The use of relative priorities in optimizing the performance of a queueing system

Relative priorities in an n-class queueing system can reduce server and customer costs. This property is demonstrated in a single server Markovian model where the goal is to minimize a non-linear cost function of class expected waiting times. Special attention is given to minimizing server’s costs when the expected waiting time of each class is restricted

Concave Switching in Single and Multihop Networks

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.Comment: 28 page

Differentiable Programming & Network Calculus: Configuration Synthesis under Delay Constraints

With the advent of standards for deterministic network behavior, synthesizing network designs under delay constraints becomes the natural next task to tackle. Network Calculus (NC) has become a key method for validating industrial networks, as it computes formally verified end-to-end delay bounds. However, analyses from the NC framework have been designed to bound the delay of one flow at a time. Attempts to use classical analyses to derive a network configuration have shown that this approach is poorly suited to practical use cases. Consider finding a delay-optimal routing configuration: one model had to be created for each routing alternative, then each flow delay had to be bounded, and then the bounds had to be compared to the given constraints. To overcome this three-step process, we introduce Differential Network Calculus. We extend NC to allow the differentiation of delay bounds w.r.t. to a wide range of network parameters - such as flow paths or priority. This opens up NC to a class of efficient nonlinear optimization techniques that exploit the gradient of the delay bound. Our numerical evaluation on the routing and priority assignment problem shows that our novel method can synthesize flow paths and priorities in a matter of seconds, outperforming existing methods by several orders of magnitude

Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work

Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Patterns for Providing Real-Time Guarantees in DOC Middleware - Doctoral Dissertation, May 2002

The advent of open and widely adopted standards such as Common Object Request Broker Architecture (CORBA) [47] has simplified and standardized the development of distributed applications. For applications with real-time constraints, including avionics, manufacturing, and defense systems, these standards are evolving to include Quality-of-Service (QoS) specifications. Operating systems such as Real-time Linux [60] have responded with interfaces and algorithms to guarantee real-time response; similarly, languages such as Real-time Java [59] include mechanisms for specifying real-time properties for threads. However, the middleware upon which large distributed applications are based has not yet addressed end-to-end guarantees of QoS specifications. Unless this challenge can be met, developers must resort to ad hoc solutions that may not scale or migrate well among different platforms. This thesis provides two contributions to the study of real-time Distributed Object Computing (DOC) middleware. First, it identifies potential bottlenecks and problems with respect to guaranteeing real-time performance in contemporary middleware. Experimental results illustrate how these problems lead to incorrect real-time behavior in contemporary middleware platforms. Second, this thesis presents designs and techniques for providing real-time QoS guarantees in DOC middleware in the context of TAO [6], an open-source and widely adopted implementation of real-time CORBA. Architectural solutions presented here are coupled with empirical evaluations of end-to-end real-time behavior. Analysis of the problems, forces, solutions, and consequences are presented in terms of patterns and frame-works, so that solutions obtained for TAO can be appropriately applied to other real-time systems

Queue normalization methods in systems GI/GI/1/m with infinite variance of service time

Queuing systems with an infinite variance of service time are considered. The average waiting time in such systems is equal to infinity at a stationary regime. We analyze the efficiency of introducing of absolute priorities with infinite number of priority classes determined by the special axis marking on intervals for possible values of service time. It is stated that queues in systems become normalized, i.e. the average queue length become finite, when using regular marking. Furthermore, request loss probabilities radically decrease when buffer size is finite. More efficient marking - exponential marking - is proposed for practical purposes in networks with fractal traffic. The optimization problems of regular and exponential markings are solved