Analysis of waiting time of M/G/1/K system with vacations under random scheduling and LCFS

This paper considers an M/G/1/K queueing system with multiple vacations under random scheduling and LCFS disciplines. As for M/G/1/K vacation models, Lee obtained the results of the joint distribution of the number of messages in the system and the remaining service or vacation time for a message. Using these expressions, we derive LSTs of the waiting time distribution under the two service disciplines. We show the calculation method for the first and the second moments of the waiting time under two service disciplines. Furthermore, we illustrate some numerical results of the mean waiting times and the coefficient of variations of the waiting time under FCFS, random scheduling and LCFS.