Marginal Productivity Indices and Linear Programming Relaxations for Dynamic Resource Allocation in Queueing Systems

Many problems concerning resource management in modern communication systems can be simplified to queueing models under Markovian assumptions. The computation of the optimal policy is however often hindered by the curse of dimensionality especially for models that support multiple traffic or job classes. The research focus naturally turns to computationally efficient bounds and high performance heuristics. In this thesis, we apply the indexability theory to the study of admission control of a single server queue and to the buffer sharing problem for a multi-class queueing system. Our main contributions are the following: we derive the Marginal Productivity Index (MPI) and give a sufficient indexability condition for the admission control model by viewing the buffer as the resource; we construct hierarchical Linear Programming (LP) relaxations for the buffer sharing problem and propose an MPI based heuristic with its performance evaluated by discrete event simulation. In our study, the admission control model is used as the building block for the MPI heuristic deployed for the buffer sharing problem. Our condition for indexability only requires that the reward function is concavelike. We also give the explicit non-recursive expression for the MPI calculation. We compare with the previous result of the indexability condition and the MPI for the admission control model that penalizes the rejection action. The study of hierarchical LP relaxations for the buffer sharing problem is based on the exact but intractable LP formulation of the continuous-time Markov Decision Process (MDP). The number of hierarchy levels is equal to the number of job classes. The last one in the hierarchy is exact and corresponds to the exponentially sized LP formulation of the MDP. The first order relaxation is obtained by relaxing the constraint that no buffer overflow may occur in any sample path to the constraint that the average buffer utilization does not exceed the available capacity. Based on the Lagrangian decomposition of the first order relaxation, we propose a heuristic policy based on the concept of MPI. Each one of the decomposed subproblems corresponds to the admission control model we described above. The link to the decomposed sub-problems is the Lagrangian multiplier for the relaxed buffer size constraint in the first order relaxation. Our simulation study indicates the near optimal performance of the heuristic in the (randomly generated) instances investigated

Feedback Control of the National Airspace System

This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian models of the National Airspace System. It is shown that the problems of scheduling and routing aircraft flows in the National Airspace System can be posed as the control of a network of queues with load-dependent service rates. Focus can then shift to developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the National Airspace System for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions.National Science Foundation (U.S.) (Contract ECCS-0745237)United States. National Aeronautics and Space Administration (Contract NNA06CN24A

Router-based algorithms for improving internet quality of service.

We begin this thesis by generalizing some results related to a recently proposed positive system model of TCP congestion control algorithms. Then, motivated by a mean ¯eld analysis of the positive system model, a novel, stateless, queue management scheme is designed: Multi-Level Comparisons with index l (MLC(l)). In the limit, MLC(l) enforces max-min fairness in a network of TCP flows. We go further, showing that counting past drops at a congested link provides su±cient information to enforce max-min fairness among long-lived flows and to reduce the flow completion times of short-lived flows. Analytical models are presented, and the accuracy of predictions are validated by packet level ns2 simulations. We then move our attention to e±cient measurement and monitoring techniques. A small active counter architecture is presented that addresses the problem of accurate approximation of statistics counter values at very-high speeds that can be both updated and estimated on a per-packet basis. These algorithms are necessary in the design of router-based flow control algorithms since on-chip Static RAM (SRAM) currently is a scarce resource, and being economical with its usage is an important task. A highly scalable method for heavy-hitter identifcation that uses our small active counters architecture is developed based on heuristic argument. Its performance is compared to several state-of-the-art algorithms and shown to out-perform them. In the last part of the thesis we discuss the delay-utilization tradeoff in the congested Internet links. While several groups of authors have recently analyzed this tradeoff, the lack of realistic assumption in their models and the extreme complexity in estimation of model parameters, reduces their applicability at real Internet links. We propose an adaptive scheme that regulates the available queue space to keep utilization at desired, high, level. As a consequence, in large-number-of-users regimes, sacrifcing 1-2% of bandwidth can result in queueing delays that are an order of magnitude smaller than in the standard BDP-bu®ering case. We go further and introduce an optimization framework for describing the problem of interest and propose an online algorithm for solving it

Router-based algorithms for improving internet quality of service.

We begin this thesis by generalizing some results related to a recently proposed positive system model of TCP congestion control algorithms. Then, motivated by a mean ¯eld analysis of the positive system model, a novel, stateless, queue management scheme is designed: Multi-Level Comparisons with index l (MLC(l)). In the limit, MLC(l) enforces max-min fairness in a network of TCP flows. We go further, showing that counting past drops at a congested link provides su±cient information to enforce max-min fairness among long-lived flows and to reduce the flow completion times of short-lived flows. Analytical models are presented, and the accuracy of predictions are validated by packet level ns2 simulations. We then move our attention to e±cient measurement and monitoring techniques. A small active counter architecture is presented that addresses the problem of accurate approximation of statistics counter values at very-high speeds that can be both updated and estimated on a per-packet basis. These algorithms are necessary in the design of router-based flow control algorithms since on-chip Static RAM (SRAM) currently is a scarce resource, and being economical with its usage is an important task. A highly scalable method for heavy-hitter identifcation that uses our small active counters architecture is developed based on heuristic argument. Its performance is compared to several state-of-the-art algorithms and shown to out-perform them. In the last part of the thesis we discuss the delay-utilization tradeoff in the congested Internet links. While several groups of authors have recently analyzed this tradeoff, the lack of realistic assumption in their models and the extreme complexity in estimation of model parameters, reduces their applicability at real Internet links. We propose an adaptive scheme that regulates the available queue space to keep utilization at desired, high, level. As a consequence, in large-number-of-users regimes, sacrifcing 1-2% of bandwidth can result in queueing delays that are an order of magnitude smaller than in the standard BDP-bu®ering case. We go further and introduce an optimization framework for describing the problem of interest and propose an online algorithm for solving it

Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

Optimal provision of distributed reserves under dynamic energy service preferences

We propose and solve a stochastic dynamic programming (DP) problem addressing the optimal provision of regulation service reserves (RSR) by controlling dynamic demand preferences in smart buildings. A major contribution over past dynamic pricing work is that we pioneer the relaxation of static, uniformly distributed utility of demand. In this paper we model explicitly the dynamics of energy service preferences leading to a non-uniform and time varying probability distribution of demand utility. More explicitly, we model active and idle duty cycle appliances in a smart building as a closed queuing system with price-controlled arrival rates into the active appliance queue. Focusing on cooling appliances, we model the utility associated with the transition from idle to active as a non-uniform time varying function. We (i) derive an analytic characterization of the optimal policy and the differential cost function, and (ii) prove optimal policy monotonicity and value function convexity. These properties enable us to propose and implement a smart assisted value iteration (AVI) algorithm and an approximate DP (ADP) that exploits related functional approximations. Numerical results demonstrate the validity of the solution techniques and the computational advantage of the proposed ADP on realistic, large-state-space problems

Business process modeling and simulation

The textbook provides the essentials of the Business Process (BP) Modeling and Simulation (M&S) from the verbal BP description to the formulation of the mathematical scheme of the model and the simulation program. Both the analytical modeling and the simulation approaches to BP M&S are considered. Special attention is given to the theoretical and practical aspects of the BP M&S. The text covers the following topics: fundamentals of the BP M&S, conceptual modeling using IDEF3 standard, cost metrics and the activity based costing, analytical modeling (queuing networks, linear and dynamic programming), simulation with GPSS, timed Petri Nets, and Crystal Ball toolkits. Case studies include BP simulations with BPwin and GPSS. The intended readers are senior graduate students and junior postgraduate students of computer science and industrial management

Job-shop scheduling with approximate methods

Imperial Users onl