scholarly journals Nonparametric Estimation of Service Time Characteristics in Infinite-Server Queues with Nonstationary Poisson Input

2019 ◽  
Vol 9 (3) ◽  
pp. 183-207
Author(s):  
Alexander Goldenshluger ◽  
David T. Koops
Keyword(s):  
Nonparametric Estimation ◽  
Service Time ◽  
Infinite Server ◽  
Poisson Input ◽  
Infinite Server Queues

On joint queue-length characteristics in infinite-server tandem queues with heavy traffic

1987 ◽  
Vol 19 (02) ◽  
pp. 474-486 ◽  
Author(s):  
Volker Schmidt
Keyword(s):  
Stationary Distribution ◽  
Simple Proof ◽  
Shot Noise ◽  
Queue Length ◽  
Heavy Traffic ◽  
Asymptotic Formulas ◽  
Tandem Queues ◽  
Infinite Server ◽  
Poisson Input ◽  
Infinite Server Queues

For m infinite-server queues with Poisson input which are connected in a series, a simple proof is given of a formula derived in [3] for the generating function of the joint customer-stationary distribution of the successive numbers of customers a randomly chosen customer finds at his arrival epochs at two queues of the system. In this connection, a shot-noise representation of the queue-length characteristics under consideration is used. Moreover, using this representation, corresonding asymptotic formulas are derived for infinite-server tandem queues with general high-density renewal input.

On joint queue-length characteristics in infinite-server tandem queues with heavy traffic

1987 ◽  
Vol 19 (2) ◽  
pp. 474-486 ◽  
Author(s):  
Volker Schmidt
Keyword(s):  
Stationary Distribution ◽  
Simple Proof ◽  
Shot Noise ◽  
Queue Length ◽  
Heavy Traffic ◽  
Asymptotic Formulas ◽  
Tandem Queues ◽  
Infinite Server ◽  
Poisson Input ◽  
Infinite Server Queues

For m infinite-server queues with Poisson input which are connected in a series, a simple proof is given of a formula derived in [3] for the generating function of the joint customer-stationary distribution of the successive numbers of customers a randomly chosen customer finds at his arrival epochs at two queues of the system. In this connection, a shot-noise representation of the queue-length characteristics under consideration is used. Moreover, using this representation, corresonding asymptotic formulas are derived for infinite-server tandem queues with general high-density renewal input.

Networks of infinite-server queues with nonstationary Poisson input

1993 ◽  
Vol 13 (1-3) ◽  
pp. 183-250 ◽  
Author(s):  
William A. Massey ◽  
Ward Whitt
Keyword(s):  
Infinite Server ◽  
Poisson Input ◽  
Infinite Server Queues

Stationary Poisson departure processes from non-stationary queues

1986 ◽  
Vol 23 (1) ◽  
pp. 256-260 ◽  
Author(s):  
Robert D. Foley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Distribution Functions ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Infinite Server ◽  
Departure Processes

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

scholarly journals The properties of the queuing model with the parallel structure

2020 ◽  
pp. 79-82
Author(s):  
O. A. Chechelnitsky
Keyword(s):  
Stationary Regime ◽  
Parallel Structure ◽  
Stochastic Dynamic ◽  
General Function ◽  
Expected Number ◽  
Queuing Model ◽  
Poisson Input ◽  
Infinite Server Queues ◽  
Result Analysis ◽  
Number Of Customers

The present article is devoted to research the multi-channelk model with the parallel structure. It means that we consider the model which consists of two infinite-server queues. The service time in the each system has general function of distribution. In this case the stochastic dynamic of our model cannot be defined by Markov chain. As a result, analysis of such models is much more difficult than that of the corresponding Markovian queueing models. Besides we assume that customers arrive to our model according a bivariate Poisson input flow. This input process is characterized by the fact that customers arrive according to a bivariate Poisson flow simultaneously. We consider the number of customers in the systems at time t. This stochastic process describes the state of our model. In present paper we find the limit joint distribution of the number of customers in the systems. In a general way (by differentiating the corresponding generating function.) we obtain the main characteristics of this distribution, such as the expected number of customers in the nodes, its variance and correlation. In the case when parameters of our model dependent on the parameter n (number of series) the limit normal distribution was obtained for the service process in the stationary regime.

Sign in / Sign up

Export Citation Format

Share Document