Stationary Distribution Convergence of the Offered Waiting Processes for GI/GI/1+GI Queues in Heavy Traffic

A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic intensity approaches one. As a consequence, the stationary distribution of a ROU process, which is a truncated normal, should approximate the scaled stationary distribution of the offered waiting time in a $GI/GI/1+GI$ queue; however, no such result has been proved. We prove the aforementioned convergence, and the convergence of the moments, in heavy traffic, thus resolving a question left open in Ward and Glynn (2005). In comparison to Kingman's classical result in Kingman (1961) showing that an exponential distribution approximates the scaled stationary offered waiting time distribution in a $GI/GI/1$ queue in heavy traffic, our result confirms that the addition of customer abandonment has a non-trivial effect on the queue stationary behavior.Comment: 29 page

Routing and Staffing when Servers are Strategic

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.Comment: First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 201

A Scalable Model for Monograph Assessment: A Case Study at Musselman Library

The evolution of monograph assessment in Musselman Library resulted in a model that sustains concurrent assessment initiatives large and small, as well as time-bound and ongoing, with the purpose of shaping collections in support of the academic and creative interests at Gettysburg College. This presentation outlines the design of the 2012 assessment model that has become the foundation for assessing our circulating monograph collection, along with how the original model has been adjusted to assess more focused targets and larger initiatives, each with rapidly approaching deadlines. Finally, this presentation summarizes the workflows needed to support continuous decision making and provides a sample of the results from the assessment initiatives described

Impact of Socialization in Elderly Public-Housing Residents

Older adults who experience social isolation have higher rates of mortality relative to their counterparts. Social interactions are an important way to combat this isolation. This research aims to better understand how social isolation in older adults living in low-income households in Richmond, Virginia (RVA) is related to their economic, physical, and psychological health status. As part of the iCubed Health and Wellness Aging Core and in collaboration with the Richmond Memorial: East End Housing Coalition for Older Adults, older adults from a selected public housing unit (n=28) self-reported their financial status, experiences with physical and psycho-social health, and feelings of social isolation. Survey participants were 71.4% female, the mean age was 69.75 years, and 25% were high school graduates. Participants averaged 34 years living in the East End and reported an average of $300 to spend on rent monthly. Overall, 55% (n=20) reported having two or more supports and 61% (n=22) reported hardly ever feeling isolated. However, a small subset of the sample reported having either no supports (5.6%, n=2) and 41.7% (n=15) lacked companionship some of the time or often. A one-way ANOVA was conducted and it was determined that participants who reported feeling left out more often were significantly more likely to report stress, anxiety, and depression (F[2, 25] = 6.998). Findings support the existence of supportive communities formed in low-income areas. Findings also indicate some older individuals residing in public housing in RVA experience social isolation and that this status is linked to poorer psycho-social health.https://scholarscompass.vcu.edu/gradposters/1048/thumbnail.jp