Related papers: Exclusive Queueing Processes and their Application…
The theory community has proposed several new heap variants in the recent past which have remained largely untested experimentally. We take the field back to the drawing board, with straightforward implementations of both classic and novel…
We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…
In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in…
In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…
We introduce a new interacting particle system on $\mathbb{Z}$, \emph{slowed $t$-TASEP}. It may be viewed as a $q$-TASEP with additional position-dependent slowing of jump rates depending on a parameter $t$, which leads to discrete and…
This note describes several open questions concerning scaling limits of queue-length processes of symmetric queues in heavy traffic, distinguishing between service-time distributions with finite and infinite variance.
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition…
We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue…
Service systems like data centers and ride-hailing are popularly modeled as queueing systems in the literature. Such systems are primarily studied in the steady state due to their analytical tractability. However, almost all applications in…
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…
The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…
Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or branch-and-bound. However, a classical priority queue constitutes a severe bottleneck…
Perimeter control is an effective urban traffic management strategy that regulates inflow to congested urban regions using aggregate network dynamics. While existing approaches primarily optimize system-level efficiency, such as total…
We present a novel approach to understand vehicular traffic jams by studying a simple model, Elementary Cellular Automaton Rule 184 (ECA 184). Using key traffic observables, such as the total delay and relaxation time, as well as…
We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…
We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes…