Optimality Analysis in K-Policy – Generalized Erlang Service Queueing Model

S. Bhuvaneeswari, B. Ramesh Kumar, R. Solaiappan, S. Murugesan

Abstract

This paper, we develops a nonlinear programming approach to construct the membership function of the performance measure in bulk arrival queueing system , in that the arrival and service rates are fuzzy numbers. The basic idea is transform to a “Generalized k – phase Erlang Fuzzy queue with infinite capacity to a family of conventional Generalized k – phase Erlang  Service queue with infinite capacity by applying - cut approach, and a pair of mixed integer nonlinear programs are formulated to calculate the upper and lower bound of the system performance measure at the different possibility level of . For practice use, the defuzzification of performance measures is also provided via Robust ranking method and carried out the defuzzification performance (Optimization)  using Chi square distribution of the goodness fit and to analyze the interval of confidence optimality. A numerical example is included.

Keywords

Fuzzy Sets; Mixed integer nonlinear programming; k-phase Erlang Distribution; Reduced Chi-square Distribution; - cut membership function

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