The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

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.

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.

Capacity to within one bit of a class of Gaussian multicast channels with interference

This paper studies the fundamental operational limits of a class of Gaussian multicast channels with an interference setting. In particular, the paper considers two base stations multicasting separate messages to distinct sets of users. In the presence of channel state information at the transmitters and at the respective receivers, the capacity region of the Gaussian multicast channel with interference is characterized to within one bit. At the crux of this result is an extension to the multicast channel with interference of the Han-Kobayashi or the Chong-Motani-Garg achievable region for the interference channel.

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 the problem 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.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

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.

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.

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.

Propagation of Microwaves in the Troposphere with Potential Application to GPS based Navigation and Meteorology with emphasis on Indian region

Global Positioning System (GPS), with its high integrity, continuous availability and reliability, revolutionized the navigation system based on radio ranging. With four or more GPS satellites in view, a GPS receiver can find its location anywhere over the globe with accuracy of few meters. High accuracy - within centimeters, or even millimeters is achievable by correcting the GPS signal with external augmentation system. The use of satellite for critical application like navigation has become a reality through the development of these augmentation systems (like W AAS, SDCM, and EGNOS, etc.) with a primary objective of providing essential integrity information needed for navigation service in their respective regions. Apart from these, many countries have initiated developing space-based regional augmentation systems like GAGAN and IRNSS of India, MSAS and QZSS of Japan, COMPASS of China, etc. In future, these regional systems will operate simultaneously and emerge as a Global Navigation Satellite System or GNSS to support a broad range of activities in the global navigation sector.Among different types of error sources in the GPS precise positioning, the propagation delay due to the atmospheric refraction is a limiting factor on the achievable accuracy using this system. The WADGPS, aimed for accurate positioning over a large area though broadcasts different errors involved in GPS ranging including ionosphere and troposphere errors, due to the large temporal and spatial variations in different atmospheric parameters especially in lower atmosphere (troposphere), the use of these broadcasted tropospheric corrections are not sufficiently accurate. This necessitated the estimation of tropospheric error based on realistic values of tropospheric refractivity. Presently available methodologies for the estimation of tropospheric delay are mostly based on the atmospheric data and GPS measurements from the mid-latitude regions, where the atmospheric conditions are significantly different from that over the tropics. No such attempts were made over the tropics. In a practical approach when the measured atmospheric parameters are not available analytical models evolved using data from mid-latitudes for this purpose alone can be used. The major drawback of these existing models is that it neglects the seasonal variation of the atmospheric parameters at stations near the equator. At tropics the model underestimates the delay in quite a few occasions. In this context, the present study is afirst and major step towards the development of models for tropospheric delay over the Indian region which is a prime requisite for future space based navigation program (GAGAN and IRNSS). Apart from the models based on the measured surface parameters, a region specific model which does not require any measured atmospheric parameter as input, but depends on latitude and day of the year was developed for the tropical region with emphasis on Indian sector.Large variability of atmospheric water vapor content in short spatial and/or temporal scales makes its measurement rather involved and expensive. A local network of GPS receivers is an effective tool for water vapor remote sensing over the land. This recently developed technique proves to be an effective tool for measuring PW. The potential of using GPS to estimate water vapor in the atmosphere at all-weather condition and with high temporal resolution is attempted. This will be useful for retrieving columnar water vapor from ground based GPS data. A good network of GPS could be a major source of water vapor information for Numerical Weather Prediction models and could act as surrogate to the data gap in microwave remote sensing for water vapor over land.

Achievable sum-rate of multiuser massive MIMO downlink in ricean fading channels

We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.

Clinical Consequences Of Tityus Bahiensis And Tityus Serrulatus Scorpion Stings In The Region Of Campinas, Southeastern Brazil.

Scorpion stings account for most envenomations by venomous animals in Brazil. A retrospective study (1994-2011) of the clinical consequences of Tityus scorpion stings in 1327 patients treated at a university hospital in Campinas, southeastern Brazil, is reported. The clinical classification, based on outcome, was: dry sting (no envenoming), class I (only local manifestations), class II (systemic manifestations), class III (life-threatening manifestations, such as shock and/or cardiac failure requiring inotropic/vasopressor agents, and/or respiratory failure), and fatal. The median patient age was 27 years (interquartile interval = 15-42 years). Scorpions were brought for identification in 47.2% of cases (Tityus bahiensis 27.7%; Tityus serrulatus 19.5%). Sting severity was classified and each accounted for the following percentage of cases: dry stings - 3.4%, class I - 79.6%, class II - 15.1%, class III - 1.8% and fatal - 0.1%. Pain was the primary local manifestation (95.5%). Systemic manifestations such as vomiting, agitation, sweating, dyspnea, bradycardia, tachycardia, tachypnea, somnolence/lethargy, cutaneous paleness, hypothermia and hypotension were detected in class II or class III + fatal groups, but were significantly more frequent in the latter group. Class III and fatal cases occurred only in children <15 years old, with scorpions being identified in 13/25 cases (T. serrulatus, n = 12; T. bahiensis, n = 1). Laboratory blood abnormalities (hyperglycemia, hypokalemia, leukocytosis, elevations in serum total CK, CK-MB and troponin T, bicarbonate consumption and an increase in base deficit and blood lactate), electrocardiographic changes (ST segment) and echocardiographic alterations (ventricular ejected fraction <54%) were frequently detected in class III patients. Seventeen patients developed pulmonary edema, 16 had cardiac failure and seven had cardiogenic shock. These results indicate that most scorpion stings involved only local manifestations, mainly pain; the greatest severity was associated with stings by T. serrulatus and in children <15 years old.

Genetic Diversity Of Giardia Duodenalis: Multilocus Genotyping Reveals Zoonotic Potential Between Clinical And Environmental Sources In A Metropolitan Region Of Brazil.

Giardia duodenalis is a flagellate protozoan that parasitizes humans and several other mammals. Protozoan contamination has been regularly documented at important environmental sites, although most of these studies were performed at the species level. There is a lack of studies that correlate environmental contamination and clinical infections in the same region. The aim of this study is to evaluate the genetic diversity of a set of clinical and environmental samples and to use the obtained data to characterize the genetic profile of the distribution of G. duodenalis and the potential for zoonotic transmission in a metropolitan region of Brazil. The genetic assemblages and subtypes of G. duodenalis isolates obtained from hospitals, a veterinary clinic, a day-care center and important environmental sites were determined via multilocus sequence-based genotyping using three unlinked gene loci. Cysts of Giardia were detected at all of the environmental sites. Mixed assemblages were detected in 25% of the total samples, and an elevated number of haplotypes was identified. The main haplotypes were shared among the groups, and new subtypes were identified at all loci. Ten multilocus genotypes were identified: 7 for assemblage A and 3 for assemblage B. There is persistent G. duodenalis contamination at important environmental sites in the city. The identified mixed assemblages likely represent mixed infections, suggesting high endemicity of Giardia in these hosts. Most Giardia isolates obtained in this study displayed zoonotic potential. The high degree of genetic diversity in the isolates obtained from both clinical and environmental samples suggests that multiple sources of infection are likely responsible for the detected contamination events. The finding that many multilocus genotypes (MLGs) and haplotypes are shared by different groups suggests that these sources of infection may be related and indicates that there is a notable risk of human infection caused by Giardia in this region.

Triatominae Survey (hemiptera: Heteroptera: Reduviidae) In The South-central Region Of The State Of Bahia, Brazil Between 2008 And 2013.

Triatomine surveillance in rural areas, artificial ecotypes, and natural ecotopes of the cities of Caturama, Ibipitanga, Macaúbas, and Seabra in the south-central region of the Brazilian state of Bahia was carried out between 2008 and 2013. Natural infection by Trypanosoma cruzi was evaluated in the specimens collected to monitor vectors of Chagas disease. A total of 1,357 specimens were collected, and four species were identified: Triatoma sordida (83%), Triatoma lenti (16.4%), Triatoma pseudomaculata (0.5%), and Panstrongylus geniculatus (0.1%). Triatoma sordida was found in four cities, only 0.7% in intradomiciliary environments. Triatoma lenti was found only in Macaúbas; 8.5% were found in intradomiciliary environments, 88.3% in peridomiciliary environments, and 3.1% in sylvatic environments. Natural infection by T. cruzi was 0.5% for T. sordida and 3.1% T. lenti. All of these cases were found in peridomiciliary environments of Macaúbas. As the results show, triatomines were found in intradomiciliary environments in three cities that were surveyed in the south-central region of the state of Bahia. Thus, an epidemiologic survey should be performed to avoid the risk of transmission to the population.

The C-terminal Region Of The Human P23 Chaperone Modulates Its Structure And Function.

The p23 protein is a chaperone widely involved in protein homeostasis, well known as an Hsp90 co-chaperone since it also controls the Hsp90 chaperone cycle. Human p23 includes a β-sheet domain, responsible for interacting with Hsp90; and a charged C-terminal region whose function is not clear, but seems to be natively unfolded. p23 can undergo caspase-dependent proteolytic cleavage to form p19 (p231-142), which is involved in apoptosis, while p23 has anti-apoptotic activity. To better elucidate the function of the human p23 C-terminal region, we studied comparatively the full-length human p23 and three C-terminal truncation mutants: p23₁₋₁₁₇; p23₁₋₁₃₁ and p23₁₋₁₄₂. Our data indicate that p23 and p19 have distinct characteristics, whereas the other two truncations behave similarly, with some differences to p23 and p19. We found that part of the C-terminal region can fold in an α-helix conformation and slightly contributes to p23 thermal-stability, suggesting that the C-terminal interacts with the β-sheet domain. As a whole, our results suggest that the C-terminal region of p23 is critical for its structure-function relationship. A mechanism where the human p23 C-terminal region behaves as an activation/inhibition module for different p23 activities is proposed.