A new queueing strategy for the Adversarial Queueing Theory

In the today's Internet and TCP/IP-networks, the queueing of packets is commonly implemented using the protocol FIFO (First In First Out). Unfortunately, FIFO performs poorly in the Adversarial Queueing Theory. Other queueing strategies are researched in this model and better results are performed by alternative queueing strategies, e.g. LIS (Longest In System). This article introduces a new queueing protocol called interval-strategy that is concerned with the reduction from dynamic to static routing. We discuss the maximum system time for a packet and estimate with up-to-date results how this can be achieved. We figure out the maximum amount of time where a packet can spend in the network (i.e. worst case system time), and argue that the universal instability of the presented interval-strategy can be reached through these results. When a large group of queueing strategies is used for queueing, we prove that the interval-strategy will be universally unstable. Finally, we calculate the maximum time of the static routing to reach an universal stable and polynomial - in detail linear - bounded interval-strategy. Afterwards we close - in order to check this upper bound - with up-to-date results about the delivery times in static routing.Comment: 8 pages, 1 figure, ps-tri

Source Routing and Scheduling in Packet Networks

We study {\em routing} and {\em scheduling} in packet-switched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is {\em admissible} if no link in the network is overloaded. We present the first on-line routing algorithm that finds a set of admissible paths whenever this is feasible. Our algorithm calculates a path for each packet as soon as it is injected at its source using a simple shortest path computation. The length of a link reflects its current congestion. We also show how our algorithm can be implemented under today's Internet routing paradigms. When the paths are known (either given by the adversary or computed as above) our goal is to schedule the packets along the given paths so that the packets experience small end-to-end delays. The best previous delay bounds for deterministic and distributed scheduling protocols were exponential in the path length. In this paper we present the first deterministic and distributed scheduling protocol that guarantees a polynomial end-to-end delay for every packet. Finally, we discuss the effects of combining routing with scheduling. We first show that some unstable scheduling protocols remain unstable no matter how the paths are chosen. However, the freedom to choose paths can make a difference. For example, we show that a ring with parallel links is stable for all greedy scheduling protocols if paths are chosen intelligently, whereas this is not the case if the adversary specifies the paths.Comment: A preliminary version of this paper appeared in the Proceedings of the 42th IEEE Annual Symposium on Foundations of Computer Science, FOCS 200

Stability of Adversarial Routing with Feedback

We consider the impact of scheduling disciplines on performance of routing in the framework of adversarial queuing. We propose an adversarial model which reflects stalling of packets due to transient failures and explicitly incorporates feedback produced by a network when packets are stalled. This adversarial model provides a methodology to study stability of routing protocols when flow-control and congestion-control mechanisms affect the volume of traffic. We show that any scheduling policy that is universally stable, in the regular model of routing that additionally allows packets to have two priorities, remains stable in the proposed adversarial model

A Common Information-Based Multiple Access Protocol Achieving Full Throughput and Linear Delay

We consider a multiple access communication system where multiple users share a common collision channel. Each user observes its local traffic and the feedback from the channel. At each time instant the feedback from the channel is one of three messages: no transmission, successful transmission, collision. The objective is to design a transmission protocol that coordinates the users' transmissions and achieves high throughput and low delay. We present a decentralized Common Information-Based Multiple Access (CIMA) protocol that has the following features: (i) it achieves the full throughput region of the collision channel; (ii) it results in a delay that is linear in the number of users, and is significantly lower than that of CSMA protocols; (iii) it avoids collisions without channel sensing

Moment conditions for a sequence with negative drift to be uniformly bounded in L^r

Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant independent of n and the particular sequence {X_n}. When p=<2 there are counterexamples showing this does not hold. In general, increments bounded in L^p lead to a uniform L^r bound on X_n^+ for any r=p-1. These results are motivated by questions about stability of queueing networks.Comment: 18 page

Robust Queueing Theory

We propose an alternative approach for studying queues based on robust optimization. We model the uncertainty in the arrivals and services via polyhedral uncertainty sets, which are inspired from the limit laws of probability. Using the generalized central limit theorem, this framework allows us to model heavy-tailed behavior characterized by bursts of rapidly occurring arrivals and long service times. We take a worst-case approach and obtain closed-form upper bounds on the system time in a multi-server queue. These expressions provide qualitative insights that mirror the conclusions obtained in the probabilistic setting for light-tailed arrivals and services and generalize them to the case of heavy-tailed behavior. We also develop a calculus for analyzing a network of queues based on the following key principles: (a) the departure from a queue, (b) the superposition, and (c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. The proposed approach (a) yields results with error percentages in single digits relative to simulation, and (b) is to a large extent insensitive to the number of servers per queue, network size, degree of feedback, and traffic intensity; it is somewhat sensitive to the degree of diversity of external arrival distributions in the network

Multiplexing regulated traffic streams: design and performance

The main network solutions for supporting QoS rely on traf- fic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only ag- gregates regulated). The regulator proposed could be based on the (dual) leaky-bucket mechanism. This explains the interest in network element per- formance (loss, delay) for leaky-bucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources’ traffic, we derive approxi- mations for both small and large buffers. Importantly, for small (large) buffers the short-term (long-term) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient tech- niques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applica- ble under more general conditions, are based on optimal resource (band- width and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system

Risk-Sensitive Optimal Control of Queues

We consider the problem of designing risk-sensitive optimal control policies for scheduling packet transmissions in a stochastic wireless network. A single client is connected to an access point (AP) through a wireless channel. Packet transmission incurs a cost $C$, while packet delivery yields a reward of $R$ units. The client maintains a finite buffer of size $B$, and a penalty of $L$ units is imposed upon packet loss which occurs due to finite queueing buffer. We show that the risk-sensitive optimal control policy for such a simple set-up is of threshold type, i.e., it is optimal to carry out packet transmissions only when $Q(t)$, i.e., the queue length at time $t$ exceeds a certain threshold $\tau$. It is also shown that the value of threshold $\tau$ increases upon increasing the cost per unit packet transmission $C$. Furthermore, it is also shown that a threshold policy with threshold equal to $\tau$ is optimal for a set of problems in which cost $C$ lies within an interval $[C_l,C_u]$. Equations that need to be solved in order to obtain $C_l,C_u$ are also provided.Comment: accepted for publication in IEEE Conference on Decision and Control 201

Requirements for Secure Clock Synchronization

This paper establishes a fundamental theory of secure clock synchronization. Accurate clock synchronization is the backbone of systems managing power distribution, financial transactions, telecommunication operations, database services, etc. Some clock synchronization (time transfer) systems, such as the Global Navigation Satellite Systems (GNSS), are based on one-way communication from a master to a slave clock. Others, such as the Network Transport Protocol (NTP), and the IEEE 1588 Precision Time Protocol (PTP), involve two-way communication between the master and slave. This paper shows that all one-way time transfer protocols are vulnerable to replay attacks that can potentially compromise timing information. A set of conditions for secure two-way clock synchronization is proposed and proved to be necessary and sufficient. It is shown that IEEE 1588 PTP, although a two-way synchronization protocol, is not compliant with these conditions, and is therefore insecure. Requirements for secure IEEE 1588 PTP are proposed, and a second example protocol is offered to illustrate the range of compliant systems.Comment: 14 pages, 9 figures, accepted for publication in IEEE Journal of Selected Topics in Signal Processin

Learning and Information in Stochastic Networks and Queues

We review the role of information and learning in the stability and optimization of queueing systems. In recent years, techniques from supervised learning, bandit learning and reinforcement learning have been applied to queueing systems supported by increasing role of information in decision making. We present observations and new results that help rationalize the application of these areas to queueing systems. We prove that the MaxWeight and BackPressure policies are an application of Blackwell's Approachability Theorem. This connects queueing theoretic results with adversarial learning. We then discuss the requirements of statistical learning for service parameter estimation. As an example, we show how queue size regret can be bounded when applying a perceptron algorithm to classify service. Next, we discuss the role of state information in improved decision making. Here we contrast the roles of epistemic information (information on uncertain parameters) and aleatoric information (information on an uncertain state). Finally we review recent advances in the theory of reinforcement learning and queueing, as well as, provide discussion on current research challenges.Comment: review articl