Data and queueing analysis of a Japanese air-traffic flow

Congestion is a major cause of inefficiency in air transportation. A question is whether delays during the arrival phase of a flight can be absorbed more fuel-efficiently in the future. In this context, we analyze Japan’s flow strategy empirically and use queueing techniques in order to gain insight into the generation of the observed delays. Based on this, we derive a rule to balance congestion delays more efficiently between ground and en-route. Whether fuel efficiency can be further improved or not will depend on the willingness to review the concept of runway pressure.     

The unbalance and bounds on the average waiting time for periodic routing to one queue

In this paper we introduce the combinatorial notion of unbalance for a periodic zero-one splitting sequence. Using this unbalance we derive an upper bound for the average expected waiting time of jobs which are routed to one queue according to a periodic zero-one splitting sequence. In the companion paper [16] the upper bound will be extended to the routing to N parallel queues.Acknowledgement.The authors would like to thank Bruno Gaujal for his hospitality during their visits to LORIA, Nancy. During one of the stimulating discussions with him the graph order was found. The authors thank Robert Tijdeman for his helpful comments.     

Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customer due dates

We consider a two-stage make-to-order manufacturing system with random demands, processing times, and distributed customer due dates. The work to each stage is released based on a planned lead time. A general approach to minimize total inventory holding and customer order tardiness cost is presented to find the optimal manufacturing capacities and planned lead times for each manufacturing stage. Expressions are derived for work-in process inventories, finished-goods-inventory and expected backorders under the assumption of a series of M/M/1 queuing systems and exponentially distributed customer required lead times. We prove that the distribution of customer required lead time has no influence on the optimal planned lead times whenever capacity is predefined but it influences the optimal capacity to invest into. For the simultaneous optimization of capacity and planned lead times we present a numerical study that shows that only marginal cost decreases can be gained by setting a planned lead time for the upstream stage and that a considerable cost penalty is incurred if capacity and planned lead time optimization are performed sequentially.     

Transform-free equations for the stationary waiting time distributions in the queue with poisson arrivals and bulk services

We study a queue with Poisson arrivals and a bulk service rule with two thresholdsN andm on the group sizes. No group of fewer thanN or more thanm customers is served. When the number of available customers is betweenN andm, all customers are served together. The principal results deal with the joint stationary distribution of the waiting time of an arriving customer and of the size of the group in which he is eventually served. After prior computation of the stationary queue length density, the evaluation of the waiting time distribution is reduced to the solution of a system of linear differential equations and a single integral equation. The process describing the waiting time is in general non-Markovian.University of Delaware, Applied Mathematics Institute, Technical Report No. 95 B, May 1984.This research was supported by Grant No. ECS-8205404 of the National Science Foundation and by a Senior U.S. Scientist Award of the Alexander von Humboldt Foundation.     

Fair cubic transition between two circles with one circle inside or tangent to the other

This paper describes a method for joining two circles with a C-shaped and an S-shaped transition curve, composed of a cubic Bézier segment. As an extension of our previous work; we show that a single cubic curve can be used for blending or for a transition curve preserving G ² continuity regardless of the distance of their centers and magnitudes of the radii which is an advantage. Our method with shape parameter provides freedom to modify the shape in a stable manner.     

On the capacity of the continuous time Gaussian channel with feedback

We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the covariance functions of the input processes, is imposed on the input processes. It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback.     

On pairs of commuting derivations of the polynomial ring in one or two variables

It is well known that each pair of commuting linear operators on a finite dimensional vector space over an algebraically closed field has a common eigenvector. We prove an analogous statement for derivations of k[x] and k[x,y] over any field k of zero characteristic. In particular, if D₁ and D₂ are commuting derivations of k[x,y] and they are linearly independent over k, then either (i) they have a common polynomial eigenfunction; i.e., a nonconstant polynomial f∈k[x,y] such that D₁(f)=λf and D₂(f)=μf for some λ,μ∈k[x,y], or (ii) they are Jacobian derivations

     

On the probability of abandonment in queues with limited sojourn and waiting times

Consider the Geo/Geo/1 queue with impatient customers and let X reflect the patience distribution. We show that systems with a smaller patience distribution X in the convex-ordering sense give rise to fewer abandonments (due to impatience), irrespective of whether customers become patient when entering the service facility.     

Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period

In this article, we consider the single machine scheduling problem with one planned setup period, with the aim of minimizing the weighted sum of the completion times. We study the WSPT and MWSPT heuristics and we show that the worst-case performance ratio is 3 for the two heuristics in some cases and it is unbounded otherwise. We also show that these worst-case performance ratios are tight.     

On the consistency and finite-sample properties of nonparametric kernel time series regression,autoregression and density estimators

Summary Kernel estimators of conditional expectations and joint probability densities are studied in the context of a vector-valued stationary time series. Weak consistency is established under minimal moment conditions and under a hierarchy of weak dependence and bandwidth conditions. Prompted by these conditions, some finite-sample theory explores the effect of serial dependence on variability of estimators, and its implications for choice of bandwidth. This research was supported by the ESRC.     

Reflection length with two parameters in the asymptotic representation theory of type B/C and applications

We introduce a two-parameter function ${?}_{q_{+},q_{?}}$ on the infinite hyperoctahedral group, which is a bivariate refinement of the reflection length. We show that this signed reflection function ${?}_{q_{+},q_{?}}$ is positive definite if and only if it is an extreme character of the infinite hyperoctahedral group and we classify the corresponding set of parameters $q_{+},q_{?}$. We construct the corresponding representations through a natural action of the hyperoctahedral group $B(n)$ on the tensor product of n copies of a vector space, which gives a two-parameter analog of the classical construction of Schur–Weyl.We apply our classification to construct a cyclic Fock space of type B generalizing the one-parameter construction in type A found previously by Bo?ejko and Guta. We also construct a new Gaussian operator acting on the cyclic Fock space of type B and we relate its moments with the Askey–Wimp–Kerov distribution by using the notion of cycles on pair-partitions, which we introduce here. Finally, we explain how to solve the analogous problem for the Coxeter groups of type D by using our main result.     

Control synthesis for discrete time systems with control and state bounds in the presence of disturbances

The problem of control in the presence of unknown but limited disturbance for a discrete-time linear system with polyhedral input and state bounds is investigated. Two problems are considered: that of reaching an assigned target set in the state space; and that of keeping the state in a given region using the available controls. In both cases, a solution is given via linear programming. A computational procedure for the control synthesis is proposed which can be implemented to obtain a feedback control.The author thanks Professor G. Leitmann for his helpful suggestions.     

On metric spaces with the properties of de Groot and Nagata in dimension one

A metric space (X,d) has the de Groot property GPn if for any points x₀,x₁,…,xn+2∈X there are positive indices i,j,k?n+2 such that i≠j and d(xi,xj)?d(x₀,xk). If, in addition, k∈{i,j} then X is said to have the Nagata property NPn. It is known that a compact metrizable space X has dimension dim(X)?n iff X has an admissible GPn-metric iff X has an admissible NPn-metric.We prove that an embedding f:(0,1)→X of the interval (0,1)⊂R into a locally connected metric space X with property GP₁ (resp. NP₁) is open, provided f is an isometric embedding (resp. f has distortion Dist(f)=‖fLip_‖⋅‖f−1Lip_‖<2). This implies that the Euclidean metric cannot be extended from the interval [−1,1] to an admissible GP₁-metric on the triode T=[−1,1]∪[0,i]. Another corollary says that a topologically homogeneous GP₁-space cannot contain an isometric copy of the interval (0,1) and a topological copy of the triode T simultaneously. Also we prove that a GP₁-metric space X containing an isometric copy of each compact NP₁-metric space has density ?c.     

On the flow of a viscous incompressible fluid between two parallel flat plates one in uniform motion and the other at rest,with unsteady pressure gradient

In the present paper an attempt is made to find the solution of the Navier-Stokes equations for the unsteady flow of a viscous incompressible fluid through a channel bounded by two parallel flat plates, the upper one in uniform motion and the other at rest, under the influence of pressure gradient (i) varying linearly with time, and (ii) decreasing exponentially with time. In the first case it is seen that the velocity of any point above the axis of the channel is more than the velocity of the point symmetrical to this below the axis of the channel.     

盈余过程的马氏性与索赔到达间隔分布为离散型的连续时间风险模型

本文研究广泛的一类连续时间风险模型盈余过程的马氏性,得到了盈余过程成为马氏过程的充分必要条件．首次建立了索赔到达间隔为离散型分布的连续时间风险模型．并对两个基本特例得到了破产概率的准确表达式．     

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.     

On the stability of Timoshenko-type systems with internal frictional dampings and discrete time delays

In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet–Dirichlet or Dirichlet–Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case.     

On two fragments with negation and without implication of the logic of residuated lattices

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H_BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed and latticed monoids, respectively. All the logical systems considered are decidable.     

在常规故障和临界人为错误条件下具有易损坏存储部件并联可修系统稳态解中p_0的最优控制

讨论了两个部件并联和一个储备部件,并且具有临界认为错误和故障的可修系统稳态解中p_0的最优控制问题.     

On the characterization of departure rules for discrete-time queueing networks with batch movements and its applications

This paper supplements and generalizes the results of sawa [11] in this special issue from the viewpoint of discrete-time networks of queues with batch arrivals and batch departures, due to Henderson and Taylor [7]. We first note that the D-rule of sawa [11] is equivalent to the specific form for the release rate function, introduced in [7]. Such forms have widely appeared in the literature, too. sawa [11] found that the D-rule can be characterized in terms of the reversed-time process of a certain vector-valued process. He obtained this characterization for a single node model. We generalize this result for networks of queues with batch arrivals and batch departures. This reveals why the specific form of the release rate function is common in the literature. Furthermore, the characterization is useful to consider traffic flows in a discrete-time queueing network.This research is partially supported by NEC C&C Laboratories.