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We consider a coupled Polya's urn scheme for social dynamics on networks. Agents hold continuum-valued opinions on a two-state issue and randomly converse with their neighbors on a graph, agreeing on one of the two states. The probability…

Probability · Mathematics 2023-07-04 Andrew Melchionna

Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the…

Optimization and Control · Mathematics 2016-10-07 Jamol Pender , Richard H. Rand , Elizabeth Wesson

We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers…

Statistics Theory · Mathematics 2007-06-13 Enrico Carlini , Fabio Rapallo

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they…

Dynamical Systems · Mathematics 2021-08-11 Philip Doldo , Jamol Pender , Richard Rand

Consider $n$ players whose "scores" are independent and identically distributed values $\{X_i\}_{i=1}^n$ from some discrete distribution $F$. We pay special attention to the cases where (i) $F$ is geometric with parameter $p\to0$ and (ii)…

Probability · Mathematics 2012-04-12 Julia Eaton , Anant Godbole , Betsy Sinclair

Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queueing systems, namely non-stationary arrivals. Non-stationary…

Dynamical Systems · Mathematics 2017-01-20 Jamol Pender , Richard H. Rand , Elizabeth Wesson

We consider a service system where agents are invited on-demand. Customers arrive exogenously as a Poisson process and join a customer queue upon arrival if no agent is available. Agents decide to accept or decline invitations after some…

Probability · Mathematics 2015-10-27 Guodong Pang , Alexander L. Stolyar

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Probability · Mathematics 2020-01-10 Yana Belopolskaya , Guodong Pang , Andrey Sarantsev , Yurii Suhov

We describe a queueing model where service is allocated as a function of queue sizes. We consider allocations policies that are insensitive to service requirements and have a maximal stability region. We take a limit where the queueing…

Probability · Mathematics 2010-07-20 N. S. Walton

We consider the serve-the-longest-queue discipline for a multiclass queue with buffers of equal size, operating under (i) the conventional and (ii) the Halfin-Whitt heavy traffic regimes, and show that while the queue length process'…

Probability · Mathematics 2016-01-07 Rami Atar , Subhamay Saha

It's a situation everyone dreads. A road is down to one lane for repairs. Traffic is let through one way until the backlog clears and then traffic is let through the other way to clear that backlog and so on. When stuck in a very long queue…

Probability · Mathematics 2024-01-09 Robert D. Foley , David R. McDonald

The supermarket model refers to a system with a large number of queues, where new customers choose d queues at random and join the one with the fewest customers. This model demonstrates the power of even small amounts of choice, as compared…

Performance · Computer Science 2022-02-18 Michael Mitzenmacher , Matteo Dell'Amico

P\'olya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of…

Probability · Mathematics 2019-12-04 Cyril Banderier , Philippe Marchal , Michael Wallner

We consider a system consisting of a server alternating between two service points. At both service points there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Ivo J. B. F. Adan

We analyse a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." The replica analysis clarifies that the preferential urn model with…

Disordered Systems and Neural Networks · Physics 2009-11-11 Jun Ohkubo , Muneki Yasuda , Kazuyuki Tanaka

A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served…

Optimization and Control · Mathematics 2022-07-26 Rahul Vaze , Jayakrishnan Nair

Motivated by health care systems with repeated services that have both personnel (nurse and physician) and space (beds) constraints, we study a restricted version of the Erlang-R model. The space restriction policies we consider are…

Motivated by applications in online marketplaces such as ride-hailing platforms and payment channel networks, we study a single-server queue with state-dependent arrival control. The service operator dynamically chooses the arrival rate as…

Optimization and Control · Mathematics 2026-02-03 Tianze Qu , Sushil Mahavir Varma

We study randomized experiments in a service system when stochastic congestion can arise from temporarily limited supply or excess demand. Such congestion gives rise to cross-unit interference between the waiting customers, and analytic…

Systems and Control · Electrical Eng. & Systems 2026-02-17 Shuangning Li , Ramesh Johari , Xu Kuang , Stefan Wager

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…

Probability · Mathematics 2010-03-17 James B. Martin , Balaji Prabhakar