489 research outputs found
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 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 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 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
LGBTQ & You: Connecting Collections with the Campus Community
Musselman Library’s LGBTQ Research Guide, established in 2012, is a resource that goes beyond connecting the library’s collections with the campus community and providing access. This research guide has generated opportunities to grow campus partnerships, foster a student’s interest in librarianship, and create a gateway for research and learning in the LGBTQ community that goes beyond the classroom. In our presentation we will outline the project from its early days as a student project to its current life as collaboration between the library and Gettysburg Colleges’ Office of LGBTQA Advocacy & Education
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