A stochastic analysis of resource sharing with logarithmic weights

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$, the logarithm of its current load. A detailed fluid scaling analysis of such a network with two nodes is presented. It is shown that the interaction of several time scales plays an important role in the evolution of such a system, in particular its coordinates may live on very different time and space scales. As a consequence, the associated stochastic processes turn out to have unusual scaling behaviors. A heavy traffic limit theorem for the invariant distribution is also proved. Finally, we present a generalization to the resource sharing algorithm for which the $\log$ function is replaced by an increasing function. Possible generalizations of these results with $J>2$ nodes or with the function $\log$ replaced by another slowly increasing function are discussed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1057 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sojourn times in non-homogeneous QBD processes with processor sharing

We study sojourn times of customers in a processor sharing model with a service rate that varies over time, depending on the number of customers and on the state of a random environment. An explicit expression is derived for the Laplace-Stieltjes transform of the sojourn time conditional on the state upon arrival and the amount of work brought into the system. Particular attention is given to the conditional mean sojourn time of a customer as a function of his required amount of work, and we establish the existence of an asymptote as the amount of work tends to infinity. The method of random time change is then extended to include the possibility of a varying service rate. By means of this method, we explain the well-established proportionality between the conditional mean sojourn time and required amount of work in processor sharing queues without random environment. Based on numerical experiments, we propose an approximation for the conditional mean sojourn time. Although first presented for exponentially distributed service requirements, the analysis is shown to extend to phase-type services. The service discipline of discriminatory processor sharing is also shown to fall within the framework

A versatile model for TCP bandwidth sharing in networks with heterogeneous users.

Enabled by the emergence of various access technologies (such as ADSL and wireless LAN), the number of users with high-speed access to the Internet is growing rapidly, and their expectation with respect to the quality-of-service of the applications has been increasing accordingly. With TCP being the ubiquitous underlying end-to-end control, this motivates the interest in easy-to-evaluate, yet accurate, performance models for a TCP-based network shared by multiple classes of users. Building on the vast body of existing models, we develop a novel versatile model that explicitly captures user heterogeneity, and takes into consideration dynamics at both the packet level and the flow level. It is described how the resulting multiple time-scale model can be numerically evaluated. Validation is done by using NS2 simulations as a benchmark. In extensive numerical experiments, we study the impact of heterogeneity in the round-trip times on user-level characteristics such as throughputs and flow transmission times, thus quantifying the resulting bias. We also investigate to what extent this bias is affected by the networks' `packet-level parameters', such as buffer sizes. We conclude by extending the single-link model in a straightforward way to a general network setting. Also in this network setting the impact of heterogeneity in round-trip times is numerically assesse

Evolution of Cooperative Thought, Theory, and Purpose

The evolution of agricultural cooperative thought, theory, and purpose in the United States is reviewed from the standpoint of the reemergence of interest in how cooperatives can provide some of the security and benefits that might be lost with gradual phasing out of federal government farm support programs. By accomplishing group action for self-help, the early development of cooperatives drew considerable attention from economists, social theorists, and politicians. Alternative schools of cooperative thought developed, but most proponents of cooperatives regarded them as having enormous potential to provide a public service role in building a more economically stable and democratic society This paper also surveys how cooperative theory was developed more rigorously in the post-WWII period. It has provided better analytical tools for understanding how and why cooperatives have changed in response to technological and economic developments, as well as to social trends, like individualism. Given the new perspectives on cooperative theory and the scope of changes in how cooperatives operate and are structured, cooperatives have even greater potential for coordinating self-help actions, but this potential needs the support of cooperative education services.Agribusiness,

Resource Management and Pricing in Networks

Resource management is important for network design and deployment. Resource management and allocation have been studied under a wide variety of scenarios --- routing in wired networks, scheduling in cellular networks, multiplexing, switching, and channel access in opportunistic networks are but a few examples. In this dissertation, we revisit resource management in the context of routing and scheduling in multihop wireless networks and pricing in single resource systems. The first issue addressed is of delays in multihop wireless networks. The resource under contention is capacity which is allocated by a joint routing and scheduling algorithm. Delay in wireless networks is a key issue gaining interest with the growth of interactive applications and proliferation of wireless networks. We start with an investigation of the back-pressure algorithm (BPA), an algorithm that activates the schedule with the largest sum of link weights in a timeslot. Though the BPA is throughput-optimal, it has poor end-to-end delays. Our investigation identifies poor routing decisions at low loads as one cause for it. We improve the delay performance of max-weight algorithms by proposing a general framework for routing and scheduling algorithms that allow directing packets towards the sink node dynamically. For a stationary environment, we explicitly formulate delay minimization as a static problem while maintaining stability. We see similar improved delay performance with the advantage of reduced per time-slot complexity. Next, the issue of pricing for flow based models is studied. The increasing popularity of cloud computing and the ease of commerce over the Internet is making pricing a key issue requiring greater attention. Although pricing has been extensively studied in the context of maximizing revenue and fairness, we take a different perspective and investigate pricing with predictability. Prior work has studied resource allocations that link insensitivity and predictability. In this dissertation, we present a detailed analysis of pricing under insensitive allocations. We study three common pricing models --- fixed rate pricing, Vickrey-Clarke-Groves (VCG) auctions, and congestion-based pricing, and provide the expected operator revenue and user payments under them. A pre-payment scheme is also proposed where users pay on arrival a fee for their estimated service costs. Such a mechanism is shown to have lower variability in payments under fixed rate pricing and VCG auctions while generating the same long-term revenue as in a post-payment scheme, where users pay the exact charge accrued during their sojourn. Our formulation and techniques further the understanding of pricing mechanisms and decision-making for the operator