Related papers: Asymptotics of Queue Length Distributions in Prior…
We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without…
This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves…
We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation…
This short communication considers an infinite-server system with overdispersed input. The objective is to identify the exact tail asymptotics of the number of customers present at a given point in time under a specific scaling of the model…
The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in…
We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally…
We analyze the time-dependent behavior of an $M/M/c$ priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace…
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 Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…
We study the exact asymptotics for the distribution of the first time $\tau_x$ a L\'evy process $X_t$ crosses a negative level $-x$. We prove that $\mathbf P(\tau_x>t)\sim V(x)\mathbf P(X_t\ge 0)/t$ as $t\to\infty$ for a certain function…
When decomposing the total orbit into $N$ sub-orbits (or simply orbits) related to each of $N$ servers and through comparing the numbers of customers in these orbits, we introduce a retrial supermarket model of $N$ identical servers, where…
We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals…
In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…
We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…
Motivated by applications in computing and telecommunication systems, we investigate the problem of estimating p-quantile of steady-state sojourn times in a single-server multi-class queueing system with non-preemptive priorities for p…
Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the…