This study investigated the relationship between bilingualism and task switching ability using a standardized measure of switching and an objective measure of bilingual language proficiency. Heritage Language (HL) speaking Spanish-English and Mandarin-English bilinguals and English speaking monolinguals completed all four subtests of the Color-Word Interference Test (CWIT), an English verbal fluency task, and a picture naming test (the Multilingual Naming Test) in English. Bilinguals also named pictures in their HL to assess HL proficiency. Spanish-English bilinguals were advantaged in task switching, exhibiting significantly smaller switching cost than monolinguals, but were disadvantaged in verbal fluency and picture naming. Additionally, performance on these cognitive and linguistic tasks was related to degree of HL proficiency, so that increased ability to name pictures in Spanish was associated with greater switching advantage, and greater disadvantage in both verbal fluency and picture naming. Mandarin-English bilinguals, who differed from the Spanish-English bilinguals on several demographic and language-use characteristics, exhibited a smaller but statistically significant switching advantage, but no linguistic disadvantage, and no clear relationship between HL proficiency and the switching advantage. Together these findings demonstrate an explicit link between objectively measured bilingual language proficiency and both bilingual advantages and disadvantages, while also showing that consequences of bilingualism for cognitive and linguistic task performance can vary across different language combinations. (JINS, 2015, 21, 531–544)

In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

We present structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties. In addition to linear holding costs, we impose either lump sum switching costs or batch set-up delays which are incurred at each instant the server processes a job in a queue different from the previous one. We use reward rate notions to unearth conditions on the holding costs and service distributions for which an exhaustive policy is optimal. For the case of two nodes connected probabilistically in tandem, we explicitly define an optimal policy under similar conditions.

We investigate the impact of switching penalties on the nature of optimal scheduling policies for systems of parallel queues without arrivals. We study two types of switching penalties incurred when switching between queues: lump sum costs and time delays. Under the assumption that the service periods of jobs in a given queue possess the same distribution, we derive an index rule that defines an optimal policy. For switching penalties that depend on the particular nodes involved in a switch, we show that although an index rule is not optimal in general, there is an exhaustive service policy that is optimal.

In this paper we characterize the optimal class of output policies in a control model of a dam having a finite capacity. The input of water into the dam is determined by a Wiener process with positive drift. Water may be released at either of two possible rates 0 or M. At any time the output rate can be increased from 0 to M with a cost of K, (K ≧ 0) or decreased from M to 0 with zero cost, any such changes taking effect instantaneously. There is a reward of A monetary units for each unit of output, (A ≧ 0). The problem is to formulate an optimal output policy which maximizes the long-run average net reward per unit time.