Reliability Analysis Of M/g/1 Queuing System With Repairable Service Station And Multiple Working Vacations

Repairable queuing is the expansion of the classical queuing theory, which service stations may be breakdown and can be repaired during the service period, The systems are widely used in manufacturing systems, communication systems and computer systems and so on. In recent years, Servi and Finn introduced working vacation policy, which plays an important role in the performance analysis of gateway router in optical networks. The breakdowns or vacations of the servers have an important impact on the performance measures and the economic profit of the system. Thus, the study on the queuing systems with integrated above mechanism has important theoretical significance and application value.In this paper, we consider the M/G/1 queuing system with repairable service station and multiple working vacations. The main contents are as follows:Firstly, reliability analysis of M/G/1 queuing model with repairable service station and multiple working vacations is presented, The model is the expansion of queuing system with multiple working vacations has been studied in reference. In this paper, we derive distribution functions of the generalized service time of the system service station during the busy period and the working vacation period respectively. We also derive the stationary queue length of the system at an arbitrary time and the stationary waiting time of customers. By using the probability decomposition method, the distribution of the first failure time of the service station and the probability of failure at t time of the service station are obtained. we also investigate some performance measures of the system and reliability indices of the unreliable server when both distribution function for the service time in a working vacation and distribution function for the service time during a service period follow an exponential distribution.Secondly, reliability analysis of M/G/1 queuing system with repairable service station and multiple working vacations and vacation interruption is presented, The model is the expansion of queuing system with multiple working vacations and vacation interruption has been studied in reference. In this paper, we derive distribution functions of the generalized service time of the system service station during the busy period and the working vacation period respectively. We also derive the stationary queue length of the system at an arbitrary time and the stationary waiting time of customers. By using the probability decomposition method the distribution of the first failure time of the service station and the probability of failure at t time of the service station are obtained.