Showing papers in "Top in 1999"
314 citations
TL;DR: In this paper, the authors generalize the Malmquist productivity index and show that the geometric mean of a pair of generalized scale indexes is equal to the reciprocal of the Tornqvist scale index.
Abstract: In 1953 Sten Malmquist, a Swedish economist and statistician, published inTrabajos de Estadistica the foundations of a productivity index which now bears his name. In this paper we generalize the Malmquist productivity index. We show that (i) the generalized Malmquist productivity index can be expressed as the product of a Malmquist productivity index and a Malmquist scale index; (ii) the generalized Malmquist productivity index can also be expressed as the ratio of a Malmquist output quantity index to a Malmquist input quantity index; (iii) the geometric mean of a pair of Malmquist scale indexes is equal to the reciprocal of the Tornqvist scale index, which implies that (iv) the geometric mean of a pair of generalized Malmquist productivity indexes is equal to a Tornqvist productivity index.
114 citations
TL;DR: Dinkelbach's algorithm can be used to solve general fractional programming and two modifications to improve the speed-up of Dinkelbachs algorithm are proposed.
Abstract: Dinkelbach's algorithm was developed to solve convex fractinal programming. This method achieves the optimal solution of the optimisation problem by means of solving a sequence of non-linear convex programming subproblems defined by a parameter. In this paper it is shown that Dinkelbach's algorithm can be used to solve general fractional programming. The applicability of the algorithm will depend on the possibility of solving the subproblems. Dinkelbach's extended algorithm is a framework to describe several algorithms which have been proposed to solve linear fractional programming, integer linear fractional programming, convex fractional programming and to generate new algorithms. The applicability of new cases as nondifferentiable fractional programming and quadratic fractional programming has been studied. We have proposed two modifications to improve the speed-up of Dinkelbachs algorithm. One is to use interpolation formulae to update the parameter which defined the subproblem and another truncates the solution of the suproblem. We give sufficient conditions for the convergence of these modifications. Computational experiments in linear fractional programming, integer linear fractional programming and non-linear fractional programming to evaluate the efficiency of these methods have been carried out.
45 citations
TL;DR: Locally Farkas-minkowski (LFM) linear inequality systems were introduced in this article, which are those systems that satisfy that any consequence of the system that is active at some solution point is also a consequence of some finite subsystem.
Abstract: This paper introduces thelocally Farkas-Minkowski (LFM) linear inequality systems in a finite dimensional Euclidean space. These systems are those ones that satisfy that any consequence of the system that is active at some solution point is also a consequence of some finite subsystem. This class includes the Farkas-Minkowski systems and verifies most of the properties that these systems possess. Moreover, it contains the locally polyhedral systems, which are the natural external representation of quasi-polyhedral sets. TheLFM systems appear to be the natural external representation of closed convex sets. A characterization based on their properties under the union of systems is provided. In linear semi-infinite programming, theLFM property is the more general constraint qualification such that the Karush-Kuhn-Tucker condition characterizes the optimal points. Furthermore, the pair of Haar dual problems has no duality gap.
42 citations
TL;DR: This paper investigates the impact of retrial phenomenon on loss probabilities and compares loss probabilities of several channel allocation schemes giving higher priority to hand-off calls in the cellular mobile wireless network, and obtains the loss probabilities, the mean waiting time and the mean queue lengths.
Abstract: In this paper, we investigate the impact of retrial phenomenon on loss probabilities and compare loss probabilities of several channel allocation schemes giving higher priority to hand-off calls in the cellular mobile wireless network. In general, two channel allocation schemes giving higher priority to hand-off calls are known; one is the scheme with the guard channels for hand-off calls and the other is the scheme with the priority queue for hand-off calls. For mathematical unified model for both schemes, we consider theMAP
1,MAP
2
/M/c/b, ∞ retrial queue with infinite retrial group, geometric loss, guard channels and finite priority queue for hand-off class. We approximate the joint distribution of two queue lengths by Neuts' method and also obtain waiting time distribution for hand-off calls. From these results, we obtain the loss probabilities, the mean waiting time and the mean queue lengths. We give numerical examples to show the impact of the repeated attempt and to compare loss probabilities of channel allocation schemes.
29 citations
TL;DR: In this paper, the authors considered an out-of-n system with repair, where failed units are brought to an orbit, if the server is found to be busy, for retrial.
Abstract: We consider ak-out-of-n system with repair. Life times of components are independent exponentially distributed random variables with parameter λ
i
when the number of working units isi. Failed units are taken for repair to a station, manned by a single server, having no waiting room. The failed units are brought to an orbit, if the server is found to be busy, for retrial. Reliability of the system is computed in the following three situations: (i) Cold system (ii) Warm system and (iii) Hot system. Several other system characteristics are derived.
26 citations
TL;DR: A probabilistic derivation of the loss probability can be expressed in a simple formula involving the waiting time probabilities in the standard M/M/c queue and a possible use of this general formula in the M/ M/c retrial queue with impatient customers is outlined.
Abstract: This paper considers theM/M/c queue in which a customer leaves when its service has not begun within a fixed interval after its arrival. The loss probability can be expressed in a simple formula involving the waiting time probabilities in the standardM/M/c queue. The purpose of this paper is to give a probabilistic derivation of this formula and to outline a possible use of this general formula in theM/M/c retrial queue with impatient customers.
26 citations
TL;DR: Numerical methods for obtaining the stationary distribution of states for multi-server retrial queues with Markovian arrival process, phase type service time distribution with two states and finite buffer; and moments of the waiting time are presented.
Abstract: We present numerical methods for obtaining the stationary distribution of states for multi-server retrial queues with Markovian arrival process, phase type service time distribution with two states and finite buffer; and moments of the waiting time. The methods are direct extensions of the ones for the single server retrial queues earlier developed by the authors. The queue is modelled as a level dependent Markov process and the generator for the process is approximated with one which is spacially homogeneous above some levelN. The levelN is chosen such that the probability associated with the homogeneous part of the approximated system is bounded by a small tolerance and the generator is eventually truncated above that level. Solutions are obtained by efficient application of block Gaussian elimination.
23 citations
TL;DR: A Markovian polling model with a mixture of exhaustive and gated type stations is considered and formulae for the expected number of customers in each station in a steady state are obtained.
Abstract: A Markovian polling model with a mixture of exhaustive and gated type stations is considered. The cuttomers are ofn different tppes and arrive to the system acccording to the Poisson distribution, in batches containing customers of all types (correlated batch arrivals). The customers who find upon arrival the server unavailable repeat their arrival individually after a random amount of time (retrial customers). The service timesT
i
and the switchover timesV
ij
are arbitrarily distributed with different distributions for the different stations. For such a model we obtain formulae for the expected number of customers in each station in a steady state. Our formulae hold also for zero switchover periods and can easily be adapted to hold for the corresponding ordinary Markovian mixed polling models with/without switchover times and correlated batch arrivals. Numerical calculations are finally used to observe system's performance.
15 citations
TL;DR: This paper deals with the single server queueing system with a Batch Markovian Arrival Process, the semi-Markovian (SM) service process, and the retrial process of a MMPP (Markov Modulated Poisson Process) type.
Abstract: This paper deals with the single server queueing system with a Batch Markovian Arrival Process (BMAP), the semi-Markovian (SM) service process, and the retrial process of a MMPP (Markov Modulated Poisson Process) type. The stationary distribution of orbit size at the embedded and arbitrary epochs is the subject of research.
14 citations
TL;DR: In this paper, a special class of Switching Processes such as Recurrent Processes of a Semi-Markov type and Processes with SemiMarkov Switches are introduced, and limit theorems of Averaging Principle and Diffusion Approximation types are given.
Abstract: Some special classes of Switching Processes such as Recurrent Processes of a Semi-Markov type and Processes with Semi-Markov Switches are introduced. Limit theorems of Averaging Principle and Diffusion Approximation types are given. Applications to the asymptotic analysis of overloading state-dependent Markov and semi-Markov queueing modelsM
SM,Q
/M
SM,Q
/1/∞ and retrial queueing systemsM/G/1/w.r in transient conditions are studied.
TL;DR: In this article, the closed form optimal solution for a class of learning by doing models, where multiplicative uncertainty is introduced in a piecewise linear cost reduction function, was found.
Abstract: We find the closed form optimal solution for a class of learning by doing models, where multiplicative uncertainty is introduced in a piecewise linear cost reduction function. Previous literature does not find the closed form optimal solution for these models. We consider a monopolist, facing a linear demand function. The optimal policy for the resulting problem is shown to be piecewise linear and continuous. The optimal output increases with unit cost for certain values of the latter. Numerical examples are provided.
TL;DR: The LOMNICKI algorithm for n/m/P/Fmax flow shop problems is unsuitable for large values of n andm because of the time and size of storage required to attain an optimal solution as mentioned in this paper.
Abstract: The LOMNICKI algorithm for n/m/P/Fmax flow-shop problems is unsuitable for large values ofn andm because of the time and size of storage required to attain an optimal solution. The form of presentation of the problem to the algorithm can influence its performance. The algorithm performance can be improved applying the algorithm to the problem and to its inverse at the same time, sharing both applications the best value and the best bound found. Further exploitation of proprieties of the inverse problem are useful also for solve hard instances of the problem.
TL;DR: In this paper, a simple analytical approach which allows rigorous mathematical analysis of the stationary characteristics under heavy traffic has been proposed, based on certain "semi-explicit" formulas for the performance characteristics.
Abstract: M/G/1 type queueing systems whose arrival rate is a function of an independent continuous time Markov chain are considered. We suggest a simple analytical approach which allows rigorous mathematical analysis of the stationary characteristics under heavy traffic. Their asymptotic behaviour is described in terms of characteristics of the modulating process (defined as a solution of a set of linear algebraic equations). The analysis is based on certain “semi-explicit” formulas for the performance characteristics.
TL;DR: Property of the time-dependent state probabilities of theMt/G/∞ queue, when the queue is assumed to start empty are studied and the main performance characteristics of the ergodicM/M/m/m-m+d queue are sums of the corresponding random variables for theErlang queues, respectively.
Abstract: In this paper, properties of the time-dependent state probabilities of theM
t
/G/∞ queue, when the queue is assumed to start empty are studied. Those results are compared with corresponding time-dependent results for theM/M/1 queue. Approximation to the time-dependent state probabilities of theM/G/m/m queue by means of the corresponding time-dependent state probabilities of theM/G/∞ queue are discussed. Through a decomposition formula it is shown that the main performance characteristics of the ergodicM/M/m/m+d queue are sums of the corresponding random variables for the ergodicM/M/m/m andM/M/1/1+(d−1) queues, respectively, weighted by the 3-rd Erlang formula (stationary probability of waiting or being lost for theM/M/m/m+d queue). Successful exact and approximation extensions of this kind of decomposition formula to theM/M/m/m+d queue with retrials are presented.
TL;DR: In this paper, the authors consider stochastic bottleneck linear prograrnming problems and prove that under some positivity conditions, these problems are reduced to deterministic bottleneck linear problems.
Abstract: In this paper we consider some stochastic bottleneck linear prograrnming problems. In the case when the coefficients of the objective functions are simple randomized, the minimum-risk approach will be used for solving these problems. We prove that, under some positivity conditions, these stochastic problems are reduced to certain deterministic bottleneck linear problems. Applications of these problems to the bottleneck spanning tree problems and bottleneck investment allocation problems are given. A simple numerical example is presented.
TL;DR: An algorithm is constructed which provides in finite steps the stable coalition structure(s) of tree-graph communication games and an allocation of the core: the restricted marginal contribution allocation.
Abstract: We construct an algorithm which provides in finite steps the stable coalition structure(s) of tree-graph communication games and an allocation of the core: the restricted marginal contribution allocation.
TL;DR: In this paper, the full set of inequalities that define the convex hull of a 0-1 knapsack constraint presented in Weismantel (1997) were obtained. But they were not used in this paper to identify maximal cliques and non-dominated extensions of consecutive minimal covers.
Abstract: In this short note we obtain the full set of inequalities that define the convex hull of a 0–1 knapsack constraint presented in Weismantel (1997). For that purpose we use our O(n) procedures for identifying maximal cliques and non-dominated extensions of consecutive minimal covers and alternates, as well as our schemes for coefficient increase based tightening cover induced inequalities and coefficient reduction based tightening general 0–1 knapsack constraints.
TL;DR: In this paper, two Erlang queueing systems with a bivariate Poisson input flow of customers are studied and functional theorems of diffusion approximation type are proved, and stationary characteristics of the mathematical model are obtained.
Abstract: The purpose of this paper is to obtain stationary characteristics of the mathematical model, which consists of two Erlang queueing systems with a bivariate Poisson input flow of customers. Functional theorems of diffusion approximation type are proved.
TL;DR: In this paper, it was shown that the Banzhaf semivalue is consistent with respect to a suitable reduced game which keeps a clear parallelism with that defined by Hart and Mas-Colell in (1989) to prove the consistency of the Shapley value.
Abstract: In this note we show that the Banzhaf semivalue is consistent with respect to a suitable reduced game which keeps a clear parallelism with that defined by Hart and Mas-Colell in (1989) to prove the consistency of the Shapley value. We also use this reduced game property to characterize the Banzhaf semivalue.
TL;DR: This note presents a scheme for tightening 0–1 knapsack constraints based on other knapsacks constraints surrogating, and shows how this can be modified to suit the needs of the £20,000 to £50,000 budget.
Abstract: In this note, we present a scheme for tightening 0–1 knapsack constraints based on other knapsack constraints surrogating.