Related papers: Integer Sequences from Queueing Theory
For delta operator $aD-bD^{p+1}$ we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case $D-\frac{1}{2}D^2$ we show that the corresponding Bessel-Carlitz polynomials are moments of the…
The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are…
Characterizations of finite sequences $\beta_{1}<\cdots<\beta_{n}$ representing expected values of order statistics from a random sample of size $n$ are given. As a by-product, a characterization of binomial mixtures, when the mixing random…
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…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…
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…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
We consider sequences of operators $U_n:L^1(X)\to M(X)$, where $X$ is a space of homogeneous type. Under certain conditions on the operators $U_n$ we give a complete characterization of convergence (divergence) sets of functional sequences…
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Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of…
In this paper we consider an M/G/1-type queue fed by a finite customer-pool. In terms of transforms, we characterize the time-dependent distribution of the number of customers and the workload, as well as the associated waiting times.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
We introduce features for massive data streams. These stream features can be thought of as "ordered moments" and generalize stream sketches from "moments of order one" to "ordered moments of arbitrary order". In analogy to classic moments,…