Related papers: Poisson Hail on a Hot Ground
In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times).…
We present a conception of the slow diffusion processes in the Euclidean spaces $\Bbb R^m, \; m\ge 1$, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow…
This paper analyzes a service system modeled as a single-server queue, in which the service provider aims to dynamically maximize the expected revenue per unit of time. This is achieved by constructing a stochastic gradient descent…
This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if…
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 fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and upon arrival decide whether or not to purchase…
In discrete time, customers arrive at random. Each waits until one of three servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. Algebraic expressions obtained for the…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…
In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…
Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…
This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems,…
Melamed's theorem states that for a Jackson queuing network, the equilibrium flow along a link follows Poisson distribution if and only if no customers can travel along the link more than once. Barbour \& Brown~(1996) considered the Poisson…
A key operational challenge for call centers is to decide, in real time, which waiting customer should be served by which available agent. This is known as skill-based routing, and the decision becomes especially difficult in large systems…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…
Staffing rules are an essential management tool in service industries for meeting target service levels. The square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that…
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…
This paper studies a spatial queueing system on a circle, polled at random locations by a myopic server that can only observe customers in a bounded neighborhood. The server operates according to a greedy policy, always serving the nearest…
We analyze the performance of an interference-limited, decode-and-forward, cooperative relaying system that comprises a source, a destination, and $N$ relays, placed arbitrarily on the plane and suffering from interference by a set of…