Age-Optimal Updates of Multiple Information Flows

In this paper, we study an age of information minimization problem, where multiple flows of update packets are sent over multiple servers to their destinations. Two online scheduling policies are proposed. When the packet generation and arrival times are synchronized across the flows, the proposed policies are shown to be (near) optimal for minimizing any time-dependent, symmetric, and non-decreasing penalty function of the ages of the flows over time in a stochastic ordering sense

Recent Advances in Accumulating Priority Queues

This thesis extends the theory underlying the Accumulating Priority Queue (APQ) in three directions. In the first, we present a multi-class multi-server accumulating priority queue with Poisson arrivals and heterogeneous services. The waiting time distributions for different classes have been derived. A conservation law for systems with heterogeneous servers has been studied. We also investigate an optimization problem to find the optimal level of heterogeneity in the multi-server system. Numerical investigations through simulation are carried out to validate the model. We next focus on a queueing system with Poisson arrivals, generally distributed service times and nonlinear priority accumulation functions. We start with an extension of the power-law APQ in Kleinrock and Finkelstein (1967), and use a general argument to show that there is a linear system of the form discussed in Stanford, Taylor, and Ziedins (2014) which has the same priority ordering of all customers present at any given instant in time, for any sample path. Beyond the power-law case, we subsequently characterize the class of nonlinear accumulating priority queues for which an equivalent linear APQ can be found, in the sense that the waiting time distributions for each of the classes are identical in both the linear and nonlinear systems. Many operational queuing systems must adhere to waiting time targets known as Key Performance Indicators (KPIs), particularly in health care applications. In the last aspect, we address an optimization problem to minimize the weighted average of the expected excess waiting time (WAE), so as to achieve the optimal performance of a system operating under KPIs. We then find that the Accumulating Priority queuing discipline is well suited to systems with KPIs, in that each class of customers progresses fairly towards timely access by its own waiting time limit. Due to the difficulties in minimizing the WAE, we introduce a surrogate objective function, the integrated weighted average excess (IWAE), which provides a useful proxy for WAE. Finally, we propose a rule of thumb in which patients in the various classes accumulate priority credit at a rate that is inversely proportional to their time limits

Scheduling for today’s computer systems: bridging theory and practice

Scheduling is a fundamental technique for improving performance in computer systems. From web servers to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers. In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems. The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time and provide results characterizing the distribution of response time and the fairness of scheduling policies. These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs

A Generalization of M/G/1 Priority Models via Accumulating Priority

Priority queueing systems are oftentimes set up so that arriving customers are placed into one of $N$ distinct priority classes. Moreover, to determine the order of service, each customer (upon arriving to the system) is assigned a priority level that is unique to the class to which it belongs. In static priority queues, the priority level of a class-$k$ ($k=1,2,\ldots,N$) customer is assumed to be constant with respect to time. This simple prioritization structure is easy to implement in practice, and as such, various types of static priority queues have been analyzed and subsequently applied to real-life queueing systems. However, the assumption of constant priority levels for the customers may not always be appropriate. Furthermore, static priority queues can often display poor system performance as their design does not provide systems managers the means to balance the classical trade-off inherent in all priority queues, that is: reducing wait times of higher priority customers consequently increases the wait times for those of lower priority. An alternative to static priority queues are accumulating priority queues, where the priority level of a class-$k$ customer is assumed to accumulate linearly at rate $b_k>0$ throughout the class-$k$ customer's time in the system. The main benefit of accumulating priority queues is the ability, through the specification of the accumulating priority rates $\{b_k\}_{k=1}^N$, to control the waiting times of each class. In the past, due to the complex nature of the accumulating prioritization structure, the control of waiting times in accumulating priority queues was limited --- being administered only through their first moments. Nowadays, with the advent of a very useful tool called the maximal priority process, it is possible to characterize the waiting time distributions of several types of accumulating priority queues. In this thesis, we incorporate the concept of accumulating priority to several previously analyzed static priority queues, and use the maximal priority process to establish the corresponding steady-state waiting time distributions. In addition, since static priority queues may be captured from accumulating priority queues, useful comparisons between the considered accumulating priority queues and their static priority counterparts are made throughout this thesis. Thus, in the end, this thesis results in a set of extensive analyses on these highly flexible accumulating priority queueing models that provide a better understanding of their overall behaviour, as well as exemplify their many advantages over their static priority equivalents

Ku-band signal design study

Analytical tools, methods and techniques for assessing the design and performance of the space shuttle orbiter data processing system (DPS) are provided. The computer data processing network is evaluated in the key areas of queueing behavior synchronization and network reliability. The structure of the data processing network is described as well as the system operation principles and the network configuration. The characteristics of the computer systems are indicated. System reliability measures are defined and studied. System and network invulnerability measures are computed. Communication path and network failure analysis techniques are included

Real-Time Communication in Packet-Switched Networks

Abstract The dramatically increased bandwidths and processing capabilities of future high-speed networks make possible many distributed real-time applications, such as sensor-based applications and multimedia services. Since these applications will have tra c characteristics and performance requirements that di er dramatically from those of current data-oriented applications, new communication network architectures and protocols will be required. In this paper we discuss the performance requirements and tra c characteristics of various real-time applications, survey recent developments in the areas of network architecture and protocols for supporting real-time services, and develop frameworks in which these, and future, research e orts can be considered