Related papers: A Polling Model with Smart Customers
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
The paper considers a queueing system with limited processor sharing. No more than n jobs may be served simultaneously. This system may be used for modeling bandwidth sharing in wireless communication systems and processes of service in…
In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\lambda n$, where $\lambda = \lambda (n) \in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers…
We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…
The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…
We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit…
This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
In this article we classify discrete-time queues based on scheduling rules and observation epochs combinations. This classification leads to {\em coherent}, {\em sub-coherent}, and {\em super-coherent} systems when {\em observed} waiting…
This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…
It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…
We consider a large distributed service system consisting of $n$ homogeneous servers with infinite capacity FIFO queues. Jobs arrive as a Poisson process of rate $\lambda n/k_n$ (for some positive constant $\lambda$ and integer $k_n$). Each…
We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local…
In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a…
Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to…
This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…
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…
Strategic customer behavior is strongly influenced by the level of information that is provided to customers. Hence, to optimize the design of queueing systems, many studies consider various versions of the same service model and compare…
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…
We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…