Well-Posedness of an N-Unit Series System with Finite Number of Vacations

Abdugeni Osman, Abdukerim Haji

College of Mathematics and Systems Science, Xinjiang University, Urumqi, China.

DOI: 10.4236/jamp.2016.48169                

Abstract

We investigate the solution of an N-unit series system with finite number of vacations. By using C0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

Keywords

N-Unit Series System, C_0-Semigroup, Dynamic Solution, Well-Posedness

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Liu, R.B., Tang, Y.H. and Luo, C.Y. (2007) A New Kind of N-Unit Series Repairable System and Its Reliability Analysis. Math. Appl, 20, 164-170.
[2]	Liu, R.B., Tang, Y.H. and Cao, B.S. (2008) A New Model for the N-Unitseries Repairable System and Its Reliability Analysis. Chinese Journal of Engineering Mathematics, 25, 421-428.
[3]	Kovalyov, M.Y., Portmann, M.C. and Oulamara, A. (2006) Optimaltesting and Repairing a Failed Series System. J. Comb. Optim, 12, 279-295. http://dx.doi.org/10.1007/s10878-006-9633-0
[4]	Liu, R.B. and Liu, Z.M. (2011) Reliability Analysis of an N-Unit Series Repairable System with Finite Number of Vacations. Operations Research and Management Science, 20, 102-107.
[5]	Engel, K.-J. and Nagel, R. (2000) One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, 194, Springer-Verlag.
[6]	Nagel, R. (1986) One-Parameter Semigroups of Positive Operators. Springer-Verlag.
[7]	Casarino, V., Engel, K.-J., Nagel, R. and Nickel, G. (2003) A Semigroup Approach to Boundary Feedback Systems. Integr. Equ. Oper. Theory, 47, 289-306. http://dx.doi.org/10.1007/s00020-002-1163-2
[8]	Greiner, G. (1987) Perturbing the Boundary Conditions of a Generator. Houston J. Math., 13, 213-229.
[9]	Haji, A. and Radl, A. (2007) A Semigroup Approach to Queueing Systems. Semigroup Forum, 75, 610-624. http://dx.doi.org/10.1007/s00233-007-0726-6