A Note on the Relationships among the Queue Lengths at Various Epochs of a Queue with BMAP Arrivals

Abstract

For a stationary queue with BMAP arrivals, Takine and Takahashi [8] present a relationship between the queue length distributions at a random epoch and at a departure epoch by using the rate conservation iaw of Miyazawa [6]. In this note, we derive the same rela tionship by using the elementary balance equation, "rate-in =rate-out." Along the same lines. we additionally derive relationships between the queue length distributions at a random epoch and at an arrival epoch. AU these relationships hold for a broad class of finite- as well as infinite-capacity queues with BMAP arrivals