Packet Forwarding with a Locally Bursty Adversary

We consider packet forwarding in the adversarial queueing theory (AQT) model introduced by Borodin et al. We introduce a refinement of the AQT (?, ?)-bounded adversary, which we call a locally bursty adversary (LBA) that parameterizes injection patterns jointly by edge utilization and packet origin. For constant (O(1)) parameters, the LBA model is strictly more permissive than the (?, ?) model. For example, there are injection patterns in the LBA model with constant parameters that can only be realized as (?, ?)-bounded injection patterns with ? + ? = ?(n) (where n is the network size). We show that the LBA model (unlike the (?, ?) model) is closed under packet bundling and discretization operations. Thus, the LBA model allows one to reduce the study of general (uniform) capacity networks and inhomogenous packet sizes to unit capacity networks with homogeneous packets. On the algorithmic side, we focus on information gathering networks - i.e., networks in which all packets share a common destination, and the union of packet routes forms a tree. We show that the Odd-Even Downhill (OED) forwarding protocol described independently by Dobrev et al. and Patt-Shamir and Rosenbaum achieves buffer space usage of O(log n) against all LBAs with constant parameters. OED is a local protocol, but we show that the upper bound is tight even when compared to centralized protocols. Our lower bound for the LBA model is in contrast to the (?, ?)-model, where centralized protocols can achieve worst-case buffer space usage O(1) for ?, ? = O(1), while the O(log n) upper bound for OED is optimal only for local protocols

Robust Routing Made Easy

Designing routing schemes is a multidimensional and complex task that depends on the objective function, the computational model (centralized vs. distributed), and the amount of uncertainty (online vs. offline). Nevertheless, there are quite a few well-studied general techniques, for a large variety of network problems. In contrast, in our view, practical techniques for designing robust routing schemes are scarce; while fault-tolerance has been studied from a number of angles, existing approaches are concerned with dealing with faults after the fact by rerouting, self-healing, or similar techniques. We argue that this comes at a high burden for the designer, as in such a system any algorithm must account for the effects of faults on communication. With the goal of initiating efforts towards addressing this issue, we showcase simple and generic transformations that can be used as a blackbox to increase resilience against (independently distributed) faults. Given a network and a routing scheme, we determine a reinforced network and corresponding routing scheme that faithfully preserves the specification and behavior of the original scheme. We show that reasonably small constant overheads in terms of size of the new network compared to the old are sufficient for substantially relaxing the reliability requirements on individual components. The main message in this paper is that the task of designing a robust routing scheme can be decoupled into (i) designing a routing scheme that meets the specification in a fault-free environment, (ii) ensuring that nodes correspond to fault-containment regions, i.e., fail (approximately) independently, and (iii) applying our transformation to obtain a reinforced network and a robust routing scheme that is fault-tolerant

Problem of channel utilization and merging flows in buffered optical burst switching networks

In the paper authors verify two problems of methods of operational research in optical burst switching. The first problem is at edge node, related to the medium access delay. The second problem is at an intermediate node related to buffering delay. A correction coefficient K of transmission speed is obtained from the first analysis. It is used in to provide a full-featured link of nominal data rate. Simulations of the second problem reveal interesting results. It is not viable to prepare routing and wavelength assignment based on end-to-end delay, i.e. link's length or number of hops, as commonly used in other frameworks (OCS, Ethernet, IP, etc.) nowadays. Other parameters such as buffering probability must be taken into consideration as well. Based on the buffering probability an estimation of the number of optical/electrical converters can be made. This paper concentrates important traffic constraints of buffered optical burst switching. It allows authors to prepare optimization algorithms for regenerators placement in CAROBS networks using methods of operational research

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