Jamol Pender

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The multi-server queue with non-homogeneous Poisson arrivals and customer abandonment is a fundamental dynamic rate queueing model for large scale service systems such as call centers and hospitals. Scaling the arrival rates and number of servers arises naturally when a manager updates a staffing schedule in response to a forecast of increased customer(More)
In this paper, we introduce a new approximation for estimating the dynamics of multiserver queues with abandonment. The approximation involves a four-dimensional dynamical system that uses the skewness and kurtosis of the queueing distribution via the Gram Charlier expansion. We show that the additional information captured in the skewness and kurtosis(More)
Large scale systems such as customer contact centers, like telephone call centers, as well as healthcare centers, like hospitals, have customer inflow-outflow dynamics with many common features. The customer arrival patterns may have time of day or seasonal effects. Moreover, customer population sizes tend to be large where the individual actions are(More)
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be(More)
Motivated by heavy traffic approximations for single server queueswith abandonment, we provide an exact expression for the moments of the truncated normal distribution using Stein’s lemma. Consequently, our moment expressions provide insight into the steady state skewness and kurtosis dynamics of single server queues with impatient customers. Moreover,(More)
In this paper, we develop a new approximation for nonstationary multiserver queues with abandonment. Our method uses the Poisson–Charlier polynomials, which are a discrete orthogonal polynomial sequence that is orthogonal with respect to the Poisson distribution. We show that by appealing to the Poisson–Charlier polynomials that we can estimate the mean,(More)