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On patient flow in hospitals: A data-based queueing-science perspective
, 2015
"... Patient flow in hospitals can be naturally modeled as a queueing network, where patients are the customers, and medical staff, beds and equipment are the servers. But are there special features of such a network that sets it apart from prevalent models of queueing networks? To address this question, ..."
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Cited by 20 (2 self)
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Patient flow in hospitals can be naturally modeled as a queueing network, where patients are the customers, and medical staff, beds and equipment are the servers. But are there special features of such a network that sets it apart from prevalent models of queueing networks? To address this question, we use Exploratory Data Analysis (EDA) to study detailed patient flow data from a large Israeli hospital. EDA reveals interesting and significant phenomena, which are not readily explained by available queueing models, and which raise questions such as: What queueing model best describes the distribution of the number of patients in the Emergency Department (ED); and how do such models accommodate existing throughput degradation during peak congestion? What time resolutions and operational regimes are relevant for modeling patient length of stay in the Internal Wards (IWs)? While routing patients from the ED to the IWs, how to control delays in concert with fair workload allocation among the wards? Which leads one to ask how to measure this workload: Is it proportional to bed occupancy levels? How is it related to patient turnover rates? Our research addresses such questions and explores their operational and scientific significance. Moreover, the above questions mostly address medical units unilaterally, but EDA underscores the need for and benefit from a comparative-integrative view: for example, comparing IWs to the Maternity and Oncology wards,
SYSTEMS WITH LARGE FLEXIBLE SERVER POOLS: INSTABILITY OF “NATURAL ” LOAD BALANCING
"... We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices) form a tree (in the graph with vertices being both custo ..."
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Cited by 9 (4 self)
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We consider general large-scale service systems with multiple customer classes and multiple server (agent) pools, mean service times depend both on the customer class and server pool. It is assumed that the allowed activities (routing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a natural (load balancing) routing/scheduling rule, Longest-Queue Freest-Server (LQFS-LB), in the many-server asymptotic regime, such that the exogenous arrival rates of the customer classes, as well as the number of agents in each pool, grow to infinity in proportion to some scaling parameter r. Equilibrium point of the system under LQBS-LB is the desired operating point, with server pool loads minimized and perfectly balanced. Our main results are as follows. (a) We show that, quite surprisingly (given the tree assumption), for certain parameter ranges, the fluid limit of the system may be unstable in the vicinity of the equilibrium point; such instability may occur if the activity graph is not “too small. ” (b) Using (a), we
Blind fair routing in large-scale service systems
, 2011
"... In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skil ..."
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Cited by 9 (1 self)
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In a call center, arriving customers must be routed to available servers, and servers that have just become available must be scheduled to help waiting customers. These dynamic routing and scheduling decisions are very difficult, because customers have different needs and servers have different skill levels. A further complication is that it is preferable that these decisions are made blindly; that is, they depend only on the system state and not on system parameter information such as call arrival rates and service speeds. This is because this information is generally not known with certainty. Ideally, a dynamic control policy for making routing and scheduling decisions balances customer and server needs, by keeping customer delays low, but still fairly dividing the workload amongst the various servers. In this paper, we propose two blind dynamic control policies for parallel server systems with multiple customer classes and server pools, one that is based on the number of customers waiting and the number of agents idling, and one that is based on customer delay times and server idling times. We show that, in the Halfin-Whitt many-server heavy traffic limiting regime, our proposed blind policies perform extremely well when the objective is to minimize customer holding or delay costs subject to “server fairness”, as defined by how the system idleness is divided among servers. To do this, we formulate an approximating diffusion control problem (DCP), and compare the performance of the non-blind DCP solution to a feasible policy for the DCP that is blind. We establish that the increase in the DCP objective function value is small over a wide range of parameter values. We then use simulation to validate that a small increase in the DCP objective function value is indicative of our proposed blind policies performing very well.
Routing and staffing in large-scale service systems: The case of homogeneous impatient customers and heterogeneous servers
, 2011
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Routing to Manage Resolution and Waiting Time in Call Centers with Heterogeneous Servers
, 2009
"... In many call centers, agents are trained to handle all arriving calls but exhibit very different performance for the same call type, where performance is defined by the average call handling time (AHT) and the call resolution probability (RP). In this paper, we explore strategies for determining whi ..."
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Cited by 5 (0 self)
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In many call centers, agents are trained to handle all arriving calls but exhibit very different performance for the same call type, where performance is defined by the average call handling time (AHT) and the call resolution probability (RP). In this paper, we explore strategies for determining which calls should be handled by which agents, where these assignments are dynamically determined based on the specific attributes of the agents and/or the current state of the system. We test several routing strategies using data obtained from a large financial service firm’s customer service call centers and present empirical performance results. These results allow us to characterize overall performance in terms of customer waiting time and overall resolution rate, identifying an efficient frontier of routing rules for this contact center. 1
A blind policy for equalizing cumulative idleness
, 2009
"... We consider a system with a single queue and multiple server pools of heterogenous exponential servers. The system operates under a policy that always routes a job to the pool with longest cumulative idleness among pools with available servers, in an attempt to achieve fairness toward servers. It is ..."
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We consider a system with a single queue and multiple server pools of heterogenous exponential servers. The system operates under a policy that always routes a job to the pool with longest cumulative idleness among pools with available servers, in an attempt to achieve fairness toward servers. It is easy to find examples of a system with a fixed number of servers, for which fairness is not achieved by this policy in any reasonable sense. Our main result shows that in the many-server regime of Halfin and Whitt, the policy does attain equalization of cumulative idleness, and that the equalization time, defined within any given precision level, remains bounded in the limit. An important feature of this policy is that it acts ‘blindly’, in that it requires no information on the service or arrival rates.
Y (2012) A fair policy for the G/GI/N queue with multiple server pools. Working paper
"... We consider the G/GI/N queue with multiple server pools, each possessing a pool-specific service time distribution. The class of non-idling routing policies which we consider are referred to as u-greedy policies. These policies route incoming customers to the server pool with the longest weighted cu ..."
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We consider the G/GI/N queue with multiple server pools, each possessing a pool-specific service time distribution. The class of non-idling routing policies which we consider are referred to as u-greedy policies. These policies route incoming customers to the server pool with the longest weighted cumulative idle time in order to equitably spread incoming work amongst the server pools in the system. Our first set of results demonstrate that asymptotically in the Halfin-Whitt regime and under any u-greedy policy, the diffusion scaled cumulative idle time processes of each of the server pools are held in fixed proportion to one another. We next provide a heavy traffic limit theorem for the process keeping track of the total number of customers in the system. Our limit may be characterized as the solution to a stochastic convolution equation which is driven by a Gaussian process. In order to prove our main results, we introduce a new methodology for studying the G/GI/N queue in the Halfin-Whitt regime which has as its starting point a simple conservation of flow identity.
Scheduling parallel servers in the non-degenerate slowdown diffusion regime: Asymptotic optimality results
, 2011
"... We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with non-degenerate slowdown. This regime is distinct from the well-studied heavy traffic diffusion regimes, namely the (single server) conventiona ..."
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Cited by 1 (0 self)
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We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with non-degenerate slowdown. This regime is distinct from the well-studied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin-Whitt regime. It has the distinguishing property that waiting times and service times are of comparable magnitudes. We establish an asymptotic lower bound on the cost and devise a sequence of policies that asymptotically attain this bound. As in the conventional regime, the asymptotics can be described by means of a Brownian control problem, the solution of which exhibits a state space collapse.
A skill based parallel service system under FCFS-ALIS - steady state, overloads, and abandonments
- Stochastic Systems
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