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.     

On the Completeness and Decidability of the Horn‐Like Fragment of the First‐Order Linear Temporal Logic

We prove the completeness and decidability of the Hornlike sequents, specifically, the socalled D₂sequents (of the firstorder linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus G_L, grounded by the author in his earlier papers, for D₂sequents we construct a D₂Sat calculus of the socalled saturated type consisting of decidable deductive procedures replacing the omegarule for the always operator. In the present paper, in order to prove the completeness and decidability of the calculus D₂Sat, we construct the socalled invariant decidable calculus D₂IN. We prove the equivalence of the calculi D₂IN, D₂Sat, and G _L ^** for the socalled saturated D₂sequents. From this equivalence, by reducing an arbitrary D₂sequent to a saturated D₂sequent, and also from the completeness of the G _L ^** calculus and decidability of the invariant calculus D₂IN, we deduce the completeness and decidability of the calculus D₂Sat in the class of D₂sequents.     

Relative E ‐Theory

The Etheory of A. Connes and N. Higson provides a new realization of Khomology based on the notion of asymptotic morphisms. In this paper we define relative Etheory, associating to a C*algebra A and an ideal I the Abelian groups Enrel(A;I). These groups are related to the Etheory groups of A and I in the familiar way by a long exact sequence and excision isomorphisms. The definition of relative Etheory is motivated by the properties of first order, elliptic differential operators on complete Riemannian manifolds. Applications will be considered in a future publication.     

Spatial shape‐preserving interpolation using ν‐splines

We present a global iterative algorithm for constructing spatial G ²continuous interpolating splines, which preserve the shape of the polygonal line that interpolates the given points. Furthermore, the algorithm can handle data exhibiting two kinds of degeneracy, namely, coplanar quadruples and collinear triplets of points. The convergence of the algorithm stems from the asymptotic properties of the curvature, torsion and Frénet frame of splines for large values of the tension parameters, which are thoroughly investigated and presented. The performance of our approach is tested on two data sets, one of synthetic nature and the other of industrial interest.     

Tableaus with Invertible Rules for Many‐Valued Modal Propositional Logics

We investigate tableaubased theorem proving for some families of manyvalued modal propositional logics. We consider manyvalued counterparts of wellknown twovalued modal logics obtained from various combinations of four basic properties of the accessibility relation, i.e., reflexivity, transitivity, seriality, and Euclideaness. For each of these logics we introduce tableau systems with certain invertible rules. We prove soundness and completeness of the presented tableau systems.     

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.     

(φ,ξ,η,λ)‐Structures of Parabolic Type

We consider (,,,)structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor . We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures.     

Stability Tests for Two Common Classes of Linear Time‐Delay and Hybrid Systems

The stability of linear timedelay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature usually causes the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained based either on extensions of classical tests applicable to delayfree systems or on approaches within the framework of twodimensional digital filters. Some of those twodimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slightadhoc adaptation of the tests for that situation.     

On Statistical Properties of the Lerch Zeta‐Function

A discrete limit theorem for the Lerch zetafunction on the complex plane is proved.     

A finite‐capacity queue with exhaustive vacation/close‐down/setup times and Markovian arrival processes

We consider a finitecapacity singleserver vacation model with closedown/setup times and Markovian arrival processes (MAP). The queueing model has potential applications in classical IP over ATM or IP switching systems, where the closedown time corresponds to an inactive timer and the setup time to the time delay to set up a switched virtual connection (SVC) by the signaling protocol. The vacation time may be considered as the time period required to release an SVC or as the time during which the server goes to set up other SVCs. By using the supplementary variable technique, we obtain the queue length distribution at an arbitrary instant, the loss probability, the setup rate, as well as the Laplace–Stieltjes transforms of both the virtual and actual waiting time distributions.     

A robust decomposition method for the analysis of production lines with unreliable machines and finite buffers

We consider production lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and all the machines have the same processing time. All machines are subject to failures. As is usually the case for production systems we assume that the failures are operation dependent [3,7]. Moreover, we assume that the times to failure and the repair times are exponentially distributed. To analyze such systems, a decomposition method was proposed by Gershwin [13]. The computational efficiency of this method was later significantly improved by the introduction of the socalled DDX algorithm [5,6]. In general, this method provides fairly accurate results. There are, however, cases for which the accuracy of this decomposition method may not be acceptable. This is the case when the reliability parameters (average failure time and average repair time) of the different machines have different orders of magnitude. Such a situation may be encountered in real production lines. In [8], an improvement of Gershwin's original decomposition method has been proposed that in general provides more accurate results in the above mentioned situation. This other method is referred to as the Generalized Exponential (GE) method. The basic difference between the GEmethod and that of Gershwin is that it uses a twomoment approximation instead of a singlemoment approximation of the repair time distributions of the equivalent machines. There are, however, still cases for which the accuracy of the GEmethod is not as good as expected. This is the case, for example, when the buffer sizes are too small in comparison with the average repair time. We present in this paper a new decomposition method that is based on a better approximation of the repair time distributions. This method uses a threemoment approximation of the repair time distributions of the equivalent machines. Numerical results show that the new method is very robust in the sense that it seems to provide accurate results in all situations.     

Spaces over a Category and Assembly Maps in Isomorphism Conjectures in K‐ and L‐Theory

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraicKandLtheory of integral group rings and to the Baum–Connes Conjecture on the topologicalKtheory of reducedC*algebras of groups. The approach is through spectra over the orbit category of a discrete groupG.We give several points of view on the assembly map for a family of subgroups and characterize such assembly maps by a universal property generalizing the results of Weiss and Williams to the equivariant setting. The main tools are spaces and spectra over a category and their associated generalized homology and cohomology theories, and homotopy limits.     

Risk programming for agricultural resource allocation: A multidimensional risk approach

This paper develops an approach to deal with risk in agricultural decisions. Although the model is in line with the Prospect ranking theory and the Partitioned multiobjective risk method, which recognise the multidimensional character of any risk measure taken in agricultural decisionmaking problems, its behavioural hypothesis and analytical development are totally different. The way in which the approach works is illustrated through a simple but wellknown example in agricultural planning.     

∈-Weak Minimal Solutions of Vector Optimization Problems with Set-Valued Maps

In this paper, we consider cone-subconvexlike vector optimization problems with set-valued maps in general spaces and derive scalarization results, -saddle point theorems, and -duality assertions using -Lagrangian multipliers.     

On the Movement of Transitive Permutation p-Groups

Let G be a transitive permutation group on a set and m a positive integer. If | – | m for every subset of and all g G, then || 2mp/(p – 1) where p is the least odd prime dividing |G|. It was shown by Mann and Praeger [13] that, for p = 3, the 3-groups G which attain this bound have exponent p. In this paper we will show a generalization of this result for any odd primes.AMS Subject Classification (2000), 20BXX     

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%.     

Chern Classes in Alexander–Spanier Cohomology

In this article we construct explicit cocycles in the AlexanderSpanier cohomological complex, representing the Chern character of an element in Ktheory     

A unified framework for pull control mechanisms in multi‐stage manufacturing systems

This paper presents a unified framework for pull production control mechanisms in multistage manufacturing systems. A pull production control mechanism in a multistage manufacturing system is a mechanism that coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. Four basic pull production control mechanisms are presented: Base Stock, Kanban, Generalized Kanban, and Extended Kanban. It is argued that on top of any of these basic coordination mechanisms, a local mechanism to control the workinprocess in each stage may be superimposed. Several cases of basic stage coordination mechanisms with stage workinprocess control are presented, and several production control systems that have appeared in the literature are shown to be equivalent to some of these cases.     

On a Positivity Property of the Riemann ξ‐Function

We consider a quantitative version of the positivity condition of the Riemann function. J. C. Lagarias obtained that for >10. The main aim of this paper is to prove the equality for 1.