Matrix analysis
Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Preference relations on a set of fuzzy utilities as a basis for decision making
Fuzzy Sets and Systems
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Vertex method for computing functions of fuzzy variables
Fuzzy Sets and Systems
On using &agr;-cuts to evaluate fuzzy equations
Fuzzy Sets and Systems
Elementary queueing theory based on possibility theory
Fuzzy Sets and Systems
Analysis and simulation of fuzzy queues
Fuzzy Sets and Systems - Special issue on industrial engineering methods
Ranking fuzzy numbers with integral value
Fuzzy Sets and Systems
A qualitative simulation approach for fuzzy dynamical models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
Parametric programming to the analysis of fuzzy queues
Fuzzy Sets and Systems
Applications of possibility and evidence theory in civil engineering
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on models for imprecise probabilities and partial knowledge
Operations Research: An Introduction (8th Edition)
Operations Research: An Introduction (8th Edition)
Fuzzy assignment of customers for a parallel queueing system with two heterogeneous servers
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
A behavioural model for vague probability assessments
Fuzzy Sets and Systems
Discussion: Further thoughts on possibilistic previsions: A rejoinder
Fuzzy Sets and Systems
Homogeneous finite-source retrial queues with server subject to breakdowns and repairs
Mathematical and Computer Modelling: An International Journal
When does the cµ rule apply to finite-population queueing systems?
Operations Research Letters
Computers & Mathematics with Applications
Simulation for queueing systems under fuzziness
International Journal of Systems Science
Mathematics and Computers in Simulation
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Finite input source queuing models have a wide range of applications in many practical situations and are frequently found in machine maintenance and repair operations. Owing to uncontrollable factors, finite input source queuing problems parameters may contain uncertainty. That is why to begin with, in this paper it is proposed the analysis, development and design of a fuzzy queuing model with finite input source in which the arrival pattern as well as the service pattern follow an exponential distribution under uncertain parameter. In order to design the system, the established optimization criterion consists in determining the optimal number of servers so as to minimize the expected total cost function per unit time. To choose among uncertain alternatives, three techniques to make decisions under uncertainty are proposed. This type of systems has a finite waiting line. As a result, the system of differential equations that governs the model's behaviour consists of a finite number of equations. In the second place, this feature of the finite input source queuing systems enables us to bring forward in this paper two new contributions: (i) in the first one the following doubt has been raised and solved: if the convergence of the probabilities p@?"i(t) obtained from the fuzzy differential equations that govern the behaviour of the finite source system is worked out; does the result match the steady-state fuzzy probabilities obtained by applying Zadeh's Extension Principle to the classic queuing model?; and (ii) it has been performed a fuzzy simulation experiment on the differential equations using Bontempi's Qua. Si. III algorithm. This enables us to know the time evolution of the probabilities p@?"i(t) and its convergence on the one hand. On the other we can compare the results of the simulation to those analytically obtained by applying Zadeh's Extension Principle. This way the validity of the proposed procedure for the simulation is verified by means of the theoretical results. The extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informing results and wider knowledge on the behaviour of the system, since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information, that is why the finite input source queuing models with uncertain data can be of more use and can have a broader range of applications.