Related papers: Transient error approximation in a L\'evy queue
This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…
To boost energy saving for the general delay-tolerant IoT networks, a two-stage and single-relay queueing communication scheme is investigated. Concretely, a traffic-aware $N$-threshold and gated-service policy are applied at the relay. As…
Network capacity region of multi-queue multi-server queueing system with random ON-OFF connectivities and stationary arrival processes is derived in this paper. Specifically, the necessary and sufficient conditions for the stability of the…
Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack…
Real-time communication applications require consistently low latency, which is often disrupted by latency spikes caused by competing flows, especially Web traffic. We identify the root cause of disruptions in such cases as the mismatch…
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy…
A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…
On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. L\'evy on-off intermittency is…
In recent years, there is a growing research about queueing models with customers who choose their service durations. In general, the model assumptions in the existing literature imply that every customer knows his service demand when he…
Motivated by a wide variety of applications, this paper introduces a general class of networks of stochastic loss systems in which congestion renders lost revenue due to customers or jobs being permanently removed from the system. We seek…
We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or…
We introduce system norms which assess transient behavior of stable Linear Time-Invariant (LTI) systems. This allows us to address undesired responses to initial conditions, finite resource consumption signals, or persistent perturbations.…
We obtain the first passage time density for a L\'{e}vy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding…
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…
We consider a set of flows passing through a set of servers. The injection rate into each flow is governed by a flow control that increases the injection rate when all the servers on the flow's path are empty and decreases the injection…
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…