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In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a…
In this paper we present a mathematical model of the train dynamics in a linear metro line system with demand-dependent run and dwell times. On every segment of the line, we consider two main constraints. The first constraint is on the…
We introduce Markov Decision Processing Networks (MDPNs) as a multiclass queueing network model where service is a controlled, finite-state Markov process. The model exhibits a decision-dependent service process where actions taken…
We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…
We consider a switched network, a fairly general constrained queueing network model that has been used successfully to model the detailed packet-level dynamics in communication networks, such as input-queued switches and wireless networks.…
The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or other social processes such as norm development. This leads to…
We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the…
Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…
We investigate some of the properties and extensions of a dynamic innovation network model recently introduced in \citep{koenig07:_effic_stabil_dynam_innov_networ}. In the model, the set of efficient graphs ranges, depending on the cost for…
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…
Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek to reap benefits of parallelization, albeit subject to a synchronization constraint at the output. Fork-Join (FJ) queuing models are used to analyze such systems.…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
In this work, we study the effects of finite buffers on the throughput and delay of line networks with erasure links. We identify the calculation of performance parameters such as throughput and delay to be equivalent to determining the…
By analyzing energy-efficient management of data centers, this paper proposes and develops a class of interesting {\it Group-Server Queues}, and establishes two representative group-server queues through loss networks and impatient…
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…
While queueing network models are powerful tools for analyzing service systems, they traditionally require substantial human effort and domain expertise to construct. To make this modeling approach more scalable and accessible, we propose a…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…