Analysis of Multiple Flows using Different High Speed TCP protocols on a General Network

We develop analytical tools for performance analysis of multiple TCP flows (which could be using TCP CUBIC, TCP Compound, TCP New Reno) passing through a multi-hop network. We first compute average window size for a single TCP connection (using CUBIC or Compound TCP) under random losses. We then consider two techniques to compute steady state throughput for different TCP flows in a multi-hop network. In the first technique, we approximate the queues as M/G/1 queues. In the second technique, we use an optimization program whose solution approximates the steady state throughput of the different flows. Our results match well with ns2 simulations.Comment: Submitted to Performance Evaluatio

Asymptotic Approximations for TCP Compound

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming the window sizes are continuous, i.e., a fluid behaviour is assumed. We validate this model theoretically. We show that under the deterministic loss model, the TCP window evolution for TCP Compound is periodic and is independent of the initial window size. We then consider the case when packets are lost randomly and independently of each other. We discuss Markov chain models to analyze performance of TCP in this scenario. We use insights from the deterministic loss model to get an appropriate scaling for the window size process and show that these scaled processes, indexed by p, the packet error rate, converge to a limit Markov chain process as p goes to 0. We show the existence and uniqueness of the stationary distribution for this limit process. Using the stationary distribution for the limit process, we obtain approximations for throughput, under random losses, for TCP Compound when packet error rates are small. We compare our results with ns2 simulations which show a good match.Comment: Longer version for NCC 201

A stochastic game framework for analyzing computational investment strategies in distributed computing

We study a stochastic game framework with dynamic set of players, for modeling and analyzing their computational investment strategies in distributed computing. Players obtain a certain reward for solving the problem or for providing their computational resources, while incur a certain cost based on the invested time and computational power. We first study a scenario where the reward is offered for solving the problem, such as in blockchain mining. We show that, in Markov perfect equilibrium, players with cost parameters exceeding a certain threshold, do not invest; while those with cost parameters less than this threshold, invest maximal power. Here, players need not know the system state. We then consider a scenario where the reward is offered for contributing to the computational power of a common central entity, such as in volunteer computing. Here, in Markov perfect equilibrium, only players with cost parameters in a relatively low range in a given state, invest. For the case where players are homogeneous, they invest proportionally to the `reward to cost' ratio. For both the scenarios, we study the effects of players' arrival and departure rates on their utilities using simulations and provide additional insights

Theoretical Analysis of High-speed Multiple TCP Connections through Multiple Routers

Abstract-We study a system of multiple routers traversed by multiple TCP connections using TCP New Reno, CUBIC and Compound. More than one router may be congested. To analyze this system we will use earlier theoretical models of TCP New Reno and CUBIC but develop a new model of TCP Compound experiencing random packet losses and queuing delays. We model the router queues as M/GI/1 queues with arrival rates controlled by TCP window flow control. We also look at an alternate approach assuming proportional fairness of TCP to find the throughputs of the multiple TCP connections. These approximations are validated through comparison with ns-2 simulations

Analytical Model for Congestion Control and Throughput with TCP CUBIC Connections

Abstract-We develop a Markov model for a TCP CUBIC connection. Next we use it to obtain approximate expressions for throughput when there may be queuing in the network. Finally we provide the throughputs different TCP CUBIC and TCP NewReno connections obtain while sharing a channel when they may have different round trip delays and packet loss probabilities. Index Terms-TCP CUBIC, Internet window flow control, High speed Internet

An asymptotic approximation for TCP CUBIC

In this paper, we derive an expression for computing the average window size of a single TCP CUBIC connection under random losses. For this we consider a throughput expression for TCP CUBIC computed earlier under deterministic periodic packet losses. We validate this expression theoretically. We then use insights from the deterministic loss-based model to scale appropriately a sequence of Markov chains with random losses indexed by the probability of loss p. We show that this sequence converges to a limiting Markov chain as p tends to 0. The stationary distribution of the limiting Markov chain is then used to derive the average window size for small packet error rates. We then use a simple approximation to extend our current results with negligible queuing to a setup with multiple connections and non-negligible queuing. We validate our model and approximations via simulations

Analytical model for congestion control and throughput with TCP CUBIC connections

We develop a Markov model for a TCP CUBIC connection. Next we use it to obtain approximate expressions for throughput when there may be queuing in the network. Finally we provide the throughputs different TCP CUBIC and TCP NewReno connections obtain while sharing a channel when they may have different round trip delays and packet loss probabilities

An asymptotic approximation for TCP compound

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming that the window sizes are continuous, i.e., a fluid behavior is assumed. We validate this model theoretically. We show that under the deterministic loss model, the TCP window evolution for TCP Compound is asymptotically periodic and is independent of the initial window size. We then consider the case when packets are lost randomly and independently of each other. We discuss Markov chain models to analyze performance of TCP in this scenario. We use insights from the deterministic loss model to get an appropriate scaling for the window size process and show that these scaled processes, indexed by p, the packet error rate, converge to a limit Markov chain process as p goes to 0. We show the existence and uniqueness of the stationary distribution for this limit process. Using the stationary distribution for the limit process, we obtain approximations for throughput, under random losses, for TCP Compound when packet error rates are small. We compare our results with ns2 simulations which show a good match and a better approximation than the fluid model at low p

Theoretical Analysis of High-speed Multiple TCP Connections through Multiple Routers

We study a system of multiple routers traversed by multiple TCP connections using TCP New Reno, CUBIC and Compound. More than one router may be congested. To analyze this system we will use earlier theoretical models of TCP New Reno and CUBIC but develop a new model of TCP Compound experiencing random packet losses and queuing delays. We model the router queues as M/GI/1 queues with arrival rates controlled by TCP window flow control. We also look at an alternate approach assuming proportional fairness of TCP to find the throughputs of the multiple TCP connections. These approximations are validated through comparison with ns-2 simulations