Increase Multiplicative Decrease Research Articles

Price-based protocols for fair resource allocation

We analyze several distributed, continuous time protocols for a fair allocation of bandwidths to flows in a network (or resources to agents). Our protocols converge to an allocation that is a logarithmic approximation, simultaneously, to all canonical social welfare functions (i.e., functions that are symmetric, concave, and nondecreasing). These protocols can be started in an arbitrary state. Although a similar protocol was known before, it only applied to the simple bandwidth allocation problem, and its stability and convergence time were not understood. In contrast, our protocols also apply to the more general case of Leontief utilities, where each user may place a different requirement on each resource. Furthermore, we prove that our protocols converge in polynomial time. The best convergence time we prove is O ( n log nc MAX a MAX / c MIN a MIN ), where n is the number of agents in the network, c MAX and c MIN are the maximum and minimum capacity of the links, and a max , a min are respectively the largest and smallest Leontief coefficients. This time is achieved by a simple Multiplicative Increase, Multiplicative Decrease (MIMD) protocol that had not been studied before in this setting. We also identify combinatorial properties of these protocols that may be useful in proving stronger convergence bounds. The final allocations by our protocols are supported by usage-sensitive dual prices that are fair in the sense that they shield light users of a resource from the impact of heavy users. Thus, our protocols can also be thought of as efficient distributed schemes for computing fair prices.

Orchestrating parallel TCP connections: Cyclic and probabilistic polling policies

The standard Transmission Control Protocol (TCP) is based on an additive rate increase in the absence of congestion, and on multiplicative decrease triggered by congestion signals. However, it does not scale well as the distances, or as the speed of the network, increase. Thus, we study some of the solutions that have been proposed to encounter this problem. These solutions include (i) splitting the transmission from a source to its destination into several parallel connections, and (ii) using Scalable TCP, which is a more aggressive version of TCP. The connection whose rate decreases when a signal arrives is chosen either at random or according to a round robin policy. Our analysis concentrates on a centrally controlled TCP system having N connections. We consider both Additive Increase Multiplicative Decrease (AIMD) and Multiplicative Increase Multiplicative Decrease (MIMD) control mechanisms. The Laplace–Stieltjes Transforms (LST) of the transmission rate of each connection at a polling instant, as well as at an arbitrary moment, are derived. Explicit results are obtained for the mean transmission rate and (in contrast to most polling models) for its second moment. For the AIMD procedure under the cyclic visit policy we show that, for both dynamic (Hamiltonian-type) and static visit orders in each cycle, the connections should be visited following a simple index rule in order to achieve maximum throughput. For the probabilistic visit policy we obtain the set of optimal probabilities that maximizes mean throughput. The analysis of the probabilistic MIMD models uses transformations yielding a system’s law of motion equivalent to that of an M/G/1 queue with batch service. The MIMD control mechanism with probabilistic strategy is further analyzed for the case where the transmission rate is bounded above.

Analysis of scalable TCP congestion control algorithm

In recent years, several more aggressive versions of TCP have been proposed which leave the Additive Increase Multiplicative Decrease (AIMD) paradigm. The motivation is to adapt TCP to networks with very large bandwidth delay products. In this paper, we study the scalable TCP (STCP) which is designed to be a Multiplicative Increase Multiplicative Decrease (MIMD) protocol. We analyze how it shares a bottleneck link with other CBR flows. We identify conditions under which the time varying queueing delay transforms the whole multiplicative increase dynamics of the window size into an additive increase dynamics, which implies that window evolution of STCP behaves as an AIMD protocol. In addition, we analyze and derive expressions for the case of very small buffer. Finally, we validate our results using ns-2 simulations.

Convergence of trajectories and optimal buffer sizing for MIMD congestion control

We study the interaction between the MIMD (Multiplicative Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We study conditions under which the system trajectories converge to limiting cycles with a single jump. Following that, we consider the problem of the optimal buffer sizing in the framework of multi-criteria optimization in which the Lagrange function corresponds to a linear combination of the average throughput and the average delay in the queue. As case studies, we consider the Slow Start phase of TCP New Reno and Scalable TCP for high speed networks.

Analysis of MIMD congestion control algorithm for high speed networks

Proposals to improve the performance of TCP in high speed networks have been recently put forward. Examples of such proposals include High Speed TCP, Scalable TCP, and FAST. In contrast to the additive increase multiplicative decrease algorithm used in the standard TCP, Scalable TCP uses a multiplicative increase multiplicative decrease (MIMD) algorithm for the window size evolution. In this paper, we present a mathematical analysis of the MIMD congestion control algorithm in the presence of random losses. Random losses are typical to wireless networks but can also be used to model losses in wireline networks with a high bandwidth-delay product. Our approach is based on showing that the logarithm of the window size evolution has the same behaviour as the workload process in a standard G/G/1 queue. The Laplace–Stieltjes transform of the equivalent queue is then shown to directly provide the throughput of the congestion control algorithm and the higher moments of the window size. Using ns-2 simulations, we validate our findings using Scalable TCP.

A Randomized Online Algorithm for Bandwidth Utilization

Protocols for data transmission over a TCP-like computer network should not only lead to efficient network utilization but also be fair to different users. Current networks accomplish these goals by some form of end-to-end congestion control. However, existing protocols assume somewhat altruistic behavior from hosts, and Karp et al. [7] have initiated a study of whether or not the host's optimum strategy is altruistic. We carry this exploration further by developing an efficient randomized algorithm for bandwidth utilization in their model. The competitive ratio of this algorithm is optimal up to a constant factor. Karp et al. had earlier studied the deterministic case and left open the randomized case.What may be of some interest is that our algorithm is essentially the classical MIMD (multiplicative increase, multiplicative decrease) strategy, which is very aggressive and non-altruistic.