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Introduction
Published in Joseph Y.-T. Leung, Handbook of SCHEDULING, 2004
RR The algorithm Round Robin devotes an equal amount of processing resources to all jobs. An understanding of RR is important because it is the underlying scheduling algorithm for many technologies. For example, the congestion control protocol within the ubiquitous TCP Internet protocol can be viewed as scheduling connections through a single bottleneck using RR. This algorithm is also called Processor Sharing, or Equi-Partition.
Likelihood ratio-based CUSUM charts for real-time monitoring the quality of service in a network of queues
Published in IISE Transactions on Healthcare Systems Engineering, 2023
Yanqing Kuang, Devashish Das, Mustafa Sir, Kalyan Pasupathy
Here we assume each service node in our partner ED is a processor-sharing queue with a state-dependent service rate function. Processor sharing queue is a model in which the available service capacity is shared by the number of customers presented in queue. The ED is a complex service environment with many shared resources (nurses, doctors, equipment, hallways, laboratory, etc) and multitasking situations, which are conceptually similar to queuing models with shared processors. Thus, the processor-sharing queue is more flexible to accommodate these complexities commonly seen in the ED service environment compared to traditional queuing systems. Other papers also have considered it for similar reasons (Armony et al., 2015; Shi et al., 2021; Whitt & Zhang, 2017). Figure 8 illustrates an example for the empirical distribution of the patient occupancy levels in one of the service nodes at our partner ED of Mayo Clinic. The occupancy level at a given time represents the total number of patients in the node. We find that assuming a processor-sharing queue with a state-dependent service rate for our partner ED can best replicate the empirical occupancy distribution curve compared to the conventional M/M/1 queue, which clearly deviates from the empirical distribution.
Routing and staffing in emergency departments: A multiclass queueing model with workload dependent service times
Published in IISE Transactions on Healthcare Systems Engineering, 2023
Siddhartha Nambiar, Maria E. Mayorga, Yunan Liu
In our work we consider team-based care; few analytical models for resource allocation in healthcare consider the fact that resources within units are partially shared, central resources. In general service systems, the use of pooled resources is related to the concept of “processor sharing” (Kleinrock, 1967). Processor sharing is a service policy where customers are all served simultaneously in a queueing system. Under processor sharing, each customer receives an equal fraction of the service capacity available. Sharing resources within a unit is an idea that is relatively new in healthcare analytics literature. Agor et al. (2017) developed a simulation model in which incoming patients are assigned to teams of providers of different skill levels. Mandelbaum et al. (2012) showed that based on empirical hospital data the Inverted-V queueing model best models patients spending time in units within a hospital. The Inverted-V model assumes that upon entering a queueing system, an agent (patient) is assigned to a “pool” of servers instead of being assigned to a single server. Several authors continued to build on this by proposing a variety of patient/customer routing algorithms in an Inverted-V queueing context (Almehdawe et al., 2013; Armony & Ward, 2010; Ward & Armony, 2013). In addition to considering pooled service, we model state-dependent service.