A two‐level queueing network model with blocking and non‐blocking messages

We analyze a novel twolevel queueing network with blocking, consisting of N level1 parallel queues linked to M level2 parallel queues. The processing of a customer by a level1 server requires additional services that are exclusively offered by level2 servers. These level2 servers are accessed through blocking and nonblocking messages issued by level1 servers. If a blocking message is issued, the level1 server gets blocked until the message is fully processed at the level2 server. The queueing network is analyzed approximately using a decomposition method, which can be viewed as a generalization of the wellknown twonode decomposition algorithm used to analyze tandem queueing networks with blocking. Numerical tests show that the algorithm has a good accuracy.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Arithmetic and other properties of certain Delphic semigroups. II

Summary This paper continues [2]. We show that the sets of infinitely divisible elements of the Delphic semigroups ⁺ (of positive renewal sequences) and P (of standard p-functions) are additively convex, and do a Choquet analysis in each case. We draw up the (M, m) diagram for members of , and deduce from it that the product topology on is metrizable. Finally we look at the arithmetic of , showing that the simples are residual in it, and partially identifying I ₀, the set of infinitely divisible elements without simple factors. Many examples are given.I am indebted to Professor D. G. Kendall for his constant help and encouragement in the course of the research leading to this paper and [2].     

Einschliessungsaussagen für Differentialoperatoren vierter Ordnung und ein Verfahren zur Berechnung von Schrankenfunktionen

For a linear fourth order ordinary differential operator M we study Range Domain Implications (RDI). Let C_o [O,1] be positive; we show under what conditions there exists a C_O[O,1] such that the following RDI holds: Mu(x) (x) (0x1) u(x) (0x1). In particular we provide a numerical procedure to calculate .RDI are used to obtain error estimations and to solve related nonlinear problems.The basic idea to prove RDI is to split M into a product of second order differential operators which are easier to handle. For the general case that there exists no global splitting the concept of a local splitting is introduced.

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The author would like to thank the European Research Office of the United States Army for their kind interest.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

Adjungierte Funktoren in der Kategorie der p-Bornologischen Räume

In the category p b of p-convex vector spaces and linear maps preserving bounded sets a p-bornological topology will be introduced on the tensor product of two spaces, likewise on the spaces of morphisms Hom(E,F). Thus one gets a pair of adjoint functors from p to p , p being the category of p-bornological spaces and continuous linear maps, and the topologies being introduced will be characterized by extreme properties with respect to the adjoint transformations.

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Dieser Arbeit liegt ein Teil der Dissertation des Autors, Kiel 1967, zugrunde.     

On the γ-Interior and γ-Closure of a Set

For a set X, let : exp X exp X satisfy A B whenever A B X. In [4], -open subsets of X, -interior iA and -closure cA of A X have been defined. The purpose of the present paper is to show that, under suitable conditions on , explicit formulas furnish iA and cA.     

Trace formulas for pair operators

In this paper we shall study the Fredholm determinant and related trace formulas for a class of operators which correspond to the restriction of integral operators with kernels of the form k(x,y) = (x)g^v(x–y)+[1–(x)]f^v(x–y) to the square |x|,|y| T and shall evaluate the limit as T . Here denotes the indicator function of the right half-line [0,) . The results obtained generalize the well known formulas of M. Kac for the classical convolution operator in which g = f .     

Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms

Summary We describe a large class of one-parameter families , {}, , of two-dimensional diffeomorphisms which arestable for <0, exhibit acycle for =0, and thereafter have a bifurcation set of positive but arbitrarily smallrelative measure for in small intervals [0, ]. A main assumption is that the basic sets involved in the cycle havelimit capacities that are not too large.The second author acknowledges hospitality and financial support from IMPA/CNPq during the period this paper was prepared     

Capacity analysis of an automated kit transportation system

In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steadystate behavior of this network is not described by a productform solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptiverepeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multiserver queues, and several nonaccumulating conveyor belts, modeled as ample servers. The AMVA algorithm exploits the property that the initial multiclass queueing network can be decomposed into a sequence of singleclass queueing networks and hence is very efficient. Comparison of numerical results of the AMVA algorithm for the throughputs for the different job classes to simulation results shows that the AMVA algorithm is also accurate. For several series of instances, the maximum relative error that we found was only 4.0%.     

L p -estimates for the solutions of second order elliptic equations

Summary We investigate the homogeneous Dirichlet problem in H^2,p for a second order elliptic partial differential equation in nondivergence form Lu=f in the case in which the leading coefficients of L belong to H^1,n(), Rⁿ. We prove that if p belongs to a suitable neighbourhood of 2, then the above problem, has a unique solution u satisfying D²u_p Cf_p; furthermore, if f H^k,p, k=1,2, ..., and the coefficients of L satisfy some natural conditions, then the solution satisfies .Lavoro eseguito nell'ambito del gruppi 40% e 60% del M.P.I.     

G-networks: a unifying model for neural and queueing networks

We survey results concerning a new stochastic network we have developed [1–7], which was initially motivated by neural network modelling [1], or — as we called it — by queueing networks with positive and negative customers [2, 3]. Indeed, it is well known that signals in neural networks are formed by impulses or action potentials, traveling much like customers in a queueing network. We call this model a G-network because it serves as a unifying basis for diverse areas of stochastic modelling in queueing networks, computer networks, computer system performance and neural networks. In its simplest version, negative and positive signals or customers circulate among a finite set of units, modelling inhibitory and excitatory signals of a neural network, or negative and positive customers of a queueing network. Signals can arrive either from other units or from the outside world. Positive signals are accumulated at the input of each unit, and constitute its signal potential. The state of each unit or neuron is its signal potential (which is equivalent to the queue length), while the network state is the vector of signal potentials at each neuron. If its potential is positive, a unit or neuron fires, and sends out signals to the other neurons or to the outside world. As it does so, its signal potential is depleted. In the Markovian case, this model has product form, i.e. the steady-state probability distribution of its potential vector is the product of the marginal probabilities of the potential at each neuron. The signal flow equations of the network, which describe the rate at which positive or negative signals arrive to each neuron, are non-linear. We discuss the relationship between this model and the usual connectionist (formal) model of neural networks, and present applications to combinatorial optimization and to image texture processing. Extensions of the model to the case of multiple signal classes, and to networks with triggered customer motion are presented. We also examine the general stability conditions which guarantee that the network has a well-defined steady-state behaviour.     

Design of manufacturing systems using queueing models

Design issues in various types of manufacturing systems such as flow lines, automatic transfer lines, job shops, flexible machining systems, flexible assembly systems and multiple cell systems are addressed in this paper. Approaches to resolving these design issues of these systems using queueing models are reviewed. In particular, we show how the structural properties that are recently derived for single and multiple stage queueing systems can be used effectively in the solution of certain design optimization problems.Supported in part by the Natural Sciences and Engineering Research Council of Canada via Operating and Strategic Grants on Modeling and Analyses of Production Systems and Modeling and Implementation of Just-in-Time Cells.Supported in part by the NSF Grants ECS-8811234 and DDM-9113008 and by Sloan Foundation Grants for the Consortium for Competitiveness and Cooperation and for the study on Competitive Semiconductor Manufacturing.     

Weyl's theorem for operator matrices

Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3.     

Special directions on contact metric three-manifolds

Blair [5] has introduced special directions on a contact metric 3-manifolds with negative sectional curvature for plane sections containing the characteristic vector field and, when is Anosov, compared such directions with the Anosov directions. In this paper we introduce the notion of Anosov-like special directions on a contact metric 3-manifold. Such directions exist, on contact metric manifolds with negative -Ricci curvature, if and only if the torsion is -parallel, namely (1.1) is satisfied. If a contact metric 3-manifold M admits Anosov-like special directions, and is -parallel, where is the Berger-Ebin operator, then is Anosov and the universal covering of M is the Lie group (2,R). We note that the notion of Anosov-like special directions is related to that of conformally Anosow flow introduced in [9] and [14] (see [6]).Supported by funds of the M.U.R.S.T. and of the University of Lecce. 1991.     

On log-hyponormal operators

LetTB(H) be a bounded linear operator on a complex Hilbert spaceH.TB(H) is called a log-hyponormal operator itT is invertible and log (TT ^*)log (T ^* T). Since log: (0, )(–,) is operator monotone, for 0<p1, every invertiblep-hyponormal operatorT, i.e., (TT ^*) ^p (T ^* T) ^p , is log-hyponormal. LetT be a log-hyponormal operator with a polar decompositionT=U|T|. In this paper, we show that the Aluthge transform is . Moreover, ifmeas ((T))=0, thenT is normal. Also, we make a log-hyponormal operator which is notp-hyponormal for any 0<p.This research was supported by Grant-in-Aid Research No. 10640185     

Some expansion formulae for Fox'sH-function of two variables involving associated Legendre functions

H- .     

On Almost β-Continuous Functions

A subset A of a topological space is said to be -open [1] if A Cl(Int(Cl(A))). A function f : X Y is said to be almost -continuous [18] if for each point x X and each open neighbourhood V of f(x) there exists a -open set U containing x such that f(U) Int(Cl(V)). Some new characterizations and several fundamental properties are obtained.     

Asymptotic estimates of approximation of continuous periodic functions by Fourier sums

Asymptotic estimates, expressed in terms of the value of the modulus of continuity of r-th order (r2) at the point t=/n of a functionf C ₂ or of the (, )-derivative of a functionf C _B C, are established for the deviations of continuous periodic functions from their Fourier sums.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 747–755, June, 1990.     

Start‐up class models in multiple‐class queues with N‐policy

In this paper, we consider multipleclass queueing systems with Npolicy in which the idle server starts service as soon as the number of customers in the startup class reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems.