In this paper we consider the workload of a storage system with the unconventional feature that the arrival times, rather than the interarrival times, are independent and identically distributed samples from a given distribution. We start by analyzing the ‘base model’ in which the arrival times are exponentially distributed, leading to a closed-form characterization of the queue’s workload at a given moment in time (i.e. in terms of Laplace–Stieltjes transforms), assuming the initial workload was 0. Then we consider four more general models, each of them having a specific additional feature: (a) the initial workload being allowed to have any arbitrary non-negative value, (b) an additional stream of Poisson arrivals, (c) phase-type arrival times, (d) balking customers. For all four variants the transform of the transient workload is identified in closed form.

Wales has not adopted the English IAPT system and has no centralized training plan for developing cognitive behavioural therapy (CBT) in Wales. However, Welsh Government policy expresses an ambition to improve access to evidence-based psychological therapies for people in Wales. This study focuses on one Welsh Health Board's plan to improve access to CBT. The study aims to benchmark support for effective delivery of CBT in the Health Board against NICE and Department of Health standards, and to establish whether the Health Board's plan is succeeding in developing staff capability and access to evidence-based CBT. Mental health staff funded by the Health Board to complete accredited training in CBT were asked to complete an online questionnaire asking about their training, accreditation, use of CBT, and experience of workplace support for delivering CBT. The standards were taken from the Department of Health competency framework for CBT, NICE guidelines and BABCP safety and confidentiality criteria. The Health Board performed well across seven standards of workplace support for the delivery of evidence-based CBT. Staff funded to undertake accredited CBT training continued to develop and to use CBT in their everyday clinical practice. The study indicates that the Health Board is succeeding in offering good standards of workplace support for CBT, including access to accredited CBT training. A recommendation is made that this be shared with other Welsh Health Boards and that a comparable study be undertaken within an IAPT service.

We consider an infinite sequence of customers of types and an infinite sequence of servers of types where a server of type j can serve a subset of customer types C(j) and where a customer of type i can be served by a subset of server types S(i). We assume that the types of customers and servers in the infinite sequences are random, independent, and identically distributed, and that customers and servers are matched according to their order in the sequence, on a first-come–first-served (FCFS) basis. We investigate this process of infinite bipartite matching. In particular, we are interested in the rate ri,j that customers of type i are assigned to servers of type j. We present a countable state Markov chain to describe this process, and for some previously unsolved instances, we prove ergodicity and existence of limiting rates, and calculate ri,j.