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This paper studies the equilibrium behavior of customers in the Geo/Geo/1 queueing system with multiple working vacations. The arriving customers decide whether to join or to balk the queueing systems based on the information of the queue…
We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the…
We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value $b$, we provide the limiting distribution for the amount of time that the workload process…
The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket…
This paper examines a single-server queueing system that serves both scheduled and strategic walk-in customers. The service discipline follows a first-come, first-served policy, with scheduled customers granted non-preemptive priority. Each…
Imagine, you enter a grocery store to buy food. How many peopledo you overlap with in this store? How much time do you overlap witheach person in the store? In this paper, we answer these questions bystudying the overlap times between…
We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding…
We consider a queueing system composed of a dispatcher that routes deterministically jobs to a set of non-observable queues working in parallel. In this setting, the fundamental problem is which policy should the dispatcher implement to…
We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…
We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for…
We consider a Markovian single server queue with impatient customers. There is a customer abandonment cost and a holding cost for customers in the system. We consider two versions of the problem. In the first version, customers pay a reward…
We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…
This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on…
We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…
We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…
We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…
A result of Ward and Glynn (2005) asserts that the sequence of scaled offered waiting time processes of the $GI/GI/1+GI$ queue converges weakly to a reflected Ornstein-Uhlenbeck process (ROU) in the positive real line, as the traffic…
The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…
We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…