For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters @math and @math , this model controls degree-dependent hopping of packets and forwarding of packets with higher performance at more busy nodes. Through a theoretical analysis and numerical simulations, we derive the condition for the concentration of packets at a few hubs. In particular, we show that the optimal @math and @math are involved in the trade-off between a detour path for @math ; In the low-performance regime at a small @math , the wandering path for @math and @math is small, neither the wandering long path with short wait trapped at nodes ( @math ), nor the short hopping path with long wait trapped at hubs ( @math ) is advisable. A uniformly random walk ( @math ) yields slightly better performance. We also discuss the congestion phenomena in a more complicated situation with packet generation at each time step.
With a different processing power at each node @cite_3 , it has also been considered that the node capacity @math is proportional to its degree @math , therefore more packets jump out from a node as the degree becomes larger. On the other hand, in the ZRP @cite_9 @cite_8 @cite_5 , the forwarding capacity at a node depends on the number of @math defined as a queue length occupied by packets at node @math . The ZRP is a solvable theoretical model for traffic dynamics. In particular, in the ZRP with a random walk at @math , the phase transition between condensation of packets at hubs and uncondensation on SF networks has been derived @cite_9 @cite_8 . For @math , a similar phase transition has been analyzed in the mean-field approximation @cite_4 .
@cite_4 @cite_8 @cite_9 @cite_3 @cite_5
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The packet pair technique estimates the capacity of a path (bottleneck bandwidth) from the dispersion (spacing) experienced by two back-to-back packets. We demonstrate that the dispersion of packet pairs in loaded paths follows a multimodal distribution, and discuss the queueing effects that cause the multiple modes. We show that the path capacity is often not the global mode, and so it cannot be estimated using standard statistical procedures. The effect of the size of the probing packets is also investigated, showing that the conventional wisdom of using maximum sized packet pairs is not optimal. We then study the dispersion of long packet trains. Increasing the length of the packet train reduces the measurement variance, but the estimates converge to a value, referred to as the asymptotic dispersion rate (ADR), that is lower than the capacity. We derive the effect of the cross traffic in the dispersion of long packet trains, showing that the ADR is not the available bandwidth in the path, as was assumed in previous work. Putting all the pieces together, we present a capacity estimation methodology that has been implemented in a tool called pathrate. In most network models for quality of service support, the communication links interconnecting the switches and gateways are assumed to have fixed bandwidth and zero error rate. This assumption of steadiness, especially in a heterogeneous internet-working environment, might be invalid owing to subnetwork multiple-access mechanism, link-level flow error control, and user mobility. Techniques are presented in this paper to characterize and analyze work-conserving communication nodes with varying output rate. In the deterministic approach, the notion of "fluctuation constraint," analogous to the "burstiness constraint" for traffic characterization, is introduced to characterize the node. In the statistical approach, the variable-rate output is modelled as an "exponentially bounded fluctuation" process in a way similar to the "exponentially bounded burstiness" method for traffic modelling. Based on these concepts, deterministic and statistical bounds on queue size and packet delay in isolated variable-rate communication server-nodes are derived, including cases of single-input and multiple-input under first-come-first-serve queueing. Queue size bounds are shown to be useful for buffer requirement and packet loss probability estimation at individual nodes. Our formulations also facilitate the computation of end-to-end performance bounds across a feedforward network of variable-rate server-nodes. Several numerical examples of interest are given in the discussion. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. In this paper, we present a methodology to analytically compute the throughput capacity, or the maximum end-to-end throughput of a given source and destination pair in a multi-hop wireless network. The end-to-end throughput capacity is computed by considering the interference due to neighboring nodes, as well as various modes of hidden node interference. Knowing the throughput capacity is important because it facilitates the design of routing policy, admission control for realtime traffic, as well as load control for wireless networks. We model location-dependent neighboring interference and we use a contention graph to represent these interference relationships. Based on the contention graph, we formulate the individual link capacity as a set of fixed point equations. The end-to-end throughput capacity can then be determined once these link capacities are obtained. To illustrate the utility of our proposed methodology, we present two important applications: (a) route optimization to determine the path with the maximum end-to-end throughput capacity and, (b) optimal offered load control for a given path so that the maximum end-to-end capacity can be achieved. Extensive simulations are carried out to verify and validate the proposed analytical methodology.