Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

Efficient priority rules

We study the assignment of indivisible objects with quotas (houses, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and renegotiation-proofness. Such a rule respects an acyclical priority structure and the allocations can be determined using the deferred acceptance algorithm.

Admission Control for TCP Flows Using Packet Classes and Edge-to-edge Measurements of Aggregates

TCP flows from applications such as the web or ftp are well supported by a Guaranteed Minimum Throughput Service (GMTS), which provides a minimum network throughput to the flow and, if possible, an extra throughput. We propose a scheme for a GMTS using Admission Control (AC) that is able to provide different minimum throughput to different users and that is suitable for "standard" TCP flows. Moreover, we consider a multidomain scenario where the scheme is used in one of the domains, and we propose some mechanisms for the interconnection with neighbor domains. The whole scheme uses a small set of packet classes in a core-stateless network where each class has a different discarding priority in queues assigned to it. The AC method involves only edge nodes and uses a special probing packet flow (marked as the highest discarding priority class) that is sent continuously from ingress to egress through a path. The available throughput in the path is obtained at the egress using measurements of flow aggregates, and then it is sent back to the ingress. At the ingress each flow is detected using an implicit way and then it is admission controlled. If it is accepted, it receives the GMTS and its packets are marked as the lowest discarding priority classes; otherwise, it receives a best-effort service. The scheme is evaluated through simulation in a simple "bottleneck" topology using different traffic loads consisting of "standard" TCP flows that carry files of varying sizes

Locating emergency services with priority rules: The priority queuing covering location problem

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is thatdemand is known and fixed. Most often, this is not the case when managers take somestrategic decisions such as locating facilities and assigning demand points to thosefacilities. In this paper we consider demand as stochastic and we model each of thefacilities as an independent queue. Stochastic models of manufacturing systems anddeterministic location models are put together in order to obtain a formula for thebacklogging probability at a potential facility location.Several solution techniques have been proposed to solve the CFLP. One of the mostrecently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, isimplemented in order to solve the model formulated. We present some computationalexperiments in order to evaluate the heuristics performance and to illustrate the use ofthis new formulation for the CFLP. The paper finishes with a simple simulationexercise.

Locating emergency services with different priorities: The priority queuing covering location problem

Previous covering models for emergency service consider all the calls to be of the sameimportance and impose the same waiting time constraints independently of the service's priority.This type of constraint is clearly inappropriate in many contexts. For example, in urban medicalemergency services, calls that involve danger to human life deserve higher priority over calls formore routine incidents. A realistic model in such a context should allow prioritizing the calls forservice.In this paper a covering model which considers different priority levels is formulated andsolved. The model heritages its formulation from previous research on Maximum CoverageModels and incorporates results from Queuing Theory, in particular Priority Queuing. Theadditional complexity incorporated in the model justifies the use of a heuristic procedure.

Minimum price variations, time priority and quotes dynamics

We analyze the impact of a minimum price variation (tick) and timepriority on the dynamics of quotes and the trading costs when competitionfor the order flow is dynamic. We find that convergence to competitiveoutcomes can take time and that the speed of convergence is influencedby the tick size, the priority rule and the characteristics of the orderarrival process. We show also that a zero minimum price variation is neveroptimal when competition for the order flow is dynamic. We compare thetrading outcomes with and without time priority. Time priority is shownto guarantee that uncompetitive spreads cannot be sustained over time.However it can sometimes result in higher trading costs. Empiricalimplications are proposed. In particular, we relate the size of thetrading costs to the frequency of new offers and the dynamics of theinside spread to the state of the book.

Location models for airline hubs behaving as M/D/c queues

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.

Headspace needle-trap analysis of priority volatile organic compounds from aqueous samples: application to the analysis of natural and waste waters

Combining headspace (HS) sampling with a needle-trap device (NTD) to determine priority volatile organic compounds (VOCs) in water samples results in improved sensitivity and efficiency when compared to conventional static HS sampling. A 22 gauge stainless steel, 51-mm needle packed with Tenax TA and Carboxen 1000 particles is used as the NTD. Three different HS-NTD sampling methodologies are evaluated and all give limits of detection for the target VOCs in the ng L−1 range. Active (purge-and-trap) HS-NTD sampling is found to give the best sensitivity but requires exhaustive control of the sampling conditions. The use of the NTD to collect the headspace gas sample results in a combined adsorption/desorption mechanism. The testing of different temperatures for the HS thermostating reveals a greater desorption effect when the sample is allowed to diffuse, whether passively or actively, through the sorbent particles. The limits of detection obtained in the simplest sampling methodology, static HS-NTD (5 mL aqueous sample in 20 mL HS vials, thermostating at 50 °C for 30 min with agitation), are sufficiently low as to permit its application to the analysis of 18 priority VOCs in natural and waste waters. In all cases compounds were detected below regulated levels

Fair and efficient student placement with couples

We study situations of allocating positions or jobs to students or workers based on priorities. An example is the assignment of medical students to hospital residencies on the basis of one or several entrance exams. For markets without couples, e.g., for ``undergraduate student placement,'' acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples, which introduces complementarities into the students' preferences, acyclicity is still necessary, but not sufficient (Theorem 4.1). A second necessary condition (Theorem 4.2) is ``priority-togetherness'' of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize pt-acyclicity (Lemma 5.1) and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism (Theorem 5.1). If in addition to pt-acyclicity we require ``reallocation-'' and ``vacancy-fairness'' for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism (Theorem 5.2). Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism (Examples 5.4, 5.5, and 5.6). We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation (Theorem 5.3).

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools.

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks.

Aplicaciones Single Program Multiple Data (SPMD) en ambientes distribuidos

Un reto al ejecutar las aplicaciones en un cluster es lograr mejorar las prestaciones utilizando los recursos de manera eficiente, y este reto es mayor al utilizar un ambiente distribuido. Teniendo en cuenta este reto, se proponen un conjunto de reglas para realizar el cómputo en cada uno de los nodos, basado en el análisis de cómputo y comunicaciones de las aplicaciones, se analiza un esquema de mapping de celdas y un método para planificar el orden de ejecución, tomando en consideración la ejecución por prioridad, donde las celdas de fronteras tienen una mayor prioridad con respecto a las celdas internas. En la experimentación se muestra el solapamiento del computo interno con las comunicaciones de las celdas fronteras, obteniendo resultados donde el Speedup aumenta y los niveles de eficiencia se mantienen por encima de un 85%, finalmente se obtiene ganancias de los tiempos de ejecución, concluyendo que si se puede diseñar un esquemas de solapamiento que permita que la ejecución de las aplicaciones SPMD en un cluster se hagan de forma eficiente.

Manejo de históricos en clusters

CISNE es un sistema de cómputo en paralelo del Departamento de Arquitectura de Computadores y Sistemas Operativos (DACSO). Para poder implementar políticas de ordenacción de colas y selección de trabajos, este sistema necesita predecir el tiempo de ejecución de las aplicaciones. Con este trabajo se pretende proveer al sistema CISNE de un método para predecir el tiempo de ejecución basado en un histórico donde se almacenarán todos los datos sobre las ejecuciones.

Models de simulació per coordinar serveis d'emergència

El projecte exposat té com a propòsit definir i implementar un model de simulació basat en la coordinació i assignació dels serveis d’emergència en accidents de trànsit. La definició del model s’ha realitzat amb l’ús de les Xarxes de Petri Acolorides i la implementació amb el software Rockwell Arena 7.0. El modelatge de la primera simulació ens mostra un model teòric basat en cues mentre que el segon, mostra un model més complet i real gràcies a la connexió mitjançant la plataforma Corba a una base de dades amb informació geogràfica de les flotes i de les rutes. Com a resultat de l’estudi i amb l’ajuda de GoogleEarth, podem realitzar simulacions gràfiques per veure els accidents generats, les flotes dels serveis i el moviment dels vehicles des de les bases fins als accidents.