Loss Probability and Delay of Finite-Buffer Queues with Discrete ON-OFF Markovian Arrivals and Geometric Service Times

摘要

Discrete-time queues are commonly used in the performance analysis of many computer and communications systems. As the independent and identically distributed (i.i.d.) arrival traffic model frequently adopted (due to its analytical tractability) in the literature does not capture some important properties of real-world traffics, such as self-similarity, long-range dependence, and burstiness, it is more realistic to model the arrival traffic as a time-correlated process. A widely used time-correlated arrival traffic model is the ON-OFF traffic model as it is capable of capturing the burstiness of real-world traffics. In particular, it is commonly adopted for modeling voice traffics, where the talker is speaking (resp., silent) in the ON (resp., OFF) periods. In this paper, we present the performance analysis of a finite-buffer queue with ON-OFF Markovian arrival traffic and geometric service times, called ON-OFF/Geom/1/B queue in this paper. We derive closed-form expressions for the packet loss probability and the average packet delay. The closed-form expressions are given in term of the buffer size of the queue, the characterizing parameters of the ON-OFF Markovian traffic, and the service rate.