INFORMS 2021 Program Book

INFORMS Anaheim 2021

MB11

2 - Adapting First-break-then-schedule to Time-relaxed Sports Timetabling

2 - Ergodicity of High Dimensional Reflected Diffusions Sayan Banerjee, University of North Carolina-Chapel Hill, Chapel Hill, NC, 27517-4073, United States, Amarjit Budhiraja, Brendan Brown We will discuss ergodicity properties of high dimensional reflected diffusions that arise as scaling limits of queueing networks in heavy traffic and interacting particle systems. As the system dimension increases, it (naturally) takes longer for the entire diffusion to approach equilibrium. However, we will present several scenarios where local statistics exhibit dimension-free convergence rates. We will explore connections of such phenomena with a discrete time Markov chain arising out of the reflection structure of these diffusions. The Atlas model, which is a `critical case’ in a certain sense, will also be discussed. The infinite Atlas model has uncountably many stationary measures, and we will obtain sufficient conditions for the initial conditions to lie in the domain of attraction of each of these measures. MB10 CC Room 304B In Person: New Applications of Queueing Theory General Session Chair: Jamol Pender, Cornell University, Ithaca, NY, 14850, United States 1 - Stochastic Models for Community Bail Funds Jamol Pender, Cornell University, Ithaca, NY, 14850, United States Bail funds have a long history of helping those who cannot afford bail in order to wait for trial at home. Not only have bail funds help release those who cannot afford their bail, but it also has had an immeasurable impact on the decision of the defendant. In this paper, we consider the first stochastic model for a community bail fund. To build our stochastic model, we uniquely combine insurance models and infinite server queues to model the bail fund. As a result, we are able to not only model the bail fund, but also assess the impact that a bail fund will have on a community. In this regard, we determine the amount of money a county might save by implementing a bail fund. Although, we cannot measure the impact on the human spirit, we can start to understand in a rigorous way, the impact of the bail fund on the community. 2 - Queues with Updating Information Philip Doldo, Cornell University, Ithaca, NY, 14853, United States Many service systems provide customers with information about the system so that customers can make an informed decision about whether to join or not. Many of these systems provide information in the form of an update. Thus, the information about the system is updated periodically in increments of size . It is known that these updates can cause oscillations in the resulting dynamics. However, it is an open problem to explicitly characterize the size of these oscillations when they occur. In this paper, we solve this open problem and show how to exactly compute the amplitude of these oscillations via a fixed point equation. We also compute closed form approximations via Taylor expansions and show that these approximations are very accurate, especially when is large. Our analysis provides new insight for systems that use updates as a way of disseminating information to customers. MB11 CC Room 304C In Person: Emerging Research in Behavioral Operations Management General Session Chair: Samer Charbaji, University of Michigan, Ann Arbor, MI, 48105, United States Co-Chair: Blair Flicker, University of South Carolina, Columbia, SC, 29208-4011, United States 1 - Team Composition and Cooperation in Queueing Systems homogenous servers. Particularly, servers specialize in one type of task, which, in our model, implies a lower cost of effort while processing that type of task. The effort chosen by servers determines the processing time of a task. We show that, theoretically, in the implied stochastic dynamic game, the choice of high effort can be sustained in the subgame-perfect equilibrium if the arrival rate is high enough regardless of team composition. Further, for intermediate arrival rates, homogeneous teams perform better than heterogeneous teams when the types of arriving tasks are independent or are serially positively correlated, and heterogeneous teams perform better in the presence of negative serial correlation in the types of tasks. Mouli Modak, Purdue University, West Lafayette, IN, United States, Yaroslav Rosokha, Masha Shunko We study a single-queue system in which heterogeneous tasks arrive stochastically and are processed by a team of either heterogeneous or

David Van Bulck, Ghent University, Belgium, Dries Goossens A popular technique to construct sports timetables is the first-break-then- schedule approach which first determines for each time slot whether a team plays at home or away, after which its opponent is determined. This approach, however, is only applicable to time-constrained schedules where each team approximately plays one game per time slot. In this talk, we adapt the first-break- then-schedule approach to time-relaxed competitions, like the NBA or NHL. In particular, we propose to first determine the so-called game-off-day patterns (GOPs) after which we construct a compatible timetable. We settle the computational complexity of this approach and show that it outperforms existing approaches to optimize rest times and differences in games played when the total number of off days is no more than twice the number of games per team. 3 - In Game Win Probability Models for Canadian Football Stephen Hill, University of North Carolina-Wilmington, Congdon Hall, Wilmington, NC, 28403-5611, United States In game win probability models are used to estimate the probability that each team in a game, at any point in a game, will ultimately win. Such models have been built for a variety of sports, however, no such models have been proposed for Canadian football. In this work in game win probability models for Canadian football are described along with several extensions. 4 - Geographic Design of Sports Leagues to Optimize Driving Time and Competitiveness Zhuo Chen, Southern Methodist Univesity, Dallas, TX, United States Club sports in metro areas are popular nowadays, however there are key concerns for organizers, which are reducing driving time due to teams commuting to facilities in different regions while keeping league divisions competitive. A three-step approach is adopted to solve this problem. Driving time data between each location is analyzed initially, and clubs are split into several groups accordingly. Teams are assigned to groups based on their location and ranking. And these two processes are merged in the end to find the best solution. Applying this process to the Tennis Competitors of Dallas, a large and well-established sports league in the Dallas area, we demonstrate that this process can rearrange existing groups in a way that not only shortens the travel time for players, but also maintains an acceptable level of competition. 5 - Demystifying the Crystal Ball in Professional Sports Eli Olinick, Southern Methodist University, Dallas, TX, 75275- 0123, United States, Mark Husted, Alexandra M. Newman Mixed integer programming (MIP) models for determining magic numbers (first place and playoff clinch and elimination) for a variety of professional sports have been proposed in the literature and implemented in practice. Often the proof that a magic number is correct relies on showing that a MIP model is infeasible. So, although fans enjoy tracking these numbers, most must take them on faith. We discuss strategies for and challenges of automating the process of justifying magic numbers to sports fans in plain English. MB09 CC Room 303D In Person: Large-Scale Analysis of Stochastic Systems General Session Chair: Debankur Mukherjee, Georgia Institute of Technology, Georgia Institute of Technology 1 - Large-scale Parallel Server Systems with Multi-component Jobs Alexander Stolyar, University of Illinois at Urbana-Champaign, Urbana, IL, 61801-2925, United States, Vsevolod Shneer A broad class of parallel server systems is considered, for whichwe prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel- on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and limits. It relies almost exclusively on three fundamental properties of the model: monotonicity; work conservation; the property that, on average, “new arriving workload prefers to go to servers with lower workloads.

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