Edges of an Imbedded Markov Chain and Rare Events Distribution in the M/G Repairman Chain

Pierre L. DOUILLET ¹

Date: 13th IS Computer Inform. Sc., 26-28/10/1998, Ankara

[RO,LE]

[CE]Edges of an Imbedded Markov Chain in the M/G Repairman Chain

[CO]13th IS on Computer and Information Science, 26-28/10/1998, Ankara

Abstract:

Abstract. The M/M model is widely used in queuing theory. Its computational simplicity is well known, and the choice of the M-law for clients arrivals is often realistic, since it is based upon the independence and memoryless property for these clients. But the choice of the M-law for the services is more often than not questionable or quite misleading. The new fact in that old problem of balancing simplicity versus relevance is the growth in power and in availability of the formal computing tools, like Maple, Axiom, etc. As an illustration, the paradigm of the repairman is reexamined, not only in its obvious M/M version but also in its M/D version (exponential mttf, deterministic mttr). With that M/D model, the chain whose states are the number of available machines is no more a Markov one, forcing to consider the more complicated 'repairing chain'. Thereafter, the time distribution of the system is obtained by considering the chain of the edges of that 'repairing chain'.