Search

We consider the patient-to-bed assignment problem that arises in hospitals. Both emergency patients who require hospital admission and elective patients who have had surgery need to be found a bed in the most appropriate ward. The patient-to-bed assignment problem arises when a bed request is made, but a bed in the most appropriate ward is unavailable. In this case, the next-best decision out of a many alternatives has to be made, according to some suitable decision making algorithm. We construct a Markov chain to model this problem in which we consider the effect on the length of stay of a patient whose treatment and recovery consists of several stages, and can be affected by stays in or transfers to less suitable wards. We formulate a dynamic program recursion to optimise an objective function and calculate the optimal decision variables, and discuss simulation techniques that are useful when the size of the problem is too large. We illustrate the theory with some numerical examples. [ABSTRACT FROM AUTHOR]

In "A Restless Bandit Model for Resource Allocation, Competition and Reservation," J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle's idea of relaxing the constraints and Weber and Weiss's proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case. We study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. It is modeled as a set of heterogeneous restless multiarmed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle's relaxation idea and Weber and Weiss' asymptotic optimality proof, we propose a simple policy and prove it to be asymptotically optimal in a regime where both arrival rates and capacities increase. We provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. The effectiveness of these results is demonstrated by numerical experiments. To the best of our knowledge, this is the first work providing asymptotic optimality results for such a resource allocation problem and such a combination of multiple RMABPs. [ABSTRACT FROM AUTHOR]

Stochastic fluid models have been widely used to model the level of a resource that changes over time, where the rate of variation depends on the state of some continuous-time Markov process. Latouche and Taylor (Queueing Syst 63:109–129, 2009) introduced an approach, using matrix analytic methods and the reduced load approximation for loss networks, to analyse networks of fluid models all driven by the same modulating process where the buffers are infinite. We extend the method to networks involving finite buffer models and illustrate the approach by deriving performance measures for a simple network as characteristics such as buffer size are varied. Our results provide insight into the situations where the infinite buffer model is a reasonable approximation to the finite buffer model. [ABSTRACT FROM AUTHOR]

AbstractWe consider a two-class priority queue in which the priority of a customer increases linearly at some constant, class-dependent rate. We describe the related maximum priority process {(M1(t),M2(t)):t≥0}, which is of interest since the stationary distribution of the maximum priority process at the times of the commencement of service gives information about the waiting time distributions of the two classes of customers. In the case where service times are exponential, we map a two-class maximum priority process {(M1(t),M2(t)):t≥0} to a tandem fluid queue, and use this mapping in order to derive the stationary distribution of {(M1(t),M2(t)):t≥0}. Further, we extended these results to the maximum priority process in which service times are phase-type distributed. We illustrate the theory with numerical examples. [ABSTRACT FROM AUTHOR]