Mathematical Modelling and Performance Analysis of Single Server Two-State Batch Arrivals and Batch Service Markovian Queue with Multiple Vacations

Abstract Here a two-state batch arrivals and batch service Markovian queue with server vacation model has been taken into consideration for its mathematical modelling and performance analysis under transient state. The present Markovian queueing model considers a single server with multiple vacations and both arrivals and services in batches of variable size. Arriving customers are processed by a single server under FIFO queue discipline and arrival process follows Poisson distribution. In addition to this, both service time and vacation time of the server follows exponential distribution. Using Laplace transforms technique, solution of governing differential-difference equations of the model has been achieved and significant performance measures of the model have been explored and some special cases have been discussed as well. Finally, some valuable conclusive observations have been found and a few suggestions for future research of the model have been focused.