Related papers: Lowest priority waiting time distribution in an ac…

We study the sojourn time in a queueing system with a single exponential server, serving a Poisson stream of customers in order of arrival. Service is provided at low or high rate, which can be adapted at exponential inspection times. When…

In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…

This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…

We study the necessity of predictive information in a class of queueing admission control problems, where a system manager is allowed to divert incoming jobs up to a fixed rate, in order to minimize the queueing delay experienced by the…

Appointment scheduling problems under uncertainty encounter a fundamental trade-off between cost minimization and customer waiting times. Most existing studies address this trade-off using a weighted sum approach, which puts little emphasis…

The Erlang loss formula, also known as the Erlang B formula, has been known for over a century and has been used in a wide range of applications, from telephony to hospital intensive care unit management. It provides the blocking…

We consider a point process $i+\xi_i$, where $i\in \bZ$ and the $\xi_{i}$'s are i.i.d. random variables with variance $\sigma^{2}$. This process, with a suitable rescaling of the distribution of $\xi_i$'s, converges to the Poisson process…

A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…

We study the problem of scheduling delay-sensitive jobs over spot and on-demand cloud instances to minimize average cost while meeting an average delay constraint. Jobs arrive as a general stochastic process, and incur different costs based…

This paper approaches the application of the waiting model with Poisson inputs and priorities in the port activity. The arrival of ships in the maritime terminal is numerically modelled, and specific parameters for the distribution…

Kingman has shown, under very weak conditions on the interarrival- and sevice-time distributions, that First-Come-First-Served minimizes the variance of the waiting time among possible service disciplines. We show, under the same…

This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…

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…

A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served…

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…

We consider the problem of dynamically scheduling J jobs on N processors for non-preemptive execution where the value of each job (or the reward garnered upon completion) decays over time. All jobs are initially available in a buffer and…

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…

We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…

We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…

This article analyzes two classes of job selection policies that control how a network of autonomous aerial vehicles delivers goods from depots to customers. Customer requests (jobs) occur according to a spatio-temporal stochastic process…