System Stability Under Adversarial Injection of Dependent Tasks

Technological changes (NFV, Osmotic Computing, Cyber-physical Systems) are making very important devising techniques to efficiently run a flow of jobs formed by dependent tasks in a set of servers. These problem can be seen as generalizations of the dynamic job-shop scheduling problem, with very rich dependency patterns and arrival assumptions. In this work, we consider a computational model of a distributed system formed by a set of servers in which jobs, that are continuously arriving, have to be executed. Every job is formed by a set of dependent tasks (i. e., each task may have to wait for others to be completed before it can be started), each of which has to be executed in one of the servers. The arrival of jobs and their properties is assumed to be controlled by a bounded adversary, whose only restriction is that it cannot overload any server. This model is a non-trivial generalization of the Adversarial Queuing Theory model of Borodin et al., and, like that model, focuses on the stability of the system: whether the number of jobs pending to be completed is bounded at all times. We show multiple results of stability and instability for this adversarial model under different combinations of the scheduling policy used at the servers, the arrival rate, and the dependence between tasks in the jobs

Performance of Scheduling Policies in Adversarial Networks with Non-synchronized Clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model (Blesa et al. in MFCS, Lecture Notes in Computer Science, vol. 3618, pp. 144–155, 2005) by considering the possibility that the router clocks in the network are not synchronized. We name the new model Non Synchronized CAQT (NSCAQT). Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. In a first approach we consider the case in which although not synchronized, all clocks run at the same speed, maintaining constant differences. In this case we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, we study the case in which clock differences can vary over time, but the maximum difference is bounded. In this model we show the universal stability of two families of policies related to SIS and LIS respectively (the priority of a packet in these policies depends on the arrival time and a function of the path traversed). The bounds we obtain in this case depend on the maximum difference between clocks. This is a necessary requirement, since we also show that LIS is not universally stable in systems without bounded clock difference. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds we prove do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these policies in a network with stochastic injection of packets

The robustness of stability under link and node failures

AbstractIn the area of communication systems, stability refers to the property of keeping the amount of traffic in the system always bounded over time. Different communication system models have been proposed in order to capture the unpredictable behavior of some users and applications. Among those proposed models the adversarial queueing theory (aqt) model turned out to be the most adequate to analyze an unpredictable network. Until now, most of the research done in this field did not consider the possibility of the adversary producing failures on the network structure. The adversarial models proposed in this work incorporate the possibility of dealing with node and link failures provoked by the adversary. Such failures produce temporal disruptions of the connectivity of the system and increase the collisions of packets in the intermediate hosts of the network, and thus the average traffic load. Under such a scenario, the network is required to be equipped with some mechanism for dealing with those collisions.In addition to proposing adversarial models for faulty systems we study the relation between the robustness of the stability of the system and the management of the queues affected by the failures. When the adversary produces link or node failures the queues associated to the corresponding links can be affected in many different ways depending on whether they can receive or serve packets, or rather that they cannot. In most of the cases, protocols and networks containing very simple topologies, which were known to be universally stable in the aqt model, turn out to be unstable under some of the newly proposed adversarial models. This shows that universal stability of networks is not a robust property in the presence of failures

Generalization of the RIN Result to Heterogeneous Networks of Aggregate Schedulers and Leaky Bucket Constrained Flows

We consider networks of FIFO aggregate schedulers. Quite surprisingly, the natural condition (node utilization inferior to one) in general is not sufficient in these networks to ensure stability (boundedness of delay and backlog at each node). Deriving good sufficient conditions for stability and delay bounds for these networks is of fundamental importance if we want to offer quality of service guarantees in such networks as DiffServ networks, high speed switches and network-on-chips. The main existing sufficient conditions for stability in these networks are the “DiffServ bound” [1] and the Route Interference Number (RIN) result [2]. We use an algebraic approach. First, we develop a model of the network as a dynamical system, and we show how the problem can be reduced to properties of the state transition function. Second, we obtain new sufficient conditions for stability valid without any of the restrictions of the “RIN result”. We show that in practical cases, when flows are leaky bucket constrained, the new sufficient conditions perform better than existing results. We also prove that the “RIN result” can be derived as a special case from our approach. We finally derive an expression for a bound to delay at all nodes

Generalization of the RIN result to heterogeneous networks of aggregate schedulers and leaky bucket constrained flows

We consider networks of FIFO aggregate schedulers. Quite surprisingly, the natural condition (node utilization inferior to one) in general is not sufficient in these networks to ensure stability (boundedness of delay and backlog at each node). Deriving good sufficient conditions for stability and delay bounds for these networks is of fundamental importance if we want to offer quality of service guarantees in such networks as Diffserv networks, high speed switches and network-on-chips. The main existing sufficient conditions for stability in these networks are the "DiffServ bound" [1] and the Route Interference Number (RIN) result [2]. We use an algebraic approach. First, we develop a model of the network as a dynamical system, and we show how the problem can be reduced to properties of the state transition function. Second, we obtain new sufficient conditions for stability valid without any of the restrictions of the "RIN result". We show that in practical cases, when flows are leaky bucket constrained, the new sufficient conditions perform better than existing results. We also prove that the "RIN result" can be derived as a special case from our approach. We finally derive an expression for a bound to delay at all nodes

A review on DISC 2005, the 19th International Symposium on Distributed Computing

DISC is an international symposium on the theory, design, analysis, implementation and application of distributed systems and networks. The well-known International Symposium on Distributed Computing is organized annually in cooperation with the European Association for Theoretical Computer Science (EATCS). This is a review on the 19th International Symposium on Distributed Computing, which took place in Kraków, Poland, on September 26--29, 2005. The proceedings of DISC 2005 are published by Springer, as volume 3724 of the Lecture Notes in Computer Science (LNCS) series. The conference website can be found at www.mimuw.edu.pl/~disc2005.Postprint (published version

Control of transport dynamics in overlay networks

Transport control is an important factor in the performance of Internet protocols, particularly in the next generation network applications involving computational steering, interactive visualization, instrument control, and transfer of large data sets. The widely deployed Transport Control Protocol is inadequate for these tasks due to its performance drawbacks. The purpose of this dissertation is to conduct a rigorous analytical study on the design and performance of transport protocols, and systematically develop a new class of protocols to overcome the limitations of current methods. Various sources of randomness exist in network performance measurements due to the stochastic nature of network traffic. We propose a new class of transport protocols that explicitly accounts for the randomness based on dynamic stochastic approximation methods. These protocols use congestion window and idle time to dynamically control the source rate to achieve transport objectives. We conduct statistical analyses to determine the main effects of these two control parameters and their interaction effects. The application of stochastic approximation methods enables us to show the analytical stability of the transport protocols and avoid pre-selecting the flow and congestion control parameters. These new protocols are successfully applied to transport control for both goodput stabilization and maximization. The experimental results show the superior performance compared to current methods particularly for Internet applications. To effectively deploy these protocols over the Internet, we develop an overlay network, which resides at the application level to provide data transmission service using User Datagram Protocol. The overlay network, together with the new protocols based on User Datagram Protocol, provides an effective environment for implementing transport control using application-level modules. We also study problems in overlay networks such as path bandwidth estimation and multiple quickest path computation. In wireless networks, most packet losses are caused by physical signal losses and do not necessarily indicate network congestion. Furthermore, the physical link connectivity in ad-hoc networks deployed in unstructured areas is unpredictable. We develop the Connectivity-Through-Time protocols that exploit the node movements to deliver data under dynamic connectivity. We integrate this protocol into overlay networks and present experimental results using network to support a team of mobile robots

An Introduction to Computer Networks

An open textbook for undergraduate and graduate courses on computer networks