The Load-Balanced Router architecture has received a lot of attention because it does not require centralized scheduling at the internal switch fabrics. In this paper we reexamine the architecture, motivated by its potential to turn off multiple components and thereby conserve energy in the presence of low traffic. We perform a detailed analysis of the queue and delay performance of a Load-Balanced Router under a simple random routing algorithm. We calculate probabilistic bounds for queue size and delay, and show that the probabilities drop exponentially with increasing queue size or delay. We also demonstrate a tradeoff in energy consumption against the queue and delay performance.
We study algorithms for carrier and rate allocation in cellular systems with distributed components such as a heterogeneous LTE system with macrocells and femtocells. Existing work on LTE systems often involves centralized techniques or requires significant signaling, and is therefore not always applicable in the presence of femtocells. More distributed CSMA-based algorithms (carrier-sense multiple access) were developed in the context of 802.11 systems and have been proven to be utility optimal. However, the proof typically assumes a single transmission rate on each carrier. Further, it relies on the CSMA collision detection mechanisms to know whether a transmission is feasible. In this paper we present a framework for LTE scheduling that is based on CSMA techniques. In particular we first prove that CSMA-based algorithms can be generalized to handle multiple transmission rates in a multi-carrier setting while maintaining utility optimality. We then show how such an algorithm can be implemented in a heterogeneous LTE system where the existing Channel Quality Indication (CQI) mechanism is used to decide transmission feasibility.
In this paper we consider the Max-Weight protocol for routing and scheduling in wireless networks under an adversarial model. This protocol has received a significant amount of attention dating back to the papers of Tassiulas and Ephremides. In particular, this protocol is known to be throughput-optimal whenever the traffic patterns and propagation conditions are governed by a stationary stochastic process. However, the standard proof of throughput optimality (which is based on the negative drift of a quadratic potential function) does not hold when the traffic patterns and the edge capacity changes over time are governed by an arbitrary adversarial process. Such an environment appears frequently in many practical wireless scenarios when the assumption that channel conditions are governed by a stationary stochastic process does not readily apply. In this paper we prove that even in the above adversarial setting, the Max-Weight protocol keeps the queues in the network stable (i.e. keeps the queue sizes bounded) whenever this is feasible by some routing and scheduling algorithm. However, the proof is somewhat more complex than the negative potential drift argument that applied in the stationary case. Our proof holds for any arbitrary interference relationships among edges. We also prove the stability of $ep$-approximate Max-Weight under the adversarial model. We conclude the paper with a discussion of queue sizes in the adversarial model as well as a set of simulation results.
These are the lecture notes for the DIMACS Tutorial Limits of Approximation Algorithms: PCPs and Unique Games held at the DIMACS Center, CoRE Building, Rutgers University on 20-21 July, 2009. This tutorial was jointly sponsored by the DIMACS Special Focus on Hardness of Approximation, the DIMACS Special Focus on Algorithmic Foundations of the Internet, and the Center for Computational Intractability with support from the National Security Agency and the National Science Foundation. The speakers at the tutorial were Matthew Andrews, Sanjeev Arora, Moses Charikar, Prahladh Harsha, Subhash Khot, Dana Moshkovitz and Lisa Zhang. The sribes were Ashkan Aazami, Dev Desai, Igor Gorodezky, Geetha Jagannathan, Alexander S. Kulikov, Darakhshan J. Mir, Alantha Newman, Aleksandar Nikolov, David Pritchard and Gwen Spencer.
We consider a set of flows passing through a set of servers. The injection rate into each flow is governed by a flow control that increases the injection rate when all the servers on the flows path are empty and decreases the injection rate when some server is congested. We show that if each servers congestion is governed by the arriving traffic at the server then the system can *oscillate*. This is in contrast to previous work on flow control where congestion was modeled as a function of the flow injection rates and the system was shown to converge to a steady state that maximizes an overall network utility.
