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TwoParameter HeavyTraffic Limits for InfiniteServer Queues
"... Abstract: In order to obtain Markov heavytraffic approximations for infiniteserver queues with general nonexponential servicetime distributions and general arrival processes, possibly with timevarying arrival rates, we establish heavytraffic limits for twoparameter stochastic processes. We ..."
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Cited by 26 (13 self)
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Abstract: In order to obtain Markov heavytraffic approximations for infiniteserver queues with general nonexponential servicetime distributions and general arrival processes, possibly with timevarying arrival rates, we establish heavytraffic limits for twoparameter stochastic processes. We
Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
, 2013
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Cited by 16 (8 self)
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manuscript (Please, provide the mansucript number!) Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.
Choosing arrival process models for service systems: tests of a nonhomogeneous Poisson process.
 Nav. Res. Logist.
, 2014
"... Abstract: Service systems such as call centers and hospital emergency rooms typically have strongly timevarying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to per ..."
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Cited by 12 (10 self)
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Abstract: Service systems such as call centers and hospital emergency rooms typically have strongly timevarying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al.
Appendix to: Choosing Arrival Process Models for Service Systems: Tests of a Nonhomogeneous Poisson Process
, 2013
"... Service systems such as call centers and hospital emergency rooms typically have strongly timevarying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statist ..."
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Cited by 3 (3 self)
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Service systems such as call centers and hospital emergency rooms typically have strongly timevarying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al. (2005). They suggested a specific statistical test based on the KolmogorovSmirnov statistic after exploiting the conditionaluniform property to transform the NHPP into a sequence of i.i.d. random variables uniformly distributed on [0, 1] and then performing a logarithmic transformation of the data. We conduct extensive simulation experiments to study the power of that statistical test and various alternatives. We conclude that the general approach of Brown et al. (2005) is excellent, but that an alternative KolmogorovSmirnov test proposed by Lewis (1965), exploiting a different transformation due to Durbin (1961), consistently has greater power. This appendix provides additional details for the
The Power of Alternative KolmogorovSmirnov Tests Based on Transformations of the Data
, 2013
"... The KolmogorovSmirnov (KS) statistical test is commonly used to determine if data can be regarded as a sample from a sequence of i.i.d. random variables with specified continuous cdf F, but with small samples it can have insufficient power, i.e., its probability of rejecting natural alternatives ca ..."
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Cited by 3 (3 self)
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The KolmogorovSmirnov (KS) statistical test is commonly used to determine if data can be regarded as a sample from a sequence of i.i.d. random variables with specified continuous cdf F, but with small samples it can have insufficient power, i.e., its probability of rejecting natural alternatives can be too low. However, Durbin [1961] showed that the power of the KS test often can be increased, for given significance level, by a wellchosen transformation of the data. Simulation experiments reported here show that the power can often be more consistently and substantially increased by modifying the original Durbin transformation by first transforming the given sequence to a sequence of mean1 exponential random variables, which is equivalent to a rate1 Poisson process, and then applying the classical conditionaluniform transformation to convert the arrival times into the order statistics of i.i.d. uniform random variables. The new KS test often has much more power, because it focuses on the cumulative sums rather than the random variables themselves.
Infiniteserver queues with batch arrivals and dependent service times
, 2011
"... Motivated by largescale service systems, we consider an infiniteserver queue with batch arrivals, where the service times are dependent within each batch. We allow the arrival rate of batches to be timevarying as well as constant. As regularity conditions, we require that the batch sizes be i.i.d ..."
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Cited by 2 (2 self)
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Motivated by largescale service systems, we consider an infiniteserver queue with batch arrivals, where the service times are dependent within each batch. We allow the arrival rate of batches to be timevarying as well as constant. As regularity conditions, we require that the batch sizes be i.i.d. and independent of the arrival process of batches, and we require that the service times within different batches be independent. We exploit a recently established heavytraffic limit for the number of busy servers to determine the performance impact of the dependence among the service times. The number of busy servers is approximately a Gaussian process. The dependence among the service times does not affect the mean number of busy servers, but it does affect the variance of the number of busy servers. Our approximations quantify the performance impact upon the variance. We conduct simulations to evaluate the heavytraffic approximations for the stationary model and the model with a timevarying arrival rate. In the simulation experiments, we use the MarshallOlkin multivariate exponential distribution to model dependent exponential service times within a batch. We also introduce a class of MarshallOlkin multivariate hyperexponential distributions to model dependent hyperexponential service times within a batch.
Stochastic greybox modeling of queueing systems: fitting birthanddeath processes to data
 QUEUEING SYST (2015) 79:391–426
, 2015
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Online Appendix to: The Power of Alternative KolmogorovSmirnov Tests Based on Transformations of the Data
"... In this appendix, we present supporting materials complementing the main paper, Kim and Whitt [2013d]. In §B, we present detailed results for our main experimental setting in Section 4.1 of the main paper; §B.1 provides additional plots that supplement Section 4.2 of the main paper. We test for Erla ..."
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Cited by 1 (1 self)
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In this appendix, we present supporting materials complementing the main paper, Kim and Whitt [2013d]. In §B, we present detailed results for our main experimental setting in Section 4.1 of the main paper; §B.1 provides additional plots that supplement Section 4.2 of the main paper. We test for Erlang, Hyperexponential, and Lognormal alternatives with different parameters in §C (supplementing Section 4.3 of the paper), and §C.1 and C.2 provide supporting average empirical distribution plots for the case of E2 and H2 with c 2 = 2. In §C.3, we take a closer look at the results of the test for LN(1, 1), since it is often the specific model suggested for the service times (e.g., see Brown et al. [2005]). In §D that complement Section 4.4 of the main paper, we see how the power increases as the sample size increases for E2, H2 with c 2 = 2, and LN(1, 4) null hypotheses. §E provides supplementary materials for Section 5 of the main paper, which is on the second normal experiment.
Interdependent, heterogeneous, and timevarying servicetime distributions in call centers
, 2016
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Queueing Syst Stochastic greybox modeling of queueing systems: fitting birthanddeath processes to data
"... Abstract This paper explores greybox modeling of queueing systems. A stationary birthanddeath (BD) process model is fitted to a segment of the sample path of the number in the system in the usual way. The birth (death) rates in each state are estimated by the observed number of arrivals (departu ..."
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Abstract This paper explores greybox modeling of queueing systems. A stationary birthanddeath (BD) process model is fitted to a segment of the sample path of the number in the system in the usual way. The birth (death) rates in each state are estimated by the observed number of arrivals (departures) in that state divided by the total time spent in that state. Under minor regularity conditions, if the queue length (number in the system) has a proper limiting steadystate distribution, then the fitted BD process has that same steadystate distribution asymptotically as the sample size increases, even if the actual queuelength process is not nearly a BD process. However, the transient behavior may be very different. We investigate what we can learn about the actual queueing system from the fitted BD process. Here we consider the standard G I /G I /s queueing model with s servers, unlimited waiting room and general independent, nonexponential, interarrivaltime and servicetime distributions. For heavily loaded sserver models, we find that the longterm transient behavior of the original process, as partially characterized by mean first passage times, can be approximated by a deterministic time transformation of the fitted BD process, exploiting the heavytraffic characterization of the variability.