Related papers: The max-plus algebra approach in modelling of queu…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…
The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…
This paper proposes a novel dynamical model for determining clearing payments in financial networks. We extend the classical Eisenberg-Noe model of financial contagion to multiple time periods, allowing financial operations to continue…
Strategic customer behavior is strongly influenced by the level of information that is provided to customers. Hence, to optimize the design of queueing systems, many studies consider various versions of the same service model and compare…
We consider data losses in a single node of a packet-switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router.…
We present in this article traffic flow and control models for the train dynamics in metro lines. The first model, written in the max-plus algebra, takes into account minimum running, dwell and safety time constraints, without any control…
In this paper the infinite server queue model in semi-Markov random environment with k Markov arrival streams, random resources of customers, and catastrophes is considered. After catastrophes occur, all customers in the model are flashed…
We extend the Markov additive methodology developed in [Ann. Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the sharp asymptotics of the steady state probability of a queueing network when one of the nodes…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
Queueing networks are typically modelled assuming that the arrival process is exogenous, and unaffected by admission control, scheduling policies, etc. In many situations, however, users choose the time of their arrival strategically,…
In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…
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…
In the present paper the infinite-server MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival of catastrophes is considered. The joint generating functions (PGF) of transient and…
Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…
Over the last two decades, network science has greatly advanced our understanding of how the collective behaviors of a complex system emerge from the interactions among its basic units. Multiplex networks, i.e. networks with many layers,…
We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling…
This paper investigates a partially observable queueing system with $N$ nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest…
Multilayer networks describe well many real interconnected communication and transportation systems, ranging from computer networks to multimodal mobility infrastructures. Here, we introduce a model in which the nodes have a limited…
Fork-join network is a class of queueing networks with applications in manufactory, healthcare and computation systems. In this paper, we develop a simulation algorithm that (1) generates i.i.d. samples of the job sojourn time, jointly with…