Related papers: $M|G|\infty$ Queue Busy Cycle Renewal Function
We consider optimizing average queueing delay and average power consumption in a nonpreemptive multi-class M/G/1 queue with dynamic power control that affects instantaneous service rates. Four problems are studied: (1) satisfying per-class…
In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…
Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…
To study the impacts of price responsive demand on the electric power system requires better load models. This paper discusses the modeling of uncertainties in aggregated thermostatically controlled loads using a state queueing (SQ) model.…
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…
The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this…
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…
We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit…
Group-buying auction has become a popular marketing strategy in the last decade. In this paper, a stochastic model is developed for an inventory system subjects to demands from group-buying auctions. The model discussed here takes into the…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions…
In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…
The mathematics of the finite single server queue with Poisson input and semi-Markov service times($M/SM/1/b$) is similar to that used for $BMAP/G/1/b$ systems. This observation results in new analytical formulas for a queue size in the…
Generating high-quality schedules for a rotating workforce is a critical task in all settings where a certain staffing level must be guaranteed beyond the capacity of single employees, such as for instance in industrial plants, hospitals,…
We present a novel mathematical framework for computing the number of maintenance cycles in a system with critical and non-critical components, where "critical" (CR) means that the component's failure is fatal for the system's operation and…
Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but also allows fluctuation measurements which may reveal the structure and dynamics of the underlying biochemical network.…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
The main goals of a switch scheme are high utilization, low queuing delay and fairness. To achieve high utilization the switch scheme can maintain non-zero (small) queues in steady state which can be used if the sources do not have data to…
Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…
Motivated by demand prediction for the custodial prison population in England and Wales, this paper describes an approach to the study of service systems using infinite server queues, where the system has non-empty initial state and the…