76 research outputs found
Controlling excessive waiting times in emergency departments: an extension of the ISA algorithm.
In an emergency department (ED), the demand for service is not constant over time. This cannot be accounted for by means of waiting lists or appointment systems, so capacity decisions are the most important tool to influence patient waiting times. Additional complexities result from the relatively small system size that characterizes an ED (i.e. a small number of physicians or nurses) and the presence of customer impatience. Assuming a single-stage multiserver M(t)/G/s(t) + G queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman and others (2008) as a method to set staffing levels throughout the day. The main advantage of our extension is that it enables the use of performance measures based on the probability of experiencing an excessive waiting time, instead of the common focus on delay probability as a performance metric.Emergency department; Personnel planning; Time-varying arrival rate;
Large deviations analysis for the queue in the Halfin-Whitt regime
We consider the FCFS 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 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
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Staffing and Scheduling to Differentiate Service in Many-Server Service Systems
This dissertation contributes to the study of a queueing system with a single pool of multiple homogeneous servers to which multiple classes of customers arrive in independent streams. The objective is to devise appropriate staffing and scheduling policies to achieve specified class-dependent service levels expressed in terms of tail probability of delays. Here staffing and scheduling are concerned with specifying a time-varying number of servers and assigning newly idle servers to a waiting customer from one of K classes, respectively. For this purpose, we propose new staffing-and-scheduling solutions under the critically-loaded and overloaded regimes. In both cases, the proposed solutions are both time dependent (coping with the time variability in the arrival pattern) and state dependent (capturing the stochastic variability in service and arrival times). We prove heavy-traffic limit theorems to substantiate the effectiveness of our proposed staffing and scheduling policies. We also conduct computer simulation experiments to provide engineering confirmation and practical insight
Holistic assessment of call centre performance
In modern call centres 60â70% of the operational costs come in the form of the human agents who take the calls. Ensuring that the call centre operates at lowest cost and maximum efficiency involves a tradeâoff of the cost of agents against lost revenue and increased customer dissatisfaction due to lost calls. Modelling the performance characteristics of a call centre in terms of the agent queue alone misses key performance influencers, specifically the interaction between channel availability at the media gateway and the time a call is queued. A blocking probability at the media gateway, as low as 0.45%, has a significant impact on the degree of queuing observed and therefore the cost and performance of the call centre. Our analysis also shows how abandonment impacts queuing delay. However, the call centre manager has less control over this than the level of contention at the media gateway. Our commercial assessment provides an evaluation of the balance between abandonment and contention, and shows that the difference in cost between the best and worst strategy is ÂŁ130K per annum, however this must be balanced against a possible additional ÂŁ2.98Â m exposure in lost calls if abandonment alone is used
Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective
A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.
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