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.

Globalization and wage inequality in South and East Asia, and Latin America: A gender approach

In this paper we analyse the reasons behind the evolution of the gender gap and wage inequality in South and East Asian and Latin American countries. Health human capital improvements, the exposure to free market openness and equal treatment enforcement laws seem to be the main exogenous variables affecting women s economic condition. During the second globalization era (in the years 1975-2000) different combinations of these variables in South East Asian and Latin American countries have had as a result the diminution of the gender gap. The main exception to this rule according to our data is China where economic reforms have been simultaneous to the increase of gender differences and inequality between men and women.This result has further normative consequences for the measure of economic inequality. Theimprovement of women s condition has as a result the diminution of the dispersion of wages.Therefore in most of the countries analysed the consequence of the diminution of the gender gapduring the second global era is the decrease of wage inequality both measured with Gini and Theil indexes.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

Restless bandits, partial conservation laws and indexability

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow fromnew linear programming formulations for the problems investigated.

The survival of the welfare state

This paper provides an analytical characterization of Markov perfectequilibria in a politico-economic model with repeated voting, whereagents vote over distortionary income redistribution. The key featureof the theory is that the future constituency of redistributive policiesdepends positively on the current level of redistribution, since thisaffects both private investments and the future distribution of voters.Agents vote rationally and fullly anticipate the effects of their politicalchoice on both private incentives and future voting outcomes. The modelfeatures multiple equilibria. In "pro-welfare" equilibria, both welfarestate policies and their effects on distribution persist forever. In"anti-welfare equilibria", even a majority of beneficiaries ofredistributive policies vote strategically so as to induce the formationof a future majority that will vote for zero redistribution.

Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficientconditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.

Equilibrium unemployment insurance

In this paper, we incorporate a positive theory of unemployment insuranceinto a dynamic overlapping generations model with search-matching frictionsand on-the-job learning-by-doing. The model shows that societies populatedby identical rational agents, but differing in the initial distributionof human capital across agents, may choose very different unemploymentinsurance levels in a politico-economic equilibrium. The interactionbetween the political decision about the level of the unemployment insuranceand the optimal search behavior of the unemployed gives rise to aself-reinforcing mechanism whichmay generate multiple steady-stateequilibria. In particular, a European-type steady-state with highunemployment, low employment turnover and high insurance can co-exist withan American-type steady-state with low unemployment, high employment turnoverand low unemployment insurance. A calibrated version of the model featurestwo distinct steady-state equilibria with unemployment levels and durationrates resembling those of the U.S. and Europe, respectively.

Drug utilization studies and data registries in primary care

This article reviews the methodology of the studies on drug utilization with particular emphasis on primary care. Population based studies of drug inappropriateness can be done with microdata from Health Electronic Records and e-prescriptions. Multilevel models estimate the influence of factors affecting the appropriateness of drug prescription at different hierarchical levels: patient, doctor, health care organization and regulatory environment.Work by the GIUMAP suggest that patient characteristics are the most important factor in the appropriateness of prescriptions with significant effects at the general practicioner level.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.

Intergenerational mobility and the informative content of surnames

We propose an alternative method for measuring intergenerational mobility. Measurements obtained fromtraditional methods (based on panel data) are scarce, difficult to compare across countries and almost impossible to get across time. In particular, this means that we do not know how intergenerational mobility is correlated with growth, income or the degree of inequality.Our proposal is to measure the informative content of surnames in one census. The more information thesurname has on the income of an individual, the more important is her background in determining her outcomes; and thus, the less mobility there is.The reason is that surnames provide information about family relationships because the distribution ofsurnames is necessarily very skewed. A large percentage of the population is bound to have a very unfrequent surname. For them the partition generated by surnames is very informative on family linkages.First, we develop a model whose endogenous variable is the joint distribution of surnames and income.There, we explore the relationship between mobility and the informative content of surnames. We allow for assortative mating to be a determinant of both.Second, we use our methodology to show that in large Spanish region the informative content of surnamesis large and consistent with the model. We also show that it has increased over time, indicating a substantial drop in the degree of mobility. Finally, using the peculiarities of the Spanish surname convention we show that the degree of assortative mating has also increased over time, in such a manner that might explain the decrease in mobility observed.Our method allows us to provide measures of mobility comparable across time. It should also allow us tostudy other issues related to inheritance.

A positive theory of geographic mobility and social insurance

This paper presents a tractable dynamic general equilibrium model thatcan explain cross-country empirical regularities in geographical mobility,unemployment and labor market institutions. Rational agents vote overunemployment insurance (UI), taking the dynamic distortionary effects ofinsurance on the performance of the labor market into consideration.Agents with higher cost of moving, i.e., more attached to their currentlocation, prefer more generous UI. The key assumption is that an agent'sattachment to a location increases the longer she has resided there. UIreduces the incentive for labor mobility and increases, therefore, thefraction of attached agents and the political support for UI. The mainresult is that this self-reinforcing mechanism can give rise to multiplesteady-states-one 'European' steady-state featuring high unemployment,low geographical mobility and high unemployment insurance, and one'American' steady-state featuring low unemployment, high mobility andlow unemployment insurance.

Duración de la incapacidad temporal tras intervención quirúrgica del ligamento cruzado anterior de la rodilla. Análisis de dos técnicas quirúrgicas.

Se estima que en España la incidencia de la lesión del ligamento cruzado anterior (L.C.A) es de 4 casos por cada 10.000 habitantes/año. Su reconstrucción quirúrgica incluye habitualmente la utilización de autoinjertos (con tejido tendinoso propio del paciente). Los dos más frecuentes son de tendón rotuliano y de tendones isquiotibiales.La lesión del L.C.A y su intervención quirúrgica hace tributario al trabajador de una incapacidad temporal (IT). No existe consenso en cuanto a la elección entre los dos injertos en la cirugía de L.C.A ni se conoce su impacto en la duración de la IT.El objetivo principal de este trabajo es describir la duración de la incapacidad temporal en función de la técnica quirúrgica de autoinjertos utilizada en la reconstrucción del ligamento cruzado anterior.Se trata de cohorte retrospectiva de 151 trabajadores que han sido tributarios de una IT por plastia de ligamento cruzado anterior de la rodilla, utilizando autoinjertos. El ámbito de estudio es una mutua de accidentes de trabajo y enfermedades profesionales de la Seguridad Social (Mutual Midat Cyclops - MC MUTUAL). Los trabajadores han sido intervenidos quirúrgicamente en la Clínica MC-Copérnico de Barcelona, por una de las técnicas (T. rotuliano o T. Isquiotibiales).Para la técnica del Tendón Rotuliano se obtuvo una muestra de 68 trabajadores intervenidos quirúrgicamente, con una DM de 121 días, y para la técnica de los Tendones Isquiotibiales se recogió una muestra de 83 intervenciones quirúrgicas, con una DM de 113. La DM total fue de 117 días de IT.El análisis de los datos no arrojó diferencias estadísticamente significativas en el tiempo de retorno al trabajo entre los trabajadores intervenidos por las técnicas quirúrgicas señaladas.