Analysis of Fuzzy Erlang ’ s Loss Queuing Model : Non Linear Programming Approach

This paper proposes a procedure for constructing the membership functions of the performance measures in a finite capacity loss queuing system with arrival rate and service rate being fuzzy numbers. To investigate the performance measures of the finite capacity loss queuing system a pair of mathematical non linear programme are formulated to calculate the upper and lower bound of system characteristics. By extending finite capacity loss queue in fuzzy environment would have wider applications.

[1]  Shih-Pin Chen,et al.  Parametric nonlinear programming approach to fuzzy queues with bulk service , 2005, Eur. J. Oper. Res..

[2]  Shih-Pin Chen,et al.  Parametric nonlinear programming for analyzing fuzzy queues with finite capacity , 2004, Eur. J. Oper. Res..

[3]  James J. Buckley,et al.  Fuzzy Queueing Theory Revisited , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[4]  Chang-Chung Li,et al.  Parametric programming to the analysis of fuzzy queues , 1999, Fuzzy Sets Syst..

[5]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[6]  Marc Roubens,et al.  Ranking and defuzzification methods based on area compensation , 1996, Fuzzy Sets Syst..

[7]  E. Lee,et al.  Analysis and simulation of fuzzy queues , 1992 .

[8]  James J. Buckley,et al.  Elementary queueing theory based on possibility theory , 1990 .

[9]  S. Chanas,et al.  Single value simulation of fuzzy variables , 1988 .

[10]  R. Yager.  A characterization of the extension principle , 1986 .

[11]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[12]  A. Bonaert.  Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[13]  J. Medhi,et al.  Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule , 1975 .

[14]  Dimitar P. Filev,et al.  Fuzzy SETS AND FUZZY LOGIC , 1996 .

[15]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[16]  E. Lee,et al.  Analysis of fuzzy queues , 1989 .

[17]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[18]  R. E. Stanford,et al.  The set of limiting distributions for a Markov chain with fuzzy transition probabilities , 1982 .

[19]  Henri Prade,et al.  An Outline of Fuzzy or Possibilistic Models for Queuing Systems , 1980 .