Scheduling Quantum Teleportation with Noisy Memories

Quantum teleportation channels can overcome the effects of photonic loss, a major challenge in the implementation of a quantum network over fiber. Teleportation channels are created by distributing an entangled state between two nodes which is a probabilistic process requiring classical communication. This causes critical delays that can cause information loss as quantum data suffers from decoherence when stored in memory. In this work, we quantify the effect of decoherence on fidelity at a node in a quantum network due to the storage of qubits in noisy memory platforms. We model the memory platform as a buffer that stores incoming qubits waiting for the creation of a teleportation channel. Memory platforms are parameterized with decoherence rate and buffer size, in addition to the order in which the incoming qubits are served. We show that fidelity at a node is a linear sum of terms, exponentially decaying with time, where the decay rate depends on the decoherence rate of the memory platform. This allows us to utilize Laplace Transforms to derive efficiently computable functions of average fidelity with respect to the load, buffer size, and decoherence rate of the memory platform. We prove that serving qubits in a Last In First Out order with pushout for buffer overflow management is optimal in terms of average fidelity. Lastly, we apply this framework to model a single repeater node to calculate the average fidelity of the teleportation channels created by this repeater assuming perfect gate operations.Comment: 10 pages, 10 figure

Another look at the transient behavior of the M/G/1 workload process

We use Palm measures, along with a simple approximation technique to derive new explicit expressions for all of the transient moments of the workload process of an M=G=1 queue. These expressions can also be used to derive a closed-form expression for the nth moment of the stationary workload, which solves the well-known Takacs recursion that generates the waiting time moments of an M=G=1 queue that serves customers in a first-come-first-serve manner

Inferring Queueing Network Models from High-precision Location Tracking Data

Stochastic performance models are widely used to analyse the performance and reliability of systems that involve the flow and processing of customers. However, traditional methods of constructing a performance model are typically manual, time-consuming, intrusive and labour-intensive. The limited amount and low quality of manually-collected data often lead to an inaccurate picture of customer flows and poor estimates of model parameters. Driven by advances in wireless sensor technologies, recent real-time location systems (RTLSs) enable the automatic, continuous and unintrusive collection of high-precision location tracking data, in both indoor and outdoor environment. This high-quality data provides an ideal basis for the construction of high-fidelity performance models. This thesis presents a four-stage data processing pipeline which takes as input high-precision location tracking data and automatically constructs a queueing network performance model approximating the underlying system. The first two stages transform raw location traces into high-level “event logs” recording when and for how long a customer entity requests service from a server entity. The third stage infers the customer flow structure and extracts samples of time delays involved in the system; including service time, customer interarrival time and customer travelling time. The fourth stage parameterises the service process and customer arrival process of the final output queueing network model. To collect large-enough location traces for the purpose of inference by conducting physical experiments is expensive, labour-intensive and time-consuming. We thus developed LocTrack- JINQS, an open-source simulation library for constructing simulations with location awareness and generating synthetic location tracking data. Finally we examine the effectiveness of the data processing pipeline through four case studies based on both synthetic and real location tracking data. The results show that the methodology performs with moderate success in inferring multi-class queueing networks composed of single-server queues with FIFO, LIFO and priority-based service disciplines; it is also capable of inferring different routing policies, including simple probabilistic routing, class-based routing and shortest-queue routing

Zero-automatic queues and product form

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all stable 0-automatic queues have a product form stationary distribution and a Poisson output process. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue with positive and negative customers

Three Sojourns in Queueing Theory

In this thesis, we present three works on queues. In chapter 1, we analyze two non-work-conserving variations of the M/G/1 preemptive LIFO queue, focusing on deriving expressions for the limiting distribution of workload and related quantities. In the first model, preempted customers return to the front of the queue with a new service time, while in the second, they return with their original service time. We use queueing theory methods such as the Rate Conservation Law, PASTA, regenerative process theory and Little's Law. Our results include stability and heavy-traffic limits, as well as tail asymptotics for stationary workload. In chapter 2, we analyze a queueing model with price-sensitive customers, where the service provider aims to maximize revenue and minimize the average queue length. Customers arrive according to a Poisson process, join the queue if their willingness-to-pay exceeds the offered price, and are served in a first-in first-out manner with exponential service times. Our model is applicable to cloud computing, make-to-order manufacturing, and food delivery. We provide performance guarantees for a class of static pricing policies that can achieve a constant fraction of the optimal revenue with a small increase in expected queue length. We present results for the single-server, multi-server, and multi-class cases and provide numerical findings to demonstrate the empirical performance of our policies. In chapter 3, we analyze the Adaptive Non-deterministic Transmission Policy (ANTP), a technique addressing the Massive Access Problem (MAP) in telecommunications, which involves delaying packets at the points of origin to reduce congestion. We frame these delays as time spent at a "cafe" before proceeding to the service facility. We present sample-path results, giving conditions under which ANTP does not change the total sojourn time of packets, and results under a general stochastic framework, focusing on stability and constructing proper stationary versions of the model. We prove Harris recurrence of an underlying Markov process and find positive recurrent regeneration points under i.i.d. assumptions

Queuing with future information

We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate $\sim\log_{1/(1-p)}\frac{1}{1-\lambda}$, as $\lambda\to 1$. In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, $(1-p)/p$, as $\lambda\to1$. We further show that the finite limit of $(1-p)/p$ can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as $\mathcal{O}(\log\frac{1}{1-\lambda})$, as $\lambda\to1$. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Road-based routing in vehicular ad hoc networks

Vehicular ad hoc networks (VANETs) can provide scalable and cost-effective solutions for applications such as traffic safety, dynamic route planning, and context-aware advertisement using short-range wireless communication. To function properly, these applications require efficient routing protocols. However, existing mobile ad hoc network routing and forwarding approaches have limited performance in VANETs. This dissertation shows that routing protocols which account for VANET-specific characteristics in their designs, such as high density and constrained mobility, can provide good performance for a large spectrum of applications. This work proposes a novel class of routing protocols as well as three forwarding optimizations for VANETs. The Road-Based using Vehicular Traffic (RBVT) routing is a novel class of routing protocols for VANETs. RBVT protocols leverage real-time vehicular traffic information to create stable road-based paths consisting of successions of road intersections that have, with high probability, network connectivity among them. Evaluations of RBVT protocols working in conjunction with geographical forwarding show delivery rate increases as much as 40% and delay decreases as much as 85% when compared with existing protocols. Three optimizations are proposed to increase forwarding performance. First, one- hop geographical forwarding is improved using a distributed receiver-based election of next hops, which leads to as much as 3 times higher delivery rates in highly congested networks. Second, theoretical analysis and simulation results demonstrate that the delay in highly congested networks can be reduced by half by switching from traditional FIFO with Taildrop queuing to LIFO with Frontdrop queuing. Third, nodes can determine suitable times to transmit data across RBVT paths or proactively replace routes before they break using analytical models that accurately predict the expected road-based path durations in VANETs

Exact Simulation Techniques in Applied Probability and Stochastic Optimization

This dissertation contains two parts. The first part introduces the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues in which the arrival process is a general renewal process and the service times are independent and identically distributed (iid); the first-in-first-out FIFO GI/GI/c queue with 2 <= c < 1. Two main simulation algorithms are given in this context, where both of them are built on the classical dominated coupling from the past (DCFTP) protocol. In particular, the first algorithm uses a coupled multi-server vacation system as the upper bound process and it manages to simulate the vacation system backward in time from stationarity at time zero. The second algorithm utilizes the DCFTP protocol as well as the Random Assignment (RA) service discipline. Both algorithms have finite expected termination time with mild moment assumptions on the interarrival time and service time distributions. Our methods are also extended to produce exact simulation algorithms for Fork-Join queues and infinite server systems. The second part presents general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. The estimators possess finite work-normalized variance under mild regularity conditions. We apply the estimators to various applications including unbiased steady-state simulation of regenerative processes, unbiased optimization in Sample Average Approximations and distribution quantile estimation

Feedback-control & queueing theory-based resource management for streaming applications

Recent advances in sensor technologies and instrumentation have led to an extraordinary growth of data sources and streaming applications. A wide variety of devices, from smart phones to dedicated sensors, have the capability of collecting and streaming large amounts of data at unprecedented rates. A number of distinct streaming data models have been proposed. Typical applications for this include smart cites & built environments for instance, where sensor-based infrastructures continue to increase in scale and variety. Understanding how such streaming content can be processed within some time threshold remains a non-trivial and important research topic. We investigate how a cloud-based computational infrastructure can autonomically respond to such streaming content, offering Quality of Service guarantees. We propose an autonomic controller (based on feedback control and queueing theory) to elastically provision virtual machines to meet performance targets associated with a particular data stream. Evaluation is carried out using a federated Cloud-based infrastructure (implemented using CometCloud) – where the allocation of new resources can be based on: (i) differences between sites, i.e. types of resources supported (e.g. GPU vs. CPU only), (ii) cost of execution; (iii) failure rate and likely resilience, etc. In particular, we demonstrate how Little’s Law –a widely used result in queuing theory– can be adapted to support dynamic control in the context of such resource provisioning