A large deviations approach to asymptotically optimal control of crisscross network in heavy traffic

In this work we study the problem of asymptotically optimal control of a well-known multi-class queuing network, referred to as the ``crisscross network,'' in heavy traffic. We consider exponential inter-arrival and service times, linear holding cost and an infinite horizon discounted cost criterion. In a suitable parameter regime, this problem has been studied in detail by Martins, Shreve and Soner [SIAM J. Control Optim. 34 (1996) 2133-2171] using viscosity solution methods. In this work, using the pathwise solution of the Brownian control problem, we present an elementary and transparent treatment of the problem (with the identical parameter regime as in [SIAM J. Control Optim. 34 (1996) 2133-2171]) using large deviation ideas introduced in [Ann. Appl. Probab. 10 (2000) 75-103, Ann. Appl. Probab. 11 (2001) 608-649]. We obtain an asymptotically optimal scheduling policy which is of threshold type. The proof is of independent interest since it is one of the few results which gives the asymptotic optimality of a control policy for a network with a more than one-dimensional workload process.Comment: Published at http://dx.doi.org/10.1214/105051605000000250 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Merging KK-means with hierarchical clustering for identifying general-shaped groups

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure but suffers from computational complexity in large datasets while $K$-means clustering is efficient but designed to identify homogeneous spherically-shaped clusters. We present a hybrid non-parametric clustering approach that amalgamates the two methods to identify general-shaped clusters and that can be applied to larger datasets. Specifically, we first partition the dataset into spherical groups using $K$-means. We next merge these groups using hierarchical methods with a data-driven distance measure as a stopping criterion. Our proposal has the potential to reveal groups with general shapes and structure in a dataset. We demonstrate good performance on several simulated and real datasets.Comment: 16 pages, 1 table, 9 figures; accepted for publication in Sta

Evaluation of haematological and behavioural changes in Channa punctatus (Bloch) on short-term exposure to a commercial-grade synthetic pyrethroid pesticide

This study aims to assess the acute toxicity of commercial-grade Cypermethrin (10% EC) and evaluate the hematological and behavioral alterations in a freshwater fish Channa punctatus upon short-term exposure to Cypermethrin. A four-day static acute toxicity test was performed to estimate the median lethal concentration (LC50) value of Cypermethrin. During the acute toxicity test, the behavior of the control and cypermethrin exposed fish was critically observed and recorded. After completing the acute toxicity test, the hematological effects of Cypermethrin in C. punctatus were evaluated using two sublethal dosages (0.08 mg/L and 0.12 mg/L). Results of the study revealed that this pesticide induced significant mortality in C. punctatus with a 96-h L50 value of 0.263 mg/L. Cypermethrin exposed fish showed hyperactivity, irritability, erratic swimming, frequent surface visit, etc. Exposure to sublethal concentrations of Cypermethrin for a short period resulted in a significant decline (P<0.05) in total erythrocytes count (TEC), packed cell volume (PCV), mean corpuscular volume (MCV), and hemoglobin (Hb) concentration as compared to control groups. In contrast, pesticide-exposed groups had a significant increase (P<0.05) in mean corpuscular hemoglobin concentration (MCHC) and total leucocyte count (TLC). It is apparent from the results of the study that this commercial formulation is toxic to the studied fish. This study also revealed hematological and behavioral alterations in C. Punctatus which could be used as biomarkers for incipient Cypermethrin intoxication

Parikh One-Counter Automata

Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ?-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs. Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered

Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic

AbstractWe address a rate control problem associated with a single server Markovian queueing system with customer abandonment in heavy traffic. The controller can choose a buffer size for the queueing system and also can dynamically control the service rate (equivalently the arrival rate) depending on the current state of the system. An infinite horizon cost minimization problem is considered here. The cost function includes a penalty for each rejected customer, a control cost related to the adjustment of the service rate and a penalty for each abandoning customer. We obtain an explicit optimal strategy for the limiting diffusion control problem (the Brownian control problem or BCP) which consists of a threshold-type optimal rejection process and a feedback-type optimal drift control. This solution is then used to construct an asymptotically optimal control policy, i.e. an optimal buffer size and an optimal service rate for the queueing system in heavy traffic. The properties of generalized regulator maps and weak convergence techniques are employed to prove the asymptotic optimality of this policy. In addition, we identify the parameter regimes where the infinite buffer size is optimal