The Queuing Systems With Breakdown Or Interruption In Vacation

Working vacation is that servers not completely stop the service but serve customers at a low rate in vacation time. This can both reduce the loss by impatient customer and can improve economic benefit. In the past few decades, vacation queuing system has been extensively studied. The analysis is mainly focused on two types of queuing system: single server vacation queue and multi-server vacation queue. Compared with the single-server vacation queue, multi-server vacation queue is more suitable for the actual situation. The results and the analysis of system performance indicators can provide good decision for service agencies and has certain reference value in practice.First, we investigate an M/M/c queuing system with N-policy and Bernoulli feedback. Through the analysis of the system and the matrix-geometric solution, we get the steady distributions for the system and the result of conditional stochastic decompositions.Second, we investigate an M/M/c queue system with setup times and Bernoulli feedback in the working vacation. In the same model, setup time and working vacations are researched. Using quasi birth and death process and matrix-geometric solution method derive the equilibrium condition of the system and the steady-state probability vectors. Furthermore, we get steady-state performance indicators of the system, and by MATLAB calculation, paper gives some numerical analysis for the results.Finally, we deals with an M/M/c working vacation queue with Bernoulli feedback and vacation interruption. When a service is completed in the vacation period, if there are at least d customers in the system, all servers will come back to the normal working level, otherwise, they continue the vacation. Using QBD process and matrix-geometric solution, we obtain the steady-state distribution for queue length and for the number of customer in system. Furthermore we indicate condition stochastic decomposition structures for queue length and waiting time under the condition that all the servers are busy.