On the Queue Length Distribution for the GI/G/1/K/V_M Queue

Abstract

We present a transform-free distribution of the steady-state queue length for the GI/G/1/K queueing system with multiple vacations under exhaustive FIFO service discipline. The method we use is a modified supplementary variable technique and the result we obtain is expressed in terms of conditional expectations of the remaining service time, the remaining interarrival time, and the remaining vacation, conditional on the queue length at the embedded points. The case K → ∞ is also considered.

Key Words:

• Modified supplementary variable technique
• Rate conservation

Acknowledgment

This work was supported by Korea Research Foundation Grant (KRF-2002-070-C00021).