Related papers: L\'evy-driven Fluid Queue with Server Breakdowns a…
Due to the stochastic nature of departure operations, working at full capacity makes major US airports very sensitive to uncertainties. Consequently, airport ground operations face critically congested taxiways and long runway queues. In…
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…
The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. The server goes on for a vacation if the inactivity prolongs more than the vacation trigger duration. Once the…
We consider many-server queueing systems with heterogeneous exponential servers and renewal arrivals. The service rate of each server is a random variable drawn from a given distribution. We develop a framework for analyzing the heavy…
The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence…
In this short communication we study a fluid queue with a finite buffer. The performance measure we are interested in is the occupation time over a finite time period, i.e., the fraction of time the workload process is below some fixed…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the…
We consider queueing systems with n parallel queues under a Join the Shortest Queue (JSQ) policy in the Halfin-Whitt heavy traffic regime. We use the martingale method to prove that a scaled process counting the number of idle servers and…
We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding…
In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…
Drone delivery systems violate a core assumption in classical queueing models: server capacity is not fixed. Drones (servers) periodically must recharge, creating random fluctuations in service availability. We introduce an Erlang--S$^{*}$…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network…
This paper presents a new method for deriving the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive L\'evy input. The priority of a non-atomic customer (particle) is a function of their class…
Understanding the detailed queueing behavior of a networking session is critical in enabling low-latency services over the Internet. Especially when the packet arrival and service rates at the queue of a link vary over time and moreover…
In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…