Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work

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

Does the Past Predict the Future? The Case of Delay Announcements in Service Systems

Motivated by the recent interest in making delay announcements in large service systems, such as call centers, we investigate the accuracy of announcing the waiting time of the Last customer to Enter Service (LES). In practice, customers typically respond to delay announcements by either balking or by becoming more or less impatient, and their response alters system performance. We study the accuracy of the LES announcement in single-class multi-server Markovian queueing models with announcement-dependent customer behavior. We show that, interestingly, even in this stylized setting, the LES announcement may not always be accurate. This motivates the need to study its accuracy carefully, and to determine conditions under which it is accurate. Since the direct analysis of the system with customer response is prohibitively difficult, we focus on many-server heavy-traffic analysis instead. We consider the quality-and-efficiency-driven (QED) and the efficiency-driven (ED) many-server heavy-traffic regimes and prove, under both regimes, that the LES prediction is asymptotically accurate if, and only if, asymptotic fluctuations in the queue length process are small as long as some regulatory conditions apply. This result provides an easy check for the accuracy of LES in practice. We supplement our theoretical results with an extensive simulation study to generate practical managerial insights

Large deviations analysis for the M/H2/n+MM/H_2/n + M queue in the Halfin-Whitt regime

We consider the FCFS $M/H_2/n + M$ queue in the Halfin-Whitt heavy traffic regime. It is known that the normalized sequence of steady-state queue length distributions is tight and converges weakly to a limiting random variable W. However, those works only describe W implicitly as the invariant measure of a complicated diffusion. Although it was proven by Gamarnik and Stolyar that the tail of W is sub-Gaussian, the actual value of $\lim_{x \rightarrow \infty}x^{-2}\log(P(W >x))$ was left open. In subsequent work, Dai and He conjectured an explicit form for this exponent, which was insensitive to the higher moments of the service distribution. We explicitly compute the true large deviations exponent for W when the abandonment rate is less than the minimum service rate, the first such result for non-Markovian queues with abandonments. Interestingly, our results resolve the conjecture of Dai and He in the negative. Our main approach is to extend the stochastic comparison framework of Gamarnik and Goldberg to the setting of abandonments, requiring several novel and non-trivial contributions. Our approach sheds light on several novel ways to think about multi-server queues with abandonments in the Halfin-Whitt regime, which should hold in considerable generality and provide new tools for analyzing these systems

Empirical Analyses Of Queues With Applications To Elections And Healthcare

In Chapter 1, we conduct a dynamic panel data study of voting resource allocation within Florida counties. We find that a 1\% increase in the percentage of voters registered as Democrat in a county results in a 2.8\% increase in the number of registered voters per poll worker. Furthermore, using a queue simulation, we estimate that a 5\% increase in voters registered as Democrat in a county could increase the average wait time to vote from 40 minutes (the estimated average wait time to vote in Florida in 2012) to approximately 100 minutes. Our study recommends that states regulate the number of voters per poll worker or voting machine in polling locations so that wait times are equated across all voters. In Chapter 2, we perform a differences-in-differences analysis on cross-sectional voter wait time data across the 2006, 2008, 2012, and 2016 Georgia elections. We estimate that polling place closures increased Georgia’s average wait time to vote in the 2016 election by 7 minutes or approximately 78\% (based on Georgia’s average wait time of 16.5 minutes in the 2016 election). This increase in the average wait time to vote suggests that in the 2016 election, Georgia may have idled its spare capacity (e.g., voting machines) following polling place closures. As a result, we suggest that states implement policies that require the redistribution of all functioning voting machines from closed polling places or at least increase transparency in how voting resources are used in elections. In Chapter 3, we use an instrumental variable estimation and find that patients prefer waiting for endoscopies in pre-op rather than reception. Additional experiments suggest that pre-op is less favorable due to its intensity (e.g., clinical, emotional). We also find that in transparent, shared waiting areas where patients do not observe the doctor assignment of others, patients may still monitor queue discipline. Finally, patients may be negatively impacted by waits that conclude after a scheduled appointment time but care less about waits that conclude early. This study emphasizes the importance of businesses managing queues where customers wait in multiple locations with different attributes

DIFFUSION APPROXIMATION FOR EFFICIENCY-DRIVEN QUEUES UNDER REFINED PATIENCE TIME SCALING

Ph.DDOCTOR OF PHILOSOPH