches N or the waiting time of the leading customer reaches T units. The steady state probability vector is shown to be of matrix-geometric type. The average queue length and the probability that the server is on vacation (or idle) are obtained. We also derive the steady state distribution of the waiting time at arrivals and show that the vacation period distribution is of phase type.     

带负顾客和N-策略的Geo^{lambda_1, lambda_2/Geo/1(MWV)排队系统分析及最优控制策略N*

分析了一个带有负顾客、N-策略控制的Geo/Geo/1多重工作休假排队系统, 其中正顾客在工作休假及正规忙期以不同的到达率进入系统. 利用拟生灭过程和矩阵几何解方法, 给出了该模型的稳态队长分布及平均队长, 以及系统分别处于假期和忙期的概率. 同时, 对该系统的忙期进行了分析, 并讨论了稳态队长分布在系统容量的优化设计中的应用. 最后, 在给定的费用结构下, 用数值计算例子确定了使系统长期单位时间内期望费用最小的最优控制策 N*.     

A two-stage prognosis model in condition based maintenance

We often observe in practice that the life of a piece of production equipment can be divided into two stages. The first stage is referred to as the normal working stage where no significant deviation from the normal operating state is observed. The second stage is called the failure delay period, since a defect may be initiated, and progressively develop into an actual failure, i.e., the equipment is in a defective stage but still working during this stage. With the help of condition monitoring, hidden defects already present in the equipment may be detected, but for maintenance planning purposes, the prediction of the initiation point of the second stage, and more importantly, the residual life thereafter is important. This paper reports on the development of a probability model to predict the initiation point of the second stage and the remaining life based on available condition monitoring information. The method for model parameters estimation is discussed and applied to real data.     

Busy period analysis of the state dependent M/M/1/K queue

In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.     

Single-Server Queues with Markov-Modulated Arrivals and Service Speed

This paper considers single-server queues with several customer classes. Arrivals of customers are governed by the underlying continuous-time Markov chain with finite states. The distribution of the amount of work brought into the system on arrival is assumed to be general, which may differ with different classes. Further, the service speed depends on the state of the underlying Markov chain. We first show that given such a queue, we can construct the corresponding new queue with constant service speed by means of a change of time scale, and the time-average quantities of interest in the original queue are given in terms of those in the new queue. Next we characterize the joint distribution of the length of a busy period and the number of customers served during the busy period in the original queue. Finally, assuming the FIFO service discipline, we derive the Laplace–Stieltjes transform of the actual waiting time distribution in the original queue.     

Multiple Equilibria and Thresholds Due to Relative Investment Costs

A dynamic model of the firm is studied in which investment costs depend on the magnitude of the investment relative to the stock of capital goods. It is shown that in general nonunique steady states can exist which can be stable or unstable. It is possible that unstable steady states occur in the concave domain of the Hamiltonian. For a particular specification, a scenario occurs with two stable steady states and one unstable steady state. The two stable steady states are long run equilibria; which one of them is reached in the long run depends on the initial state. In case the Hamiltonian is locally concave around the unstable steady state, this steady state is the threshold that separates the domain of initial conditions that each of the stable steady states attracts. The unstable steady state is a node and investment is a continuous function of the capital stock. If the unstable steady state lies in the nonconcave domain of the Hamiltonian, this steady state can either be a node or a focus. Furthermore, continuity can (but need not) be retained similarly to the concave case, a fact which has been entirely overlooked in the literature.