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.

Abstract: Service systems such as call centers and hospital emergency rooms typically have strongly time-varying 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.

The Kolmogorov-Smirnov (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 well-chosen 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 mean-1 exponential random variables, which is equivalent to a rate-1 Poisson process, and then applying the classical conditional-uniform 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.

This paper investigates extensions to feed-forward queueing networks of an algorithm to set staffing levels (the number of servers) to stabilize performance in an Mt/GI/st + GI multi-server queue with a time-varying arrival rate. The model has a non-homogeneous Poisson process (NHPP), customer abandonment, and non-exponential service and patience distri-butions. For a single queue, simulation experiments showed that the algorithm successfully stabilizes abandonment probabilities and expected delays over a wide range of Quality-of-Service (QoS) targets. A limit theorem showed that stable performance at fixed QoS targets is achieved asymptotically as the scale increases (by letting the arrival rate grow while holding the service and patience distributions fixed). Here we extend that limit theorem to a feed-forward queueing network. However, these fixed QoS targets provide low QoS as the scale increases. Hence, these limits primarily support the algorithm with a low QoS target. For a high QoS target, effectiveness depends on the NHPP property, but the departure process never is exactly an NHPP. Thus, we investigate when a departure process can be regarded as approximately an NHPP. We show that index of dispersion for counts is effective for determining when a departure process is approximately an NHPP in this setting. In the important common case when all queues have high QoS targets, we show that both: (i) the departure process is approximately an NHPP from this perspective and (ii) the algorithm is effective.

medical-surgical wards. Because SDUs are less richly staffed than ICUs, they are less costly to operate; however, they also are unable to provide the level of care required by the sickest patients. There is an ongoing debate in the medical community as to whether and how SDUs should be used. On one hand, an SDU alleviates ICU congestion by providing a safe environment for post-ICU patients before they are stable enough to be transferred to the general wards. On the other hand, an SDU can take capacity away from the already over-congested ICU. In this work, we propose a queueing model to capture the dynamics of patient flows through the ICU and SDU in order to determine how to size the ICU and SDU. We account for the fact that patients may abandon if they have to wait too long for a bed, while others may get bumped out of a bed if a new patient is more critical. Using fluid and diffusion analysis, we examine the tradeoff between reserving capacity in the ICU for the most critical patients versus gaining additional capacity achieved by allocating nurses to the SDUs due to the lower staffing requirement. Despite the complex patient flow dynamics, we leverage a state-space collapse result in our diffusion analysis to establish the optimal allocation of nurses to units. We find that under some circumstances the optimal size of the SDU is zero, while in other cases, having a sizable SDU may be beneficial. The insights from our work will be useful for hospital managers determining how to allocate nurses to the hospital units, which subsequently determines the size of each unit.

Abstract not found

Patients nationwide experience difficulties in accessing medical appointments in a timely manner due to long backlogs. Meanwhile, patients do not always show up for their scheduled services, with significant no-show rates. Unattended appointments result in under-utilization of a clinic’s valuable resources, and limit the access for other patients who could have filled the missed slots. Medical practices aim to utilize their valuable resources efficiently, provide timely access to care, and at the same time they strive to provide short waits for patients present at the medical facility. We study the joint problem of determining the panel size of a medical practice and the number of offered appointment slots per day, so that patients do not face long backlogs and the clinic is not overcrowded. We explicitly model the two separate time scales involved in accessing medical care: appointment delay (order of days, weeks) and clinic delay (order of minutes, hours). We analyze the two queueing systems associated with each type of delay, and provide explicit expressions for the performance measures of interest based on diffusion approximations. In our analysis we capture many features of the complex reality of outpatient care, including patients ’ non-punctuality, no-shows, balking behavior, and stochastic service times. Two additional distinctive characteristics of this study are the balking behavior of the patients who face long appointment backlogs, and the transient-state analysis of the clinic delay, which allow the study of a

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.

This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and cat-egorise works in the field, allowing for researchers and practitioners to explore the various types of results that exist. This bibliography attempts to include all known works that satisfy both of these requirements: • Works that deal with queueing models. • Works that contain contributions related to methodology of parameter esti-mation, state estimation, hypothesis testing, confidence interval and/or actual data-sets of application areas. It also includes reference to selected additional related material in Section 8. There are additional works not mentioned in this bibliography that are mildly re-lated. This includes methods for parameter estimation of point processes, methods for parameter estimation of stochastic matrix analytic models as well as inference, estimation and tomography of communication networks not directly modelled as queueing networks. Our attempt is to make this bibliography exhaustive, yet there are possibly some papers that we have missed. As it is updated continuously, additions and comments are welcomed. The sections below categorise the works based on several categories. A single paper may appear in several categories simultaneously. The final section lists all works in chronological order along with short descriptions of the contributions. This bibliography is maintained at

Analytical approximations are developed to determine the time-dependent offered load (effective demand) and appropriate staffing levels that stabilize performance at desig-nated targets in a many-server queueing model with time-varying arrival rates, customer abandonment from queue and random feedback with additional delay after completing service. To provide a flexible model that can be readily fit to system data, the model has history-dependent Bernoulli routing, where the feedback probabilities, service-time and patience distributions all may depend on the visit number. Before returning to receive a new service, the fed-back customers experience delays in an infinite-server or finite-capacity queue, where the parameters may again depend on the visit number. A new refined modified-offered-load approximation is developed to obtain good results with low waiting-time targets. Simulation experiments confirm that the approximations are effective. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases.