An Analytical Queuing Model for Long Range Dependent Arrivals and Variable Service Capacity

Since the finding of long-range-dependent (LRD) traffic as a ubiquitous phenomenon in communication networks, analytical modelling of queuing systems subject to such type of traffic has attracted tremendous research interests. Due to the inherent difficulty and complexity of modelling fractal-like LRD traffic, existing studies have usually focused on queuing systems with constant service capacity. Given the fading nature of wireless channels under realistic working environments, it is very necessary to investigate the performance behavior of queuing systems with variable service capacity. To this end, this paper presents a new analytical model for single server queuing systems with LRD input traffic and variable service capacity. Specifically, we derive the close-form expressions for calculating the upper and lower bounds of the tail distribution of queue length in the queuing system. Resorting to extensive comparisons between analytical bounds and simulation results, we validate the effectiveness and accuracy of the model. We further adopt the model to analyze the effects of variable service capacity on the system performance.