Look-ahead policies for admission to a single server loss system

Consider a single server loss system in which the server, being idle, may reject or accept an arriving customer for service depending on the state at the arrival epoch. It is assumed that at every arrival epoch the server knows the service time of the arriving customer, the arrival time of the next customer and the service time. The server gets a fixed reward for every customer admitted to the system. The form of an optimal stationary policy is investigated for the discounted and average reward cases

Queuing with future information

We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate $\sim\log_{1/(1-p)}\frac{1}{1-\lambda}$, as $\lambda\to 1$. In sharp contrast, when all future arrival and service times are revealed beforehand, the optimal average queue length converges to a finite constant, $(1-p)/p$, as $\lambda\to1$. We further show that the finite limit of $(1-p)/p$ can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as $\mathcal{O}(\log\frac{1}{1-\lambda})$, as $\lambda\to1$. This leads to the conjecture of an interesting duality between queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic order results and equilibrium joining rules for the Bernoulli Feedback Queue

We consider customer joining behaviour for a system that consists of a FCFS queue with Bernoulli feedback. A consequence of the feedback characteristic is that the sojourn time of a customer already in the system depends on the joining decisions taken by future arrivals to the system. By establishing stochastic order results for coupled versions of the system, we establish the existence of homogeneous Nash equilibrium joining policies for both single and multiple customer types which are distinguished through distinct quality of service preference parameters. Further, it is shown that for a single customer type, the homogeneous policy is unique

A Data-Driven Approach for Operational Improvement in Emergency Departments

Emergency departments (EDs) in the US are experiencing significant stress from crowding, of which one of the main contributors is the lengthy boarding process, which is the process of to-be-admit patients waiting in the ED for the hospital to ready beds for them. We explored ways to reduce crowding by initiating hospital bed request (BeRT) early on for likely to-be-admit patients. In Chapter 2, we modeled the ED patient flow as a Markov decision process. With the objective of balancing the tradeoff between waiting cost and the cost of false early BeRTs, we found the optimal early BeRT policy to be of threshold type, where the threshold is a function of census and patients probability of admission. Chapter 3 built a fluid model, where patients flow into the ED (a fluid tank) as continuous fluid flowing at a time-dependent deterministic rate. To control the number of false early BeRTs, we imposed a constraint on the length of time for the early BeRT option. The optimal policy that minimizes the fluid level (congestion level) in the ED dictates that when ED is under heavy traffic regime, one should BeRT early as early, and as long, as allowed. In chapter 4, we looked at several early BeRT heuristics that are inspired by the theoretical optimal policies found previously. We tested and compared their performances in terms of length-of-stay and waiting time using a simulation model built for the UNC ED based on 2012 patient data. We observed that as the admission probability distributions of the patient population became less variable, the heuristics that take more information into account performed better. Lastly, we offered a different perspective on ED crowding in Chapter 5, where we explored the association between ED cencus and providers’ triage and admission decisions. We found that the more crowded the ED was, the more conservative providers were, in that nurses tend to triage more patients as critical, and physicians tend to admit more patients into the hospital.Doctor of Philosoph

Better Admission Control and Disk Scheduling for Multimedia Applications

General purpose operating systems have been designed to provide fast, loss-free disk service to all applications. However, multimedia applications are capable of tolerating some data loss, but are very sensitive to variation in disk service timing. Present research efforts to handle multimedia applications assume pessimistic disk behaviour when deciding to admit new multimedia connections so as not to violate the real-time application constraints. However, since multimedia applications are ``soft\u27 real-time applications that can tolerate some loss, we propose an optimistic scheme for admission control which uses average case values for disk access. Typically, disk scheduling mechanisms for multimedia applications reduce disk access times by only trying to minimize movement to subsequent blocks after sequencing based on Earliest Deadline First. We propose to implement a disk scheduling algorithm that uses knowledge of the media stored and permissible loss and jitter for each client, in addition to the physical parameters used by the other scheduling algorithms. We will evaluate our approach by implementing our admission control policy and disk scheduling algorithm in Linux and measuring the quality of various multimedia streams. If successful, the contributions of this thesis are the development of new admission control and flexible disk scheduling algorithm for improved multimedia quality of service

Information Design for Congested Social Services: Optimal Need-Based Persuasion

We study the effectiveness of information design in reducing congestion in social services catering to users with varied levels of need. In the absence of price discrimination and centralized admission, the provider relies on sharing information about wait times to improve welfare. We consider a stylized model with heterogeneous users who differ in their private outside options: low-need users have an acceptable outside option to the social service, whereas high-need users have no viable outside option. Upon arrival, a user decides to wait for the service by joining an unobservable first-come-first-serve queue, or leave and seek her outside option. To reduce congestion and improve social outcomes, the service provider seeks to persuade more low-need users to avail their outside option, and thus better serve high-need users. We characterize the Pareto-optimal signaling mechanisms and compare their welfare outcomes against several benchmarks. We show that if either type is the overwhelming majority of the population, information design does not provide improvement over sharing full information or no information. On the other hand, when the population is a mixture of the two types, information design not only Pareto dominates full-information and no-information mechanisms, in some regimes it also achieves the same welfare as the "first-best", i.e., the Pareto-optimal centralized admission policy with knowledge of users' types.Comment: Accepted for publication in the 21st ACM Conference on Economics and Computation (EC'20). 40 pages, 6 figure

Utility Optimal Scheduling and Admission Control for Adaptive Video Streaming in Small Cell Networks

We consider the jointly optimal design of a transmission scheduling and admission control policy for adaptive video streaming over small cell networks. We formulate the problem as a dynamic network utility maximization and observe that it naturally decomposes into two subproblems: admission control and transmission scheduling. The resulting algorithms are simple and suitable for distributed implementation. The admission control decisions involve each user choosing the quality of the video chunk asked for download, based on the network congestion in its neighborhood. This form of admission control is compatible with the current video streaming technology based on the DASH protocol over TCP connections. Through simulations, we evaluate the performance of the proposed algorithm under realistic assumptions for a small-cell network.Comment: 5 pages, 4 figures. Accepted and will be presented at IEEE International Symposium on Information Theory (ISIT) 201

The optimal look-ahead policy for admission to a single server system

This paper considers a service system with a single server, finite waiting room, and a renewal arrival process. Customers who arrive while the server is busy are lost. Upon completing service, the server chooses between two actions:\ud either he immediately starts a new service, provided a customer is present, or\ud he admits the newly arrived customer to the system, but delays service pending\ud the next arrival, whereupon he again chooses between these two actions. This\ud process continues until either the system is full or a new service is started.\ud Once a service has been started, all customers who arrive while the server is busy are lost. We assume that at each decision epoch the server knows the arrival epoch of the first arriving customer. We show that there exists an optimal control-limit policy that minimizes the average expected idle time per customer served (equivalently, maximizes the average number of customers served per unit of time). The special case of Poisson arrivals leads to an explicit expression for this delay that generalizes exisiting results

Empirical Studies in Hospital Emergency Departments

This dissertation focuses on the operational impacts of crowding in hospital emergency departments. The body of this work is comprised of three essays. In the first essay, Waiting Patiently: An Empirical Study of Queue Abandonment in an Emergency Department, we study queue abandonment, or left without being seen. We show that abandonment is not only influenced by wait time, but also by the queue length and the observable queue flows during the waiting exposure. We show that patients are sensitive to being jumped in the line and that patients respond differently to people more sick and less sick moving through the system. This study shows that managers have an opportunity to impact abandonment behavior by altering what information is available to waiting customers. In the second essay, Doctors Under Load: An Empirical Study of State-Dependent Service Times in Emergency Care, we show that when crowded, multiple mechanisms in the emergency department act to retard patient treatment, but care providers adjust their clinical behavior to accelerate the service. We identify two mechanisms that providers use to accelerate the system: early task initiation and task reduction. In contrast to other recent works, we find the net effect of these countervailing forces to be an increase in service time when the system is crowded. Further, we use simulation to show that ignoring state-dependent service times leads to modeling errors that could cause hospitals to overinvest in human and physical resources. In the final essay, The Financial Consequences of Lost Demand and Reducing Boarding in Hospital Emergency Departments, we use discrete event simulation to estimate the number of patients lost to Left Without Being Seen and ambulance diversion as a result of patients waiting in the emergency department for an inpatient bed (known as boarding). These lost patients represent both a failure of the emergency department to meet the needs of those seeking care and lost revenue for the hospital. We show that dynamic bed management policies that proactively cancel some non-emergency patients when the hospital is near capacity can lead to reduced boarding, increased number of patients served, and increased hospital revenue