The impact of queue length information on buffer overflow in parallel queues

Abstract

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. In the first part of the paper, we characterize the buffer overflow exponents and the likeliest overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponent can be simply expressed in terms of the total system occupancy exponent of m parallel queues, for some m ≤ N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that LQF scheduling has superior overflow exponents compared to queue blind policies such as processor sharing (PS) and random scheduling. However, we show that the overflow exponent of the LQF policy can be preserved under arbitrarily infrequent queue length information.