Stability of periodic polling system with BMAP arrivals

This paper considers the stability of BMAP/GI/1 periodic polling models with mixed service disciplines. The server attends the N stations in a repeating sequence of stages. Customers arrive to the stations according to batch Markov arrival processes (BMAPs). The service times of the stations are general independent and identically distributed. The characterization of global stability of the system, the order of instability of stations and the necessary and sufficient condition for the stability are given. Our stability analysis is based on the investigation of the embedded Markovian chains at the polling epochs, which allows a much simpler discussion than the formerly applied approaches. This work can also be seen as a survey on stability of a quite general set of polling models, since the majority of the known results of the field is a special case of the presented ones.Queueing Stability Polling model Service discipline BMAP

Performance Analysis and Optimization of an Adaptive Admission Control Scheme in Cognitive Radio Networks

In cognitive radio networks, if all the secondary user (SU) packets join the system without any restrictions, the average latency of the SU packets will be greater, especially when the traffic load of the system is higher. For this, we propose an adaptive admission control scheme with a system access probability for the SU packets in this paper. We suppose the system access probability is inversely proportional to the total number of packets in the system and introduce an Adaptive Factor to adjust the system access probability. Accordingly, we build a discrete-time preemptive queueing model with adjustable joining rate. In order to obtain the steady-state distribution of the queueing model exactly, we construct a two-dimensional Markov chain. Moreover, we derive the formulas for the blocking rate, the throughput, and the average latency of the SU packets. Afterwards, we provide numerical results to investigate the influence of the Adaptive Factor on different performance measures. We also give the individually optimal strategy and the socially optimal strategy from the standpoints of the SU packets. Finally, we provide a pricing mechanism to coordinate the two optimal strategies