58 research outputs found
A short note on the monotonicity of the Erlang C formula in the Halfin-Whitt regime
We prove a monotonicity condition satisfied by the Erlang C formula when computed in
the Halfin-Whitt regime. This property was recently conjectured in Janssen et al. [2011
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
The restricted Erlang-R queue:finite-size effects in service systems with returning customers
Motivated by health care systems with repeated services that have both personnel (nurse and physician) and space (beds) constraints, we study a restricted version of the Erlang-R model. The space restriction policies we consider are blocking or holding in a pre-entrant queue. We develop many-server approximations for the system performance measures when either policy applies, and explore the connection between them. We show that capacity allocation of both resources should be determined simultaneously, and derive the methodology to determine it explicitly. We show that the system dynamics is captured by the fraction of needy time in the network, and that returning customers should be accounted for both in steady-state and time-varying conditions. We demonstrate the application of our policies in two case studies of resource allocation in hospitals
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