A note on networks of infinite-server queues

1981 ◽  
Vol 18 (2) ◽  
pp. 561-567 ◽  
Author(s):  
J. Michael Harrison ◽  
Austin J. Lemoine
Keyword(s):  
Steady State ◽  
Open Systems ◽  
External Source ◽  
Time Dependent ◽  
Infinite Server ◽  
Closed Systems ◽  
The Subject ◽  
Infinite Server Queues ◽  
Number Of Customers ◽  
Networks Of Queues

The subject of this paper is networks of queues with an infinite number of servers at each node in the system. Our purpose is to point out that independent motions of customers in the system, which are characteristic of infinite-server networks, lead in a simple way to time-dependent distributions of state, and thence to steady-state distributions; moreover, these steady-state distributions often exhibit an invariance with regard to distributions of service in the network. We consider closed systems in which a fixed and finite number of customers circulate through the network and no external arrivals or departures are permitted, and open systems in which customers originate from an external source according to a Poisson process, possibly non-homogeneous, and each customer eventually leaves the system.

A note on networks of infinite-server queues

1981 ◽  
Vol 18 (02) ◽  
pp. 561-567 ◽  
Author(s):  
J. Michael Harrison ◽  
Austin J. Lemoine
Keyword(s):  
Steady State ◽  
Open Systems ◽  
External Source ◽  
Time Dependent ◽  
Infinite Server ◽  
Closed Systems ◽  
The Subject ◽  
Infinite Server Queues ◽  
Number Of Customers ◽  
Networks Of Queues

The subject of this paper is networks of queues with an infinite number of servers at each node in the system. Our purpose is to point out that independent motions of customers in the system, which are characteristic of infinite-server networks, lead in a simple way to time-dependent distributions of state, and thence to steady-state distributions; moreover, these steady-state distributions often exhibit an invariance with regard to distributions of service in the network. We consider closed systems in which a fixed and finite number of customers circulate through the network and no external arrivals or departures are permitted, and open systems in which customers originate from an external source according to a Poisson process, possibly non-homogeneous, and each customer eventually leaves the system.

Experimental investigations of the externally heated valve engine model

2001 ◽  
Vol 215 (4) ◽  
pp. 487-494 ◽  
Author(s):  
L Brzeski ◽  
Z Kazimierski
Keyword(s):  
Computer Simulation ◽  
Measurement System ◽  
External Source ◽  
Time Dependent ◽  
Experimental Investigations ◽  
Pressure Transducers ◽  
Engine Model ◽  
Experimental Stand ◽  
The Subject ◽  
Valve Engine

The experimental investigations of the first model of the externally heated valve engine carried out during 1998-9 are the subject of this paper. The working gas of the engine is air. A detailed description of the engine equipped with two consecutively working heaters is given. Two kinds of heaters were constructed and investigated. The experimental stand and the measurement system are described. In this first stage of the engine investigation, electric radiators were used as the external source of heat. The main aim of the experimental investigations was focused on measurements of time-dependent pressures inside the expander and compressor cylinders. The pressures were measured by means of two kinds of pressure transducers (piezoresistive and piezoelectric) to get confidence in the obtained results. The conducted investigations prove that The engine model has an operating ability. Comparisons of the experimental and theoretical pressures inside the expander and compressor show a satisfactory agreement. It confirms that the engine operates according to the original thermodynamical cycle and exhibits the internal power and efficiency predicted by the computer simulation. The experiences gained during these investigations have been used to modify the engine model, which is outlined in this paper.

On the time-dependent occupancy and backlog distributions for the GI/G/∞ queue

1999 ◽  
Vol 36 (2) ◽  
pp. 558-569 ◽  
Author(s):  
H. Ayhan ◽  
J. Limon-Robles ◽  
M. A. Wortman
Keyword(s):  
Integral Equations ◽  
Numerical Evaluation ◽  
Queueing System ◽  
Sample Path ◽  
Time Dependent ◽  
Infinite Server ◽  
First Arrival ◽  
Number Of Customers

We consider an infinite server queueing system. An examination of sample path dynamics allows a straightforward development of integral equations having solutions that give time-dependent occupancy (number of customers) and backlog (unfinished work) distributions (conditioned on the time of the first arrival) for the GI/G/∞ queue. These integral equations are amenable to numerical evaluation and can be generalized to characterize GIX/G/∞ queue. Two examples are given to illustrate the results.

scholarly journals Infinite-server queues with Hawkes input

2018 ◽  
Vol 55 (3) ◽  
pp. 920-943 ◽  
Author(s):  
D. T. Koops ◽  
M. Saxena ◽  
O. J. Boxma ◽  
M. Mandjes
Keyword(s):  
Heavy Traffic ◽  
Probability Generating Function ◽  
Arrival Process ◽  
Hawkes Process ◽  
Asymptotic Results ◽  
Recursive Procedure ◽  
Infinite Server ◽  
Infinite Server Queues ◽  
Heavy Tailed ◽  
Number Of Customers

Abstract In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a Markovian nature. We obtain a system of differential equations that characterizes the joint distribution of the arrival intensity and the number of customers. Moreover, we provide a recursive procedure that explicitly identifies (transient and stationary) moments. Subsequently, we allow for non-Markovian Hawkes arrival processes and nonexponential service times. By viewing the Hawkes process as a branching process, we find that the probability generating function of the number of customers in the system can be expressed in terms of the solution of a fixed-point equation. We also include various asymptotic results: we derive the tail of the distribution of the number of customers for the case that the intensity jumps of the Hawkes process are heavy tailed, and we consider a heavy-traffic regime. We conclude by discussing how our results can be used computationally and by verifying the numerical results via simulations.

scholarly journals ANALYSIS OF MARKOV-MODULATED INFINITE-SERVER QUEUES IN THE CENTRAL-LIMIT REGIME

2015 ◽  
Vol 29 (3) ◽  
pp. 433-459 ◽  
Author(s):  
Joke Blom ◽  
Koen De Turck ◽  
Michel Mandjes
Keyword(s):  
Central Limit ◽  
Background Process ◽  
Infinite Server ◽  
Deviation Matrix ◽  
Finite State ◽  
Transition Rate Matrix ◽  
Service Rates ◽  
Infinite Server Queues ◽  
Markov Modulated ◽  
Number Of Customers

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q≡(qij)i,j=1d. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems (CLTs) for the number of customers in the system at time t≥0, in the asymptotic regime in which the arrival rates λi are scaled by a factor N, and the transition rates qij by a factor Nα, with α∈ℝ+. The specific value of α has a crucial impact on the result: (i) for α>1 the system essentially behaves as an M/M/∞ queue, and in the CLT the centered process has to be normalized by √N; (ii) for α<1, the centered process has to be normalized by N1−α/2, with the deviation matrix appearing in the expression for the variance.

On the time-dependent occupancy and backlog distributions for the GI/G/∞ queue

1999 ◽  
Vol 36 (02) ◽  
pp. 558-569
Author(s):  
H. Ayhan ◽  
J. Limon-Robles ◽  
M. A. Wortman
Keyword(s):  
Integral Equations ◽  
Numerical Evaluation ◽  
Queueing System ◽  
Sample Path ◽  
Time Dependent ◽  
Infinite Server ◽  
First Arrival ◽  
Number Of Customers

We consider an infinite server queueing system. An examination of sample path dynamics allows a straightforward development of integral equations having solutions that give time-dependent occupancy (number of customers) and backlog (unfinished work) distributions (conditioned on the time of the first arrival) for the GI/G/∞ queue. These integral equations are amenable to numerical evaluation and can be generalized to characterize GI X /G/∞ queue. Two examples are given to illustrate the results.

scholarly journals Ground- and excited-state characteristics in photovoltaic polymer N2200

RSC Advances ◽  
2021 ◽  
Author(s):  
Guanzhao Wen ◽  
Xianshao Zou ◽  
Rong Hu ◽  
Jun Peng ◽  
Zhifeng Chen ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Excited State ◽  
Steady State ◽  
Excited States ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Time Dependent ◽  
Functional Theory ◽  
Time Resolved ◽  
Dependent Density

Ground- and excited-states properties of N2200 have been studied by steady-state and time-resolved spectroscopies as well as time-dependent density functional theory calculations.

Sign in / Sign up

Export Citation Format

Share Document