Related papers: Integer Sequences from Queueing Theory

Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…

Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle…

Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…

We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…

We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted…

We prove a number of limiting distributions for statistics for unimodal sequences of positive integers by adapting a probabilistic framework for integer partitions introduced by Fristedt. The difficulty in applying the direct analogue of…

Interacting networks are different in nature to single networks. The study of queuing processes on interacting networks is underdeveloped. It presents new mathematical challenges and is of importance to applications. This area of operations…

We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…

This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…

Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…

In this article, for modelling numeral systems, the operator approach, which is introduced in [25], is generalized for a certain case. An example of such numeral systems is introduced and considered.

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through…

Different kinds of models are used to study various natural and technical phenomena. Usually, the researcher is limited to using a certain kind of model approach, not using others (or even not realizing the existence of other model…

Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single…

We define impulse response sequence in the set of all linear recurring sequences satisfying a linear recurrence relation of order $r$. The generating function and expression of the impulse response sequence are presented. Some identities of…

In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…