Related papers: A queueing model with independent arrivals, and it…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
Understanding the detailed queueing behavior of a networking session is critical in enabling low-latency services over the Internet. Especially when the packet arrival and service rates at the queue of a link vary over time and moreover…
This paper develops fluid limits for nonstationary many-server loss systems with general service-time distributions. For the zero-buffer $M_t/G/n/n$ queuing model, we prove a functional strong law of large numbers for the fraction of busy…
A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the…
In transportation and other types of facilities, various queues arise when the demands of service are higher than the supplies, and many point and fluid queue models have been proposed to study such queueing systems. However, there has been…
In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account…
We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from…
We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…
We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes…
We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial…
We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…
In this paper, we consider an $N$-queue overloaded polling network attended by a single cyclically roving server. Upon the completion of his service, a customer is either routed to another queue or leaves the system. All the switches are…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
Bounding the queue length in a multiserver queue is a central challenge in queueing theory. Even for the classical $G/G/n$ queue with homogeneous servers, it is highly non-trivial to derive a simple and accurate bound for the steady-state…