Abstract
In this paper, we study the strong stability in the M/G/1 queueing system with breakdowns and repairs after perturbation of the breakdown’s parameter. Using the approximation conditions in the classical M/G/1 system, we obtain stability inequalities with exact computation of the constants. Thus, we can approximate the characteristics of the M/G/1 queueing system with breakdowns and repairs by the classical M/G/1 corresponding ones.
Highlights
It is common to assume that the service station have not failed
A more realistic queueing model is a model which its service station is unable from time to time to deliver service to its customers
After perturbing the breakdown’s parameter, we estimate the deviation of its transition operator, and we give an upper bound to the approximation error (Section 4)
Summary
It is common to assume that the service station have not failed. [5] investigated the controllable M/Hk/1 queueing system with unreliable server They developed analytic closed-form solutions and provided a sensitivity analysis. Analytic closed-form solutions could be obtained only for certain special unreliable models Even in these cases, the complexity of these analytical formulas does not allow exploiting them in the practice, that is the case of the generating function of the various limiting distributions or Laplace transform (see for example [11]). For this reason, there exists, when modelling a real system, a common technique for substituting the real but complicated elements governing a queueing system by simpler ones in some sens close to the real elements. After perturbing the breakdown’s parameter, we estimate the deviation of its transition operator, and we give an upper bound to the approximation error (Section 4)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
