We consider a collection of statistically identical two-state continuous time Markov chains (channels). A controller continuously selects a channel with the view of maximizing infinite horizon average reward. A switching cost is paid upon channel changes. We consider two cases: full observation (all channels observed simultaneously) and partial observation (only the current channel observed). We analyze the difference in performance between these cases for various policies. For the partial observation case with two channels or an infinite number of channels, we explicitly characterize an optimal threshold for two sensible policies which we name “call-gapping” and “cool-off.” Our results present a qualitative view on the interaction of the number of channels, the available information, and the switching costs.

We consider the assignment of servers to two phases of service in a two-stage tandem queueing system when customers can abandon from each stage of service. New jobs arrive at both stations. Jobs arriving at station 1 may go through both phases of service and jobs arriving at station 2 may go through only one phase of service. Stage-dependent holding and lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations are developed that minimize discounted expected and long-run average costs. Because uniformization is not possible, we use the continuous-time framework and sample path arguments to analyze control policies. Our main results are conditions under which priority rules are optimal for the single-server model. We then propose and evaluate threshold policies for allocating one or more servers between the two stages in a numerical study. These policies prioritize a phase of service before “switching” to the other phase when total congestion exceeds a certain number. Results provide insight into how to adjust the switching rule to significantly reduce costs for specific input parameters as well as more general multi-server situations when neither preemption or abandonments are allowed during service and service and abandonment times are not exponential.

Standard server assignment policies for multi-server queueing stations include the noncollaborative policy, where the servers work in parallel on different jobs; and the fully collaborative policy, where the servers work together on the same job. However, if each job can be decomposed into subtasks with no precedence relationships, then we consider a form of server coordination named task assignment where the servers work in parallel on different subtasks of the same job. We identify the task assignment policy that maximizes the long-run average throughput of a queueing station with finite internal buffers when blocked servers can be idled or reassigned to either replace or collaborate with other servers on unblocked subtasks. We then compare the server coordination policies and show that the task assignment is best when the servers are highly specialized; otherwise, the fully collaborative or noncollaborative policies are preferable depending on whether the synergy level among the servers is high or not. We also provide numerical results that quantify our previous comparison. Finally, we address buffer allocation in longer lines where there are precedence relationships between some of the tasks, and present numerical results that suggest our comparisons for one queueing station generalize to longer lines.

Using yearly panel data from 2011 to 2017 on New Zealand District Health Boards (DHBs), this study combines principal component analysis and data envelopment intertemporal analysis with the double-bootstrap approach to estimate the technical efficiency of health care providers along with the trend of efficiency performances. The results show that although most large DHBs have improved their level of technical efficiency between 2011 and 2017, the majority of medium- and small-sized DHBs have not seen any noticeable improvement in their level of technical efficiency. The results also show that large and tertiary DHBs operate at a high level of technical efficiency. In contrast, most of the medium- and small-sized DHBs posted some of the lowest technical efficiency scores. Furthermore, the results show that medium- and small-sized DHBs have a higher average length of hospital stays which is found to be associated with decreasing levels of technical efficiency scores.

As more people move back into densely populated cities, bike sharing is emerging as an important mode of urban mobility. In a typical bike-sharing system (BSS), riders arrive at a station and take a bike if it is available. After retrieving a bike, they ride it for a while, then return it to a station near their final destinations. Since space is limited in cities, each station has a finite capacity of docks, which cannot hold more bikes than its capacity. In this paper, we study BSSs with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with k bikes. The mean-field limit and the central limit theorem provide insight on the mean, variance, and sample path dynamics of large-scale BSSs. We also leverage our results to estimate confidence intervals for various performance measures such as the proportion of empty stations, the proportion of full stations, and the number of bikes in circulation. These performance measures have the potential to inform the operations and design of future BSSs.

We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

We study an online capacity planning problem in which arriving patients require a series of appointments at several departments, within a certain access time target.

This research is motivated by a study of rehabilitation planning practices at the Sint Maartenskliniek hospital (the Netherlands). In practice, the prescribed treatments and activities are typically booked starting in the first available week, leaving no space for urgent patients who require a series of appointments at a short notice. This leads to the rescheduling of appointments or long access times for urgent patients, which has a negative effect on the quality of care and on patient satisfaction.

We propose an approach for allocating capacity to patients at the moment of their arrival, in such a way that the total number of requests booked within their corresponding access time targets is maximized. The model considers online decision making regarding multi-priority, multi-appointment, and multi-resource capacity allocation. We formulate this problem as a Markov decision process (MDP) that takes into account the current patient schedule, and future arrivals. We develop an approximate dynamic programming (ADP) algorithm to obtain approximate optimal capacity allocation policies. We provide insights into the characteristics of the optimal policies and evaluate the performance of the resulting policies using simulation.

For rare blood groups the recruitment of donor relatives, for example siblings, is expected to be effective, since the probability of a similar rare blood group is likely. However, the likelihood differs between blood groups and is not commonly available. This paper provides a unified mathematical formulation to calculate such likelihoods. From a mathematical and probabilistic point of view, it is shown that these likelihoods can be obtained from the computation of a stationary genotype distribution. This, in turn, can be brought down to a system of quadratic stochastic operators. A generic mathematical approach is presented which directly leads to a stationary genotype distribution for arbitrary blood groups. The approach enables an exact computation for the effectiveness of recruiting next of kin for blood donorship. Next to an illustration of computations for ‘standard’ ABO and Rhesus-D blood groups, it is particularly illustrated for the extended Rhesus blood group system. Also other applications requiring next of kin blood group associations can be solved directly by using the unified mathematical formulation.

The Right Whale Sighting Advisory System (RWSAS) is a National Oceanic and Atmospheric Administration (NOAA) Fisheries program designed to reduce collisions between vessels and critically endangered North Atlantic right whales. The vessel speed restriction that is part of the RWSAS presents navigation stakeholders with numerous challenges, owing to concerns about increased risks of ship grounding and collisions within ports. In this paper, we present a multi-methodology framework for assessing the impact of the vessel speed restriction on navigational safety. Empirically, we base our discussion in a first-order analysis of ship grounding risk for the Charleston Entrance Channel. Our analysis proceeds in three parts. We begin by using fault and event tree analyses to assess a relevant set of grounding-related event progression and failure probabilities. The influence of alternative vessel speed restrictions on ship grounding risk are then explored via a Bayesian network model that utilises the previously specified fault and event tree models for its partial specification and enumeration. Our analysis suggests that the speed restriction can, under certain reasonable assumptions, be seen to adversely impact the risk of ship grounding accidents in the Charleston Entrance Channel. We conclude with a summary of our findings and recommendations for future research.

This paper describes a Multi-Criteria-Analysis (MCA)-based Decision Support System (DSS) developed for the management of incidents in maritime traffic. The developed DSS helps to organise a large quantity of information related to emergency management, spatial data and “live” data (radar data, weather forecasting data), to make it available to decision makers in a comprehensible and user-friendly way. Special care has been taken to model human Decision-Making (DM) processes during incident situations. Since the DM process is always multi-criterial, a Multi-Criteria Decision-Making (MCDM) method called Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE) is used. However, a simplified variation of PROMETHEE II has been utilised to make results more understandable to non-expert users. The aim of this research is to incorporate effective DSS in human DM processes, thus reducing the possibility of making poor decisions. The concept of Web MCA-based DSS is presented as a case study: Web DSS developed for the east coast of the Adriatic Sea.

From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing model for this scenario and use a Markov decision process formulation to analyze assignment policies that minimize holding costs. We show that the classic cμ rule is generally not optimal when service or cost requirements can change. Even for a two-class customer model where a class 1 task becomes a class 2 task upon waiting, we show that additional orderings of the service rates are needed to ensure the optimality of simple priority rules. We then show that seemingly-intuitive switching curve structures are also not optimal in general. We study these scenarios and provide conditions under which they do hold. Lastly, we show that results from the two-class model do not extend to when there are n≥3 customer classes. More broadly, we find that simple priority rules are not optimal. We provide sufficient conditions under which a simple priority rule holds. In short, allowing service and/or cost requirements to change fundamentally changes the structure of the optimal policy for resource allocation in queueing systems.

This paper deals with two ideas appeared during the last developing phase in Artificial Intelligence: Reservoir Computing (RC) and Random Neural Networks. Both have been very successful in many applications. We propose a new model belonging to the first class, taking the structure of the second for its dynamics. The new model is called Echo State Queuing Network. The paper positions the model in the global Machine Learning area, and provides examples of its use and performances. We show on largely used benchmarks that it is a very accurate tool, and we illustrate how it compares with standard RC models.

Relying only on the classical Bahadur–Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (as n→∞) of

$$ {\open P}\left({\max_{i\in\{1,\ldots,d_x\}}\bar X_{i,n} \les \min_{i\in\{1,\ldots,d_y\}}\bar Y_{i,n}}\right),$$

${\bar X}_{i,n}{\rm s}$

${\bar Y}_{i,n}{\rm s}$

${\open E}X \gt {\open E}Y$

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

Many real-world scheduling problems can be modeled as Multi-mode Resource ConstrainedProject Scheduling Problems (MRCPSP). However, the MRCPSP is a strong NP-hard problem andvery difficult to be solved. The purpose of this research is to investigate a moreefficient alternative based on ant algorithm to solve MRCPSP. To enhance the generalityalong with efficiency of the algorithm, the rule pool is designed to manage numerouspriority rules for MRCPSP. Each ant is provided with an independent thread and endowedwith the learning ability to dynamically select the excellent priority rules. In addition,all the ants in the ant algorithm have the prejudgment ability to avoid infeasible routesbased on the branch and bound method. The algorithm is tested on the well-known benchmarkinstances in PSPLIB. The computational results validate the effectiveness of the proposedalgorithm.