We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. While saturated-buffer scenarios have been widely investigated and yield useful throughput estimates for persistent sessions, they fail to capture the fluctuations in buffer contents over time, and provide no insight in the delay performance of flows with intermittent packet arrivals. Motivated by that issue, we explore in the present paper random-access networks with buffer dynamics, where flows with empty buffers refrain from competition for the medium. The occurrence of empty buffers thus results in a complex dynamic interaction between activity states and buffer contents, which severely complicates the performance analysis. Hence we focus on a many-sources regime where the total number of nodes grows large, which not only offers mathematical tractability but is also highly relevant with the densification of wireless networks as the Internet of Things emerges. We exploit time scale separation properties to prove that the properly scaled buffer occupancy process converges to the solution of a deterministic initial-value problem, and establish the existence and uniqueness of the associated fixed point. This approach simplifies the performance analysis of networks with huge numbers of nodes to a low-dimensional fixed-point calculation. For the case of a complete interference graph, we demonstrate asymptotic stability, provide a simple closed-form expression for the fixed point, and prove interchange of the mean-field and steady-state limits. This yields asymptotically exact approximations for key performance metrics, in particular the stationary buffer content and packet delay distributions. The methodological framework that we develop easily extends to various model refinements as will be illustrated by several examples.
Real-life scenarios however involve unsaturated networks. Packets arrive at the various nodes according to exogenous processes, and buffers may drain from time to time as packets are transmitted. In particular, in IoT applications, sources are likely to generate packets only sporadically, with fairly tight delay constraints, and often have empty buffers. Since empty nodes temporarily refrain from the medium competition, the activity process is strictly intertwined with the buffer content process. In this situation, the product-form solution no longer holds @cite_1 @cite_11 and an exact stationary analysis does not seem tractable. Furthermore, not even stability conditions for the queueing dynamics in the nodes' buffers are known, let alone results for the stationary distribution of the buffer content process.
@cite_1 @cite_11
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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. In this paper, we study the performance of Device-to-Device (D2D) communications with dynamic interference. In specific, we analyze the performance of frequency reuse among D2D links with dynamic data arrival setting. We first consider the arrival and departure processes of packets in a non-saturated buffer, which result in varying interference on a link based on the change of its backlogged state. The packet-level system behavior is then represented by a coupled processor queuing model, where the service rate varies with time due to both the fast fading and the dynamic interference effects. In order to analyze the queuing model, we formulate it as a Discrete Time Markov Chain (DTMC) and compute its steady-state distribution. Since the state space of the DTMC grows exponentially with the number of D2D links, we use the model decomposition and some iteration techniques in Stochastic Petri Nets (SPNs) to derive its approximate steady state solution, which is used to obtain the approximate performance metrics of the D2D communications in terms of average queue length, mean throughput, average packet delay and packet dropping probability of each link. Simulations are performed to verify the analytical results under different traffic loads and interference conditions. Abstract In this work we analyze a novel queueing system for modeling cooperative wireless networks. We consider a network of three saturated source users, say a central and two background users, two relay nodes and a common destination node. When the central user fails to transmit a packet directly to the destination, it forwards a copy of the blocked packet at both relay nodes in order to exploit the spatial diversity they provide. Moreover, each relay node receives also blocked packets from a dedicated background user. Relay nodes assist source users by retransmitting their blocked packets to the destination. Due to the complex interdependence among relays, and the wireless interference, the retransmission rate of a relay is affected by the state of the other. We consider a three-dimensional Markov process, investigate its stability, and study its steady-state performance using the theory of boundary value problems. Explicit expressions for the expected delay in the symmetrical model, and a generalization to N > 2 relay nodes are also given. Numerical examples are obtained and show insights into the system performance. We study a basic buffer management problem that arises in network switches. Consider @math input ports, each of which is equipped with a buffer (queue) of limited capacity. Data packets arrive online and can be stored in the buffers if space permits; otherwise packet loss occurs. In each time step the switch can transmit one packet from one of the buffers to the output port. The goal is to maximize the number of transmitted packets. Simple arguments show that any work-conserving algorithm, which serves any nonempty buffer, is 2-competitive. Azar and Richter recently presented a randomized online algorithm and gave lower bounds for deterministic and randomized strategies. In practice, greedy algorithms are very important because they are fast, use little extra memory, and reduce packet loss by always serving a longest queue. In this paper we first settle the competitive performance of the entire family of greedy strategies. We prove that greedy algorithms are not better than 2-competitive no matter how ties are broken. Our lower bound proof uses a new recursive construction for building adversarial buffer configurations that may be of independent interest. We also give improved lower bounds for deterministic and randomized online algorithms. In this paper we present the first deterministic online algorithm that is better than 2-competitive. We develop a modified greedy algorithm, called semigreedy, and prove that it achieves a competitive ratio of @math . The new algorithm is simple, fast, and uses little extra memory. Only when the risk of packet loss is low does it not serve the longest queue. Additionally we study scenarios when an online algorithm is granted additional resources. We consider resource augmentation with respect to memory and speed; i.e., an online algorithm may be given larger buffers or higher transmission rates. We analyze greedy and other online strategies.