An optimal control of a periodically nonstationary generalized automaton under fuzzy conditions

The general problem of successively making optimal decisions on controlling a periodically nonstationary generalized automaton with fuzzy objective and fuzzy constraints on the control is solved. An example of a solution is given.     

Fcfs-scheduling in a hard real-time environment under rush-hour conditions

We investigate some real-time behaviour of a (discrete time) single server system with FCFS (first come first serve) task scheduling under rush-hour conditions. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadlineT.Relying on a simple general probability model, asymptotic formulas concerning the mean and the variance of SRD(T) are determined; for instance, if the average arrival rate is larger than the departure rate, the expectation of SRD(T) is proved to fulfilE[SRD(T)]=c ₁+O(T ^–3) forT, wherec ₁ denotes some constant. If the arrival rate equals the departure rate, we findE[SRD(T)]c ₂ T ⁱ for somei2.     

Scheduling real-time tasks for dependability

Real-time systems are increasingly used in applications whose failure may result in large economic and human costs. Since many such systems operate in environments that are non-deterministic, and possibly hazardous, it is extremely important that the systems be dependable, namely the deadlines of tasks must be met even in the presence of particular failures. In order to enhance the dependability of a real-time system, we study the problem of scheduling a set of real-time tasks to meet their deadlines in the presence of processor failures. We first prove that the problem of scheduling a set of non-preemptive tasks on more than two processors to tolerate one arbitrary processor failure is NP-complete even when the tasks share a common deadline. Heuristic algorithms are then proposed to solve this problem. The schedules generated by the heuristic algorithms can tolerate one arbitrary processor failure in the worst case. The analysis and experimental data show that the performance of the algorithms is near-optimal.     

Routing and capacity assignment in backbone communication networks under time varying traffic conditions

This paper studies the problem of assigning capacities to links in a backbone communication network and determining the routes used by messages for all communicating node pairs in the network under time varying traffic conditions. The best routes are to be chosen from among all possible routes in the network. Tradeoffs between link costs and response time to users are achieved by specifying an upper limit on the average link queueing delay in the network. The goal is to minimize total link fixed and variable costs. The topology of the network and the end-to-end traffic requirements during the different busy-hours are assumed to be known. The problem is formulated as a mathematical programming model. An efficient solution procedure based on a Lagrangian relaxation of the problem is developed. The results of extensive computational experiments across a variety of networks are reported. These results indicate that the solution procedure is effective for a wide range of traffic loads and cost structures.     

Necessity for algebraic parabolicity conditions for nonstationary problems

It is known that single-valued solvability of nonstationary problems in spaces W₂ ^(l) with a priori estimate holds in the evaluation of some algebraic parabolicity conditions. It is proved in this note that the parabolicity conditions result from this estimate. (6 References)Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 615–625, December, 1967.     

Stability of vehicles under nonstationary crosswind excitation

Strong crosswind gusts have great influence on the stability of railway and road vehicles. They may lead to accidents and also to a discomfort for the road vehicle driver. Risk assessment for overturning of railway and road vehicles is usually calculated based on the stationary situation or at least on wind-tunnel experiments that are mostly carried out with a static vehicle model. Nonstationary excitation due to wind turbulence occurs if the vehicle accelerates or decelerates. Increasing vehicle speed relative to wind speed will move the energy content of the spectrum to a higher frequency range. It has been realized that nonstationary wind has a great influence on vehicle stability especially when the vehicle speed is high. Thus in order to assess the overturning risk in a more realistic way, a nonstationary wind model together with its interaction with the vehicle should be taken into consideration.This paper proposes a nonstationary wind turbulence model for the investigation of crosswind stability of ground vehicles. A wind model with nonstationary turbulence as well as the wind effects to the moving vehicle in a nonstationary situation (acceleration/deceleration) is described. Nonstationary aerodynamic forces are considered together with the interaction between the moving vehicle system and the wind turbulence. Failure probabilities are computed and reliability analyses are carried out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Grapho-analytical method of calculating the deformation of a viscoelastic rod in axial tension under nonstationary temperature conditions

The strains in the material are calculated on the basis of a compound mechanical model consisting of a system of individual elastico-viscous models of the Maxwell type. This model makes it possible to allow for the time dependence of the temperatures and stresses in the cross sections of bodies of simple shape—rod, plate, thin-walled shell—and to calculate the strains under nonstationary temperature conditions from the creep curves for reinforced plastics with allowance for the previous loading history both under a constant load and for an arbitrary loading law.Mekhanika Polimerov, Vol. 2, No. 3, pp. 413–420, 1966     

Monitoring the packet gap of real-time packet traffic

Real-time packet traffic is characterized by a strict deadline on the end-to-end time delay and an upper bound on the information loss. Due to the high correlation among consecutive packets, the individual packet loss does not well characterize the performance of real-time packet sessions. An additional measure of packet loss is necessary to adequately assess the quality of each real-time connection. The additional measure considered here is the average number of consecutively lost packets, also called the average packet gap. We derive a closed form for the average packet gap for the multiclassG/G/m/B queueing system in equilibrium and show that it only depends on the loss behavior of two consecutive packets. This result considerably simplifies the monitoring process of real-time packet traffic sessions. If the packet loss process is markovian, the consecutive packet loss has a geometric distribution.     

Quantile forecasting and data-driven inventory management under nonstationary demand

In this paper, a single-step framework for predicting quantiles of time series is presented. Subsequently, we propose that this technique can be adopted as a data-driven approach to determine stock levels in the environment of newsvendor problem and its multi-period extension. Theoretical and empirical findings suggest that our method is effective at modeling both weakly stationary and some nonstationary time series. On both simulated and real-world datasets, the proposed approach outperforms existing statistical methods and yields good newsvendor solutions.     

Scheduling workforce relief breaks in advance versus in real-time

This paper focuses upon employee rest breaks, or reliefs, in workforce scheduling. Historically, the workforce scheduling literature has largely ignored reliefs, as less than 18% of the 64 papers we surveyed scheduled reliefs. The argument has been that one need not schedule reliefs in advance, since they can easily be scheduled in real-time. We find this argument to be flawed. We show that failing to schedule reliefs in advance will have one of two undesirable outcomes. First, there will be a less profitable deployment of labor should all reliefs actually be taken in real-time. Second, if some reliefs are never assigned or if relief-timing restrictions are relaxed so that more reliefs may be assigned in real-time, there will be a disgruntled and less productive workforce and perhaps violations of contractual obligations. Our findings are supported by anecdotal evidence drawn from commercial labor scheduling software.     

Scheduling algorithms based on necessary optimality conditions

Translated from Issledovaniya po Prikladnoi Matematike, No. 10, pp. 102–110, 1984.     

Scheduling control for Markov-modulated single-server multiclass queueing systems in heavy traffic

This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite-state Markov process that modulates the arrival and service rates in the system. Various cases are considered: fast changing environment, fixed environment, and slowly changing environment. In all cases, the arrival rates are environment dependent, whereas the service rates are environment dependent when the environment Markov process is changing fast, and are assumed to be constant in the other two cases. In each of the cases, using weak convergence analysis, in particular functional limit theorems for Poisson processes and ergodic Markov processes, it is shown that an appropriate “averaged” version of the classical \(c\mu \) -policy (the priority policy that favors classes with higher values of the product of holding cost \(c\) and service rate \(\mu \) ) is asymptotically optimal for an infinite horizon discounted cost criterion.     

Dynamic programming—neural network real-time traffic adaptive signal control algorithm

In this paper, an “intelligent” isolated intersection control system was developed. The developed “intelligent” system makes “real time” decisions as to whether to extend (and how much) current green time. The model developed is based on the combination of the dynamic programming and neural networks. Many tests show that the outcome (the extension of the green time) of the proposed neural network is nearly equal to the best solution. Practically negligible CPU times were achieved, and were thus absolutely acceptable for the “real time” application of the developed algorithm.     

Two approaches to optimal routing and admission control in systems with real-time traffic

This paper addresses the problem of routing and admission control of real-time traffic in a queueing system where customers must begin service within given deadlines (or complete service within given deadlines), otherwise they are considered lost. Performance in such systems is measured by the probability a customer is lost. For a system ofK parallel servers with a probabilistic routing and admission control scheme, the problem of the optimal routing and admission control is considered and two approaches are presented. Assuming the availability of a closed-form expression for the probability of loss at each server, the problem is solved under general conditions and properties of the optimal flow allocation are given. However, such closed-form expressions are often unavailable. This motivates a second approach, which involves a gradient-based stochastic optimization algorithm with on-line gradient estimation. The gradient estimation problem for loss probabilities is solved through a recently-developed smoothed perturbation analysis (SPA) technique. The effectiveness of on-line stochastic optimization using this type of gradient estimator is demonstrated by combining the SPA algorithm with a sampling-controlled stochastic optimization algorithm for the aforementioned routing and admission control problem.This work was supported in part by the Office of Naval Research under Contract N00014-87-K-0304, by the Rome Air Development Center under Contract F30602-88-D-0027, by NASA under Contract NAG 2-595, and by the National Science Foundation under Grant EID-92-12122.The authors are grateful to Don Towsley for several contributions to Section 2 and to an anonymous reviewer for pointing out a redundant assumption in the proof of Lemma 2.1.     

Scheduling jobs under an aging effect

In this paper a scheduling problem that takes into consideration a phenomenoncalled ‘aging effect’ with reference to Computer Numerical Controldrilling or cutting machines is investigated. In the aftermath of this effect anexecution of jobs leads to a deterioration of a machine; thus processing timesof jobs increase and the production facility becomes less efficient. However, itis highly desirable to minimize the negative influence of this effect. Ingeneral, it can be done by formulating such a problem in the scheduling contextand optimizing an order of jobs to minimize the given criterion. Therefore, onthis basis a makespan minimization problem on a single machine with releasedates and the aging effect is formulated, where the job processing times aredescribed by non-decreasing functions dependent on fatigue (wear) of machine. Itis proved that even the special cases of the problem are NP-hard. Moreover, someproblems equivalences are shown and polynomially solvable cases are alsoprovided.     

Scheduling under a Non-renewable Resource Constraint

This paper examines a single-machine, non-renewable-resource-constrained scheduling problem where jobs have arbitrary processing times and resource requirements. Unit supply of a resource is assumed at each time period. Performance criterion is makespan. It is proved that this problem is identical to the two-machine flowshop problem, enabling the use of Johnson's algorithm. Immediate extensions of this result are presented.     

Scheduling time-dependent jobs under mixed deterioration

We consider a new model of time-dependent scheduling. A set of deteriorating jobs has to be processed on a single machine which is available starting from a non-zero time. The processing times of some jobs from this set are constant, while other ones are either proportional or linear functions of the job starting times. The applied criteria of schedule optimality include the maximum completion time, the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We delineate a sharp boundary between computationally easy and difficult problems, showing polynomially solvable and NP-hard cases.