Super-Exponential Solution in Markovian Supermarket Models: Framework and Challenge

Marcel F. Neuts opened a key door in numerical computation of stochastic models by means of phase-type (PH) distributions and Markovian arrival processes (MAPs). To celebrate his 75th birthday, this paper reports a more general framework of Markovian supermarket models, including a system of differential equations for the fraction measure and a system of nonlinear equations for the fixed point. To understand this framework heuristically, this paper gives a detailed analysis for three important supermarket examples: M/G/1 type, GI/M/1 type and multiple choices, explains how to derive the system of differential equations by means of density-dependent jump Markov processes, and shows that the fixed point may be simply super-exponential through solving the system of nonlinear equations. Note that supermarket models are a class of complicated queueing systems and their analysis can not apply popular queueing theory, it is necessary in the study of supermarket models to summarize such a more general framework which enables us to focus on important research issues. On this line, this paper develops matrix-analytical methods of Markovian supermarket models. We hope this will be able to open a new avenue in performance evaluation of supermarket models by means of matrix-analytical methods.Comment: Randomized load balancing, supermarket model, matrix-analytic method, super-exponential solution, density-dependent jump Markov process, Batch Markovian Arrival Process (BMAP), phase-type (PH) distribution, fixed poin

Effects of carbon reduction labels: Evidence from scanner data

We investigate the effects of carbon reduction labels using a detailed scanner data set. Using a difference-in-differences estimation strategy, we find that having a carbon label has no impact on detergent prices or demand. We also investigate possible heterogeneous effects of carbon labels using the synthetic control method. We find no evidence to indicate that the prices for the counterfactual detergents without the label would have been any different from the prices of the carbon-labeled detergents. We investigate the reasons for these results and conclude that the specific design of the carbon label is responsible for its lack of success

Identify successful marketing communication strategies that apply to a small hair salon

A selected organisation provides hair dressing services and hair products to customers. The aim of this report is to analyse how the small hair salon could improve their marketing communication strategies in order to attract more customers and enhance the relationship between customers and the organisation. The approach to collecting information was to use a questionnaire with 50 participants, to gather primary information and to conduct a secondary research study. The result of this research was to decide that the role of a successful marketing communication strategy is to attract the customer to consume. In order to make the marketing communication strategy successful, it needs to choose a suitable channel that enables it to connect with the customer. New media is an effective channel that can promote the business to the customer and interact with them. New media is also suitable for a small business to use. A recommendation for the organisation is they create their own website page, Facebook page, YouTube video and WeChat group to promote themselves and interact with customers. Those channels are popular in New Zealand, with a high number of active users. Most the organisation customers like to use those channels too, so if the organisation applies those channels to their marketing communication strategy they will be able to attract customers and persuade them to consume more products