A Parametric Nonlinear Programming Approach to Analyzing Cyclic Queueing Networks in Fuzzy Environments

Abstract

Queueing theory has a wide range of applications in engineering and in the sciences. Jackson networks are a widely studied class of queueing systems, with applications in models of machine repair, communication and in computer networks. Real world data is imprecise, and thus there is an intrinsic fuzziness associated with the data. This fuzziness is resolved through the use of fuzzy theoretic techniques. In this paper, we study cyclic queueing systems, a special class of Jackson networks, in fuzzy environments, wherein the data is intrinsically imprecise. We propose a solution procedure that enables one to arrive at the fuzzified performance measures of such systems. The analysis is effectively reduced to that of an optimization problem, which lies under the purview of parametric nonlinear programming. We also use the Yager ranking index to arrive at the equivalent crisp performance measures. A numerical example is solved to illustrate the solution procedure.