Related papers: On The Waiting Time for A M/M/1 Queue with Impatie…
We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait, and in which the server, upon becoming free when one or more…
In many cognitive radio applications, there are multiple types of message queues. Existing queueing analysis works in underlay CR networks failed to discuss packets heterogeneity. Therefore high priority packets with impatient waiting time…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
We consider a system with N unit-service-rate queues in tandem, with exogenous arrivals of rate lambda at queue 1, under a back-pressure (MaxWeight) algorithm: service at queue n is blocked unless its queue length is greater than that of…
In this paper, we study the maximum waiting time $\max_{i\leq N}W_i(\cdot)$ in an $N$-server fork-join queue with heavy-tailed services as $N\to\infty$. The service times are the product of two random variables. One random variable has a…
Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this…
We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been…
Consider a sequence X_1, X_2,... of i.i.d. uniform random variables taking values in the alphabet set {1,2,...,d}. A k-superpattern is a realization of X_1,...,X_t that contains, as an embedded subsequence, each of the non-order-isomorphic…
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…
The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to…
We present a new approach to the problem of enumerating permutations of length n that avoid a fixed consecutive pattern of length m. We use this idea to give explicit upper and lower bounds on the number of permutations avoiding a pattern…
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems…
There are two contributions to the literature in this note. Firstly, we point out that under some weak conditions the result in Swensen (1986) on the remaining loads in a GI/M/$c$ queue with impatient customers, derived under the assumption…
Consider the following birth and death process with the following infinitesimal transition probabilities {\lambda}(k) ={\lambda}/(1+k) and {\mu}(k) = {\mu}k with {\lambda},{\mu}> 0. This process has known as a discouragement queue [5].…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some…
Response times contain information about economically relevant but unobserved variables like willingness to pay, preference intensity, quality, or happiness. We provide a general characterization of the properties of latent variables that…
The growth of Machine-Type Communication (MTC) increases the relevance of queuing scenarios with deterministic service times. In this letter, we present a model for queues without waiting lines and with degenerate service time distributions…
The waiting time distribution $w(\tau)$, i.e. the probability for a delay $\tau$ between two subsequent transition (`jumps') of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled…
We study a random walk in a N dimensional hypercube and exhibit results about stopping times when N diverges. The first theorem discusses the time in which two coupling processes spend to meet. A corollary provides a majorant for the…