A fluid model for a relay node in an ad-hoc network: the case of heavy-tailed input

Relay nodes in an ad-hoc network can be modelled as fluid queues, in which the available service capacity is shared by the input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along a random amount of work. The total transmission capacity is fairly shared, meaning that, when n jobs are present, each job transmits traffic into the queue at rate 1/(n+1) while the queue is drained at the same rate of 1/(n + 1). Where previous studies mainly concentrated on the case of exponentially distributed job sizes, the present paper addresses regularly varying jobs. The focus lies on the tail asymptotics of the sojourn time S. Using sample-path arguments, it is proven that P {S > x} behaves roughly as the residual job size, i.e., if the job sizes are regularly varying of index –v, the tail of S is regularly varying of index 1 – v. In addition, we address the tail asymptotics of other performance metrics, such as the workload in the queue, the flow transfer time and the queueing delay

Performance of TCP-friendly streaming sessions in the presence of heavy-tailed elastic flows

We consider a fixed number of streaming sessions which share a bottleneck link with a dynamic population of elastic flows. Motivated by extensive measurement studies, 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. TCP-friendly rate control protocols provide a promising mechanism for avoiding severe fluctuations in the transmission rate, while ensuring fairness with competing TCP-controlled flows. Adopting the Processor-Sharing (PS) discipline to model the bandwidth sharing, we investigate the asymptotic 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 by exploiting a useful relationship with a Processor-Sharing queue with perm

Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic wait

Optimal admission control in queues with workload-dependent service rates

We consider a queueing 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 derive a criterion for determining the optimal threshold valu

Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals

We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a determin

Optimal patient protocols in regional acute stroke care

In acute stroke care two proven reperfusion treatments exist: (1) a blood thinner and (2) an interventional procedure. The interventional procedure can only be given in a stroke centre with specialized facilities. Rapid initiation of either is key to improving the functional outcome (often emphasized by the common phrase in acute stroke care “time=brain”). Delays between the moment the ambulance is called and the initiation of one or both reperfusion treatment(s) should therefore be as short as possible. The speed of the process strongly depends on five factors: patient location, regional patient allocation by emergency medical services (EMS), travel times of EMS, treatment locations, and in-hospital delays. Regional patient allocation by EMS and treatment locations are sub-optimally configured in daily practice. Our aim is to construct

Avoiding hospital admissions and delayed transfers of care by improved access to intermediate care: A simulation study

Objective: The current waiting times for intermediate care in the Netherlands prohibit timely access, leading to unwanted and costly hospital admissions. We propose alternative policies for improvement of intermediate care and estimate the effects on the waiting times, hospitalization, and the number of patient replacements. Design: Simulation study. Setting and Participants: For our case study, data were used of older adults who received intermediate care in Amsterdam, the Netherlands, in 2019. For this target group, in- and outflows and patient characteristics were identified. Methods: A process map of the main pathways into and out of the intermediate care was obtained and a discrete event simulation (DES) was built. We demonstrate the use of our DES for intermediate care by evaluating possible policy changes for a real-life case study in Amsterdam. Results: By means of a sensitivity analysis with the DES, we show that in Amsterdam the waiting times are not a result of a lack in bed capacity but are due to an inefficient triage and application process. Older adults have to wait a median of 1.8 days for admission, leading to hospitalization. If the application process becomes more efficient and evening and weekend admissions are allowed, we find that unwanted hospitalization can be decreased substantially. Conclusion and Implications: In this study, a simulation model is developed for intermediate care that can serve as a basis for policy decisions. Our case study shows that the waiting times for health care facilities are not always solved by increasing bed capacity. This underlines the necessity for a data-driven approach to identify logistic bottlenecks and find the best ways to solve them

Reduced waiting times by preference-based allocation of patients to nursing homes

Objectives: The long waiting times for nursing homes can be reduced by applying advanced waiting-line management. In this article, we implement a preference-based allocation model for older adults to nursing homes, evaluate the performance in a simulation setting for 2 case studies, and discuss the implementation in practice.Design: Simulation study.Setting and Participants: Older adults requiring somatic nursing home care, from an urban region (Rotterdam) and a rural region (Twente) in the Netherlands.Methods: Data about nursing homes and capacities for the 2 case studies were identified. A set of preference profiles was defined with aims regarding waiting time preferences and flexibility. Guidelines for implementation of the model in practice were obtained by addressing the tasks of all stakeholders. Thereafter, the simulation was run to compare the current practice with the allocation model based on specified outcome measures about waiting times and preferences.Results: We found that the allocation model decreased the waiting times in both case studies. Compared with the current practice policy, the allocation model reduced the waiting times until placement by at least a factor of 2 (from 166 to 80 days in Rotterdam and 178 to 82 days in Twente). Moreover, more of the older adults ended up in their preferred nursing home and the aims of the distinct preference profiles were satisfied.Conclusions and Implications: The results show that the allocation model outperforms commonly used waiting-line policies for nursing homes, while meeting individual preferences to a larger extent. Moreover, the model is easy to implement and of a generic nature and can, therefore, be extended to other settings as well (eg, to allocate older adults to home care or daycare). Finally, this research shows the potential of mathematical models in the care domain for older adults to face the increasing need for cost-effective solutions.</p

Optimal admission control in queues with workload-dependent service rates

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