Related papers: Mean Field Queues with Delayed Information
A Mean-Field theory is presented and applied to a Cellular Automata model of distributed packet-switched networks. It is proved that, under a certain set of assumptions, the critical input traffic is inversely proportional to the free…
We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…
This paper considers a communication system where a source sends time-sensitive information to its destination via queues in tandem. We assume that the arrival process as well as the service process (of each server) are memoryless, and each…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…
In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…
We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After…
Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…
Queueing theory is used for modeling biological processes, traffic flows and many more real-life situations. Beyond that, queues describe systems out of equilibrium and can thus be considered as minimal models of non-equilibrium statistical…
This article examines the queueing performance of communication systems that transmit encoded data over unreliable channels. A fading formulation suitable for wireless environments is considered where errors are caused by a discrete channel…
Load balancing plays a crucial role in many large scale systems. Several different load balancing principles have been proposed in the literature, such as Join-Shortest-Queue (JSQ) and its variations, or Join-Below-Threshold. We provide a…
The non-stationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large scale multi-server service systems that may experience customer abandonments, such as call centers, hospitals, and…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched to one of…
The blocking problem naturally arises in transportation systems as multiple vehicles with different itineraries share available resources. In this paper, we investigate the impact of the blocking problem to the waiting time at the…
Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical…