Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

Cyclo[(6-amino-6-deoxy-d-galactonic acid)4]: a new class of carbopeptoid-cyclodextrin

The formation of the 28-membered ring cyclo[(6-amino-6-deoxy-d-galactonic acid)₄] by cyclisation of a protected open chain fully hydroxylated nylon 6 linear tetramer in modest yield provides the first example of a new class of carbopeptoid-cyclodextrin.     

The synthesis of the drugstore beetle pheromone (Stegobinone)

2,3-Dihydro-2,3,5-trimethyl-6-(1-methyl-2-oxobutyl)-4H-pyran-4-one ($\text{1}$ (Stegobinone), the sex pheromone of the drugstore beetle, was successfully prepared from 4,6-dimethyl-3,5,7-nonatrione ($\text{2}$) by a biogenetically plausible scheme.     

A simple approach to carbocyclic thromboxane A2 from a cyclubutane

A short route from the cyclobutane derivative (1) to the key intermediate (4) allows easy access to the carbocyclic thromboxane A₂ analogue (5).     

Exploring the performance of small- and medium-sized enterprises through the credit crunch

Small- and medium-sized enterprises (SMEs) are major contributors to most western economies. They are often supported by government policies, and in the UK the government encourages banks to lend to them. It is generally believed that the credit crunch has had an impact on the performance of SMEs. This study looks at the impact of the crunch using large samples from 2007 through to 2010. It looks at performance by region, age and industrial sector (SIC code). It then proceeds to explore the modelling of default over the years, with a focus on young businesses. It was found that there is a degree of stability within the models, though the level of default varies across years. Young businesses, as has been found before, are shown to be more vulnerable.     

A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints

Classical analyses of the dynamic control of multi-class queueing systems frequently yield simple priority policies as optimal. However, such policies can often result in excessive queue lengths for the low priority jobs/customers. We propose a stochastic optimisation problem in the context of a two class M/M/1 system which seeks to mitigate this through the imposition of constraints on the second moments of queue lengths. We analyse the performance of two families of parametrised heuristic policies for this problem. To evaluate these policies we develop lower bounds on the optimum cost through the achievable region approach. A numerical study points to the strength of performance of threshold policies and to directions for future research.