A simple approximation for mean waiting time in M/G/1 queue with vacations and limited service discipline

This paper considers the M/G/1 queueing system with multiple vacations and E-limited service disciplines. In this kind of system, the server continues serving customers until either a prespecified number of customers have been served consecutively or the system becomes empty, and then goes on multiple vacations. Using stochastic decomposition and conditional probability arguments, the authors develop a new transform-free approximation for the mean waiting time in the system. In some special cases, the results become exact. Numerical tests indicate that the approximation is acceptably accurate.