Related papers: Integer Sequences from Queueing Theory
We provide an efficient encoding of the natural numbers {0,1,2,3,...} as strings of nested parentheses {(),(()),(()()),((())),...}, or considered inversely, an efficient enumeration of such strings. The technique is based on the recursive…
Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…
In [13] and [14], we found so-called the reccurence diagram. This paper is the application of such recurrence diagram. As a first application for the reccurence diagram, we will re-compute the well-known moment series of the generating…
Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been…
The subject of this paper is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from observations of the queue--length process at the points of the…
We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue…
The theory of operator integrals is used to determine the moment operators of the Cartesian margins of the phase space observables generated by the mixtures of the number states. The moments of the $x$-margin are polynomials of the position…
This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…
The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…
We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…
This note describes several open questions concerning scaling limits of queue-length processes of symmetric queues in heavy traffic, distinguishing between service-time distributions with finite and infinite variance.
The problems arising when the moments of service time distributions, for which the MGinf queue system busy period and busy cycle become very easy to study, are presented and it is shown how to overcome them. The busy cycle renewal function…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
74 new integer sequences are introduced in number theory, and for each of them is given a characterization, followed by open problems. each one a general question: how many primes each sequence has.
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered…
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1} <= 2 t_i. A "Meeussen sequence" is an increasing sequence of positive integers (m_1,m_2,...) such that m_1=1, every nonnegative…