Description

Queueing Colloquium 2019

Everyone is welcome to attend this Colloquium which will feature the following speakers:

11.00 - 12.00 Lerzan Örmeci (Koç University) - Strategic Customers in Systems with Batch Arrivals: The Effect of Flexibility
12.00 - 13.00 Lunch
13.00 - 13.45 Liron Ravner (UvA - TU/e) - Statistical estimation of the input to a queue by Poisson probing
13.45 - 14.30 Bernd Heidergott (VU) - Generalized Gradient Estimators for Maximum Likelihood Estimation with a view on Model
Calibration
14.30 - 15.00 Coffee break
15.00 - 15.45 Fiona Sloothaak (TU/e) - Battery swapping stations for electric vehicles: a queueing perspective
15.45 - 16.30 Jasper Goseling (UT) - Performance Bounds for Random Walks in the Positive Orthant

16.30 Reception

Please register (free of costs) before May 13: https://forms.gle/UhRVQyBzugWEhY6T9

Abstracts

Lerzan Örmeci: Strategic Customers in Systems with Batch Arrivals: The Effect of Flexibility
We consider a service or production system that receives customers arriving in groups but serves each customer individually. Customers face a convoluted manifestation of the "join-balk" dilemma when they try to balance the payoff  obtained from service with the costs caused by waiting in the queue: if they are bound to join or balk as a group, then some of them may be forced to join so that the net benefit of the entire group is maximized. On the other hand, if a part of the group can enter the system while the others balk, then their individual interest plays the major role in their decision. When all arriving groups act strategically, it is of interest to predict the resulting join-balk strategies under equilibrium, as well as their effects on system performance, customer throughput, total customer welfare in both cases. We consider these questions in the framework of a single server Markovian queue with batch arrivals and random batch sizes. We explicitly consider two cases with respect to the entrance decision rules: the 0-1 case, in which the entire batch decides to either join or balk, and the partial case, where the batch is allowed to join partially (i.e., only a fraction of the customers decides to join). We analyze and compare how the customers behave in equilibrium under both rules and the corresponding implications on the social welfare. We also evaluate the effect of a set-up cost incurred for each batch on
join-balk decisions and performance measures.
This is a joint work with O. Boudali and A. B. Burnetas

Liron Ravner: Statistical estimation of the input to a queue by Poisson probing
In many queueing scenarios the arrival process of work to the queue may be unknown and so statistical inference by observing system performance is called for. For example, a communication network with a bottleneck link that has unknown sources of input. This is often a challenging task as time dependent samples from a queue have an intractable joint distribution. In this work we suggest a tractable approach that relies on sampling the workload process at random times according to an external Poisson process. We assume that the input is a Lévy process, which includes the special case of the classical M/G/1 model. We construct a method-of moments based estimator for the characteristic exponent (generating function) of the input distribution. The estimator relies on transient properties of the queue rather than steady-state approximations. Verifiable conditions for consistency and asymptotic
normality are provided, along with explicit expressions for the asymptotic variance. We show that an estimator satisfying these
conditions can be constructed for a class of models including the M/G/1 queue. Our estimation method can be further applied in more elaborate systems such as tandem and tree networks, and also for sequential testing of hypothesis regarding the input distribution.
Based on joint work with: Onno Boxma, Michel Mandjes, Cornelia Wichelhaus.

Bernd Heidergott: Generalized Gradient Estimators for Maximum Likelihood Estimation with a view on Model Calibration
Stochastic derivative estimation plays a central role in both sensitivity analysis and gradient-based optimization. An actively
studied problem is to obtain an unbiased stochastic derivative estimator for a discontinuous sample performance. In this talk, we propose a new method to estimate the derivative for the expectation of a discontinuous sample performance. The proposed estimator is unbiased and has an analytical form. Many derivative estimation problems in probability constraints, statistical quality control, and financial derivatives can be handled by the new method in a general framework. Exploiting the fact that our estimator can handle discontinuous sample performance, we discuss the particular case of gradient-based simulated maximum likelihood estimation (MLE) for estimating unknown parameters in a stochastic model without assuming that the likelihoods of the observations are available in closed form. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures.
We take the viewpoint that, when the input model is potentially misspecified and as such the consistency of MLE no longer holds, it
could be beneficial to fit the output data instead of the input data. In general, MLE is an asymptotic minimizer of the Kullback-Leibler (KL) between the conjectured model and the data. Thus, applying MLE on the output level attempts to minimize the statistical discrepancy between models and data when the output prediction accuracy is essential, which is often the case when building stochastic models. This idea of 'best fitting'  at the output level is similar to the training of machine'learning algorithms, which in recent years have been developed to find reliable representations of observed (output) data by statistical (econometric) models. In our talk, we will advocate the use of causal models rather than statistical ones.
Joint work with: Nanne Dieleman,  Michael C. Fu, Jian-Qiang Hu, Henry Lamm, and Yijie Peng

Fiona Sloothaak: Battery swapping stations for electric vehicles: a queueing perspective
In the last decade, there has been an increasing penetration of electric vehicles (EVs) as it is perceived as one of the more promising solutions to reduce carbon emission. Yet, the adoption of this technology remains slow, partly due to issues with long battery charging times. In this talk, we consider the concept of battery swapping stations where EV users can quickly exchange their almost depleted batteries by full batteries. We take a queueing perspective by modeling this framework as a closed queueing system operating in a Quality-and-Efficiency-Driven (QED) policy. This policy yields favorable effects: EV users experience low waiting times, while battery swapping stations do not needlessly keep extensively many spare batteries. Moreover, we show a state-space
collapse result for the setting where EV users are inclined to swap their batteries at the station that is least loaded (among the stations in its direct vicinity). This result implies a resource pooling effect takes place, causing all stations to be approximately equally busy at all times.

Jasper Goseling: Performance Bounds for Random Walks in the Positive Orthant
In this talk a a framework for constructing bounds on stationary performance measures of homogeneous random walks in the positive orthant using the Markov reward approach is presented. These bounds are established in terms of the stationary performance measure of a perturbed random walk whose stationary distribution is known explicitly. In particular, a construction of inhomogeneous boundary transition rates for the perturbed random walk is proposed. It is shown that for any given distribution that is a sum of geometric terms, inhomogeneous boundary transition rates can be constructed such that the given distribution is indeed the stationary distribution of the perturbed random walk. Moreover, an explicit expression for the error bound based on the inhomogeneous perturbation is given.
Joint work with Xinwei Bai

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