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ABSTRACTThis paper presents a three-step conceptual framework that can be used to structure the care-related capacity planning process in a nursing home context. The proposed framework provides a sound practical vehicle to organise client-centred care without overstretching available capacity. Within this framework, an MILP for shift scheduling and a Genetic Algorithm (GA) for task-scheduling are proposed. To investigate the performance of the proposed framework, it is benchmarked against the current situation. The results show that considerable improvements can be achieved in terms of efficiency and waiting time. More specifically, it is shown that very modest waiting times can be achieved without exceeding available capacity, despite the fluctuations in care demand across the day.

In a home care setting, high-quality care is typically associated with continuity of care. In addition, the increasing pressure due to labor shortages calls for cost-efficient operations. This paper focuses on obtaining cost-efficient daily schedules over a longer time horizon, with balanced shift lengths, while ensuring continuity of care (using the continuity of care index). To address this challenge, we propose a novel method based on blueprint routes. This method generates daily schedules by constructing optimized shifts and routes with regard to travel time, (time window) waiting time, and shift costs based on hourly wages. To ensure continuity of care, the daily scheduling decisions are strategically guided using the concept named blueprint routes. The blueprint routes are pre-optimized (partial) routes that help to align the daily schedules to achieve continuity of care in the subsequent nurse-to-shift assignment. Model-based evolutionary algorithms are employed to overcome the NP-hardness of the routing problem and nurse-to-shift assignment. Real-life-based numerical experiments demonstrate that continuity of care does not have to compromise home care schedule costs significantly.

We consider a queuing system with a workload-dependent service rate. We specifically assume that the service rate is first increasing and then decreasing as a function of the amount of work. The latter qualitative behavior is quite common in practical situations, such as production systems. The admission of work into the system is controlled by a policy for accepting or rejecting jobs, depending on the state of the system. We seek an admission control policy that maximizes the long-run throughput. Under certain conditions, we show that a threshold policy is optimal, and we derive a criterion for determining the optimal threshold value.

Abstract We consider M/G/1 queues with workload-dependent arrival rate, service speed, and restricted accessibility. The admittance of customers typically depends on the amount of work found upon arrival in addition to its own service requirement. Typical examples are the finite dam, systems with customer impatience and queues regulated by the complete rejection discipline. Our study is motivated by queueing scenarios where the arrival rate and/or speed of the server depends on the amount of work present, like production systems and the Internet.

We consider the loss probability of a customer in a single-server queue with finite buffer and partial rejection and show that it can be identified with the tail distribution of the cycle maximum of the associated infinite-buffer queue. This equivalence is shown to hold for the GI/G/1 queue and for dams with state-dependent release rates. To prove this equivalence, we use a duality for stochastically monotone recursions, developed by Asmussen and Sigman (1996). As an application, we obtain several exact and asymptotic results for the loss probability and extend Takács' formula for the cycle maximum in the M/G/1 queue to dams with variable release rate.

We consider a fixed number of streaming sessions sharing a bottleneck link with a dynamic population of elastic flows. We assume that the sizes of the elastic flows exhibit heavy-tailed characteristics. The elastic flows are TCP-controlled, while the transmission rates of the streaming applications are governed by a so-called TCP-friendly rate control protocol. Adopting the Processor-Sharing (PS) discipline to model the bandwidth sharing, we investigate the tail distribution of the deficit in service received by the streaming sessions compared to a nominal service target. The latter metric provides an indication for the quality experienced by the streaming applications. The results yield valuable qualitative insight into the occurrence of persistent quality disruption for the streaming users. We also examine the delay performance of the elastic flows.