Performance analysis of a threshold-based discrete-time queue using maximum entropy

The provision of guaranteed QoS for various Internet traffic types has become a challenging problem for researchers. New Internet applications, mostly multimedia-based, require differentiated treatments under certain QoS constraints. Due to a rapid increase in these new services, Internet routers are facing serious traffic congestion problems. This paper presents an approximate analytical performance model in a discrete-time queue, based on closed form expressions using queue threshold, to control the congestion caused by the bursty Internet traffic. The methodology of maximum entropy (ME) has been used to characterize closed form expressions for the state and blocking probabilities. A discrete-time GGeo/GGeo/1/{N1, N2} censored queue with finite capacity, N2, external compound Bernoulli traffic process and generalised geometric transmission times under a first come first serve (FCFS) rule and arrival first (AF) buffer management policy has been used for the solution process. To satisfy the low delay along with high throughput, a threshold, N1, has been incorporated to slow the arrival process from mean arrival rate λ1 to λ2 once the instantaneous queue length has been reached, otherwise the source operates normally. This creates an implicit feedback from the queue to the arrival process. The system can be potentially used as a model for congestion control based on the Random Early Detection (RED) mechanism. Typical numerical experiments have been included to show the credibility of ME solution against simulation for various performance measures and to demonstrate the performance evaluation of the proposed analytical model.