The effect of downtime frequency at fixed machine availability in queuing systems

As efficient and accurate schemes, queuing models have usually been applied to approximate the behavior and characteristics of a system. However, most queuing models do not consider service interruptions. Although the previous studies have attempted to modify queuing models using availability, the frequency of server failure under fixed availability is still not considered. As previous study showed, the different frequency of server breakdown will result in various variations of service time as well as cycle time, even in a constant utilization level. This work presents a novel modified queuing model by applying availability and Mean Time to Repaired (MTTR). Consequently, the frequency of failure under fixed machine availability can be defined clearly in this model. In this work, Machine failure is regarded as an irregular customer to determine its impact on the system. The required service time and arrival rate of these irregular customers represent the behavior of machine breakdown. Therefore, the influence of machine failure on system performance is defined. The cycle time of each product with machine failure is also estimated accurately. Furthermore, the effect of various frequency of machine breakdown in a constant availability level is discovered in the result of simulation experiments. The experiments results also support that the proposed model could estimate the cycle time more accurately.