Related papers: Upper and Lower Class Functions for Maximum Likeli…
In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the…
This paper studies the heavy-traffic asymptotics for the multiclass FIFO M${}^X$/G/1 queue. We first derive the probability generating function of the joint queue length distribution. Using the probability generating function, we then…
We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground-background scheduling policy in heavy traffic. The growth rate of its mean, as well as the limiting distribution, are…
We consider a multi-class single server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of…
This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this…
In network quality of service provisioning, premium services generally require to keep a very small loss probability, which is infeasible to measure directly. The proposed virtual queue scheme estimates the small packet loss probability of…
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…
This paper deals with a single-server queue with modulated arrivals, service requirements and service capacity. In our first result, we derive the mean of the total workload assuming generally distributed service requirements and any…
Since Age of Information (AoI) has been proposed as a metric that quantifies the freshness of information updates in a communication system, there has been a constant effort in understanding and optimizing different statistics of the AoI…
We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it changes…
How should we schedule jobs to minimize mean queue length? In the preemptive M/G/1 queue, we know the optimal policy is the Gittins policy, which uses any available information about jobs' remaining service times to dynamically prioritize…
Classification tasks are common across many fields and applications where the decision maker's action is limited by resource constraints. In direct marketing only a subset of customers is contacted; scarce human resources limit the number…
In this paper we establish square-function estimates on the double and single layer potentials for divergence-form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This…
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…
We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…
Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover,…
Solving a Riccati equation, induced by the study of the transient behaviour of the MGInf queue system, a collection of service times distributions is determined. For the MGInf queue, which service time distribution is a member of that…
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…
We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing…
Serving systems for Large Language Models (LLMs) improve throughput by processing several requests concurrently. However, multiplexing hardware resources between concurrent requests involves non-trivial scheduling decisions. Practical…