Related papers: Self-averaging property of queuing systems
This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting…
In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a…
We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…
A multi-channel queueing system is considered. The arriving requests differ in their type. Requests of each type arrive according to a Poisson process. The number of channels required for service with the rate equal to 1 depends of the…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a…
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…
A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…
In continuous time, customers arrive at random. Each waits until one of $c$ servers is available; each thereafter departs at random. The distribution of maximum line length of idle customers was studied over 25 years ago. We revisit two…
Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…
We study a multi-server queueing system with a periodic arrival rate and customers whose joining decision is based on their patience and a delay proxy. Specifically, each customer has a patience level sampled from a common distribution.…
This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/$\infty$ queue. They describe in particular the exponential dissipation of…
Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional…
This paper aims at semi-parametrically estimating the input process to a L\'evy-driven queue by sampling the workload process at Poisson times. We construct a method-of-moments based estimator for the L\'evy process' characteristic…
We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$…
In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…
We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…