The Queuing Systems With Breakdown Or Interruption In Vacation

The queuing systems with breakdown in vacation and the queuing with interruptionin vacation are extension of classical queuing theory. In the modern society, which scienceand technology have very large progresses, the purpose of service agencies is consideredto provide customers with good service as much as possible. To a certain extent, the resultsthat device from this paper, especially the analysis and reseach of the system performanceindex, can be better to help service agencies which can give good and fast services tocustomers and is conducive to the actual application, so as to improve utilization and theeconomic benefits of the services agencies. Thus, the studies of the queuing systemsprovide some useful references for the future study on queuing system of practicalapplication, and have important theoretical significance and practical application value.First, we investigate an M/M/2/N repairable queuing system with asynchronousvacation and heterogeneous servers. In the same model, heterogeneous servers, multiplevacations and breakdown of the service agences are considered and researched. A simpleand obvious iterative formulas of the steady-state probability vectors are obtained by usinga method of blocking matrix and analying the model. Then we obtain reliability indices,and by MATLAB calculation, paper gives some numerical analysis for the results.Second, we investigate an M/M/1queue system with setup times and breakdown inthe working vacation. In the same model, setup time and single working vacation, andbreakdown of the service agencies are researched. Using quasi birth and death process andmatrix-geometric solution method derive the equilibrium condition of the system and thesteady-state probability vectors. Furthermore, we get stationary indices, such assteady-state availability and steady-state fault frequency, and by MATLAB calculation,paper gives some numerical analysis for the results.Finally, we deals with an M/M/1queue, and the vacation interruption is controlled byBernoulli, which the working vacation is resumed to a regular busy period withprobability p or continues the vacation with probability1p. Using QBD process andmatrix-geometric solution, we obtain the steady-state distributions, for the number of customer in system and prove the result of stochastic decomposition of the queue lengthand gain the mean of the system size.