a batch arrival queue with exponential working vacations
Many real systems with a multi-purpose production facility, such as some stochastic production and inventory control model, alternate between the normal production period and lower speed production period. In this paper, we model a general two-period alternating system by a batch arrival queue with exponential working vacations. Combining Embedded Markov chain and the M/G/1-type matrix analytic approach, we carry out the stationary analysis to present the system performance indices, including the queue length, waiting time and system utilization, et. al. A variety of numerical results are presented to show the effects of the system parameters on the system process.
batch arrival working vacations m/g/1-type matrix stochastic decomposition