Analysis Of M/M/C Queueing System With Blocking

Previous research on the queuing system is based on the changes of service rules andthe adjustment of vacation policies. However, in this article, we aim to start with theclassical M/M/1queuing model and establish a queuing system with blocking by addingrandom blocks to the customer arrival process. Then we will study the variation indifferent indicators of queuing system (blocked queue length,service queue length,waitingtime, staying Time etc.) caused by blocking through the numerical analysis andsystem-simulation methods. Next we will evaluate the influence of stability indicators ofvacation policies and vacation queuing systems affected by blocking.Queuing system with the blocking has been a totally new research direction inqueueing theory. In this article we will first establish two-dimensional Markov processesaccording to specific circumstances of blocking and obtain the matrix geometric solutionthrough Q matrix of the Quasi Birth and Death Process, process, then we obtain thestability distribution of queuing system with blocking by finding the non-zero solutions ofthe balance equation. Furthermore, we can also study M/M/c queuing system withblocking from the perspective of computer simulation by using Monte Carlo method. Inspecific, we adjust parameters characterizing service attributes, traffic arrival patterns andblock process, then evaluate how these parameters affect the blocking system. Moreover,by using variable-control method, we estimate to what extent the vacation policy of oursystem with block is dependent on blocking.In this article, we obtain various indicators of the queuing system with blocking bynumerical analysis and computer simulation method respectively, and we verify theeffectiveness of our model and the reliability of the simulation system. We aim tooptimize the queuing system with blocking via the evaluation of the influence of eachparameter on the system with block and those of the corresponding vacation system, sothat we can provide the optimal vacation policy and save the energy effectively and reducethe system operating cost.