Related papers: Stochastic Monotonicity of Markovian Multi-class Q…
The Multi-class Queueing Network (McQN) arises as a natural multi-class extension of the traditional (single-class) Jackson network. In a single-class network subcriticality (i.e. subunitary nominal workload at every station) entails…
Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for…
In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any}…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
We re-visit the global - relative to control policies - stability of multiclass queueing networks. In these, as is known, it is generally insufficient that the nominal utilization at each server is below 100%. Certain policies, although…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are…
In this paper, we characterize the stability region of multi-queue multi-server (MQMS) queueing systems with stationary channel and packet arrival processes. Toward this, the necessary and sufficient conditions for the stability of the…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
The basic adjoint relationship (BAR) approach is an analysis technique based on the stationary equation of a Markov process. This approach was introduced to study heavy-traffic, steady-state convergence of generalized Jackson networks in…
Network capacity region of multi-queue multi-server queueing system with random ON-OFF connectivities and stationary arrival processes is derived in this paper. Specifically, the necessary and sufficient conditions for the stability of the…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…
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 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 analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model…
Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a…