FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach

Abstract

The present paper investigates the customers’ balking behavior in a double orbit retrial queueing system having two types of customers namely, ordinary and premium class customers. Upon finding the server busy, most of the arriving customers join ordinary orbit whereas a few of the customers join the premium orbit by paying extra amount. The steady state analytical solution for the probability distribution and system performance measures are derived by using probability generating function. A profit function based on customers’ reward-cost is constructed and analyzed using customers’ joining strategy. Markovian double orbit retrial model is then transformed into fuzzy FM/FM/1 queueing model with balking by using system parameters expressed as linguistic variables. Based on Zadeh's extension principle and α − cut method, parametric nonlinear programing (P-NLP) approach is used to determine fuzzified indices. Furthermore, the ranking index method is used to defuzzify the performance measures. The sensitivity analysis and cost optimization are performed for the crisp queueing model by taking a numerical illustration.