scholarly journals Bayesian prediction of the transient behaviour and busy period in short- and long-tailed queueing systems

2008 ◽  
Vol 52 (3) ◽  
pp. 1615-1635 ◽  
Author(s):  
M. Concepción Ausín ◽  
Michael P. Wiper ◽  
Rosa E. Lillo
Keyword(s):  
Busy Period ◽  
Queueing Systems ◽  
Bayesian Prediction ◽  
Transient Behaviour

On some diffusion approximations to queueing systems

1986 ◽  
Vol 18 (4) ◽  
pp. 991-1014 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Closed Form ◽  
Busy Period ◽  
Queueing System ◽  
Diffusion Processes ◽  
Queueing Systems ◽  
Diffusion Approximations ◽  
Transient Behaviour ◽  
Closed Form Solutions ◽  
Continuous Models ◽  
Reflecting Boundaries

For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein–Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.

On some diffusion approximations to queueing systems

1986 ◽  
Vol 18 (04) ◽  
pp. 991-1014 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Closed Form ◽  
Busy Period ◽  
Queueing System ◽  
Diffusion Processes ◽  
Queueing Systems ◽  
Diffusion Approximations ◽  
Transient Behaviour ◽  
Closed Form Solutions ◽  
Continuous Models ◽  
Reflecting Boundaries

For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein–Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.

The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

1967 ◽  
Vol 4 (01) ◽  
pp. 162-179 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Busy Period ◽  
Transition Probabilities ◽  
Queueing Systems ◽  
Entrance Time ◽  
Distribution Of The Maximum ◽  
Number Of Customers

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

On some time-non-homogeneous diffusion approximations to queueing systems

1987 ◽  
Vol 19 (4) ◽  
pp. 974-994 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Approximation ◽  
Busy Period ◽  
Queueing Systems ◽  
Time Dependent ◽  
Single Server ◽  
Time Varying ◽  
Diffusion Approximations ◽  
Linear Drift ◽  
Transition Functions ◽  
Fcfs Discipline

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

Asymptotic analysis of queueing systems with identical service

1996 ◽  
Vol 33 (1) ◽  
pp. 267-281 ◽  
Author(s):  
F. I. Karpelevitch ◽  
A. Ya. Kreinin
Keyword(s):  
Weak Convergence ◽  
Asymptotic Analysis ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Stationary Regime ◽  
Convergence Theory ◽  
Transient Behaviour ◽  
Limit Behaviour ◽  
Phase Systems ◽  
Multi Phase

We consider a heavy traffic regime in queueing systems with identical service. These systems belong to the class of multi-phase systems with dependent service times in different service nodes. We study the limit behaviour of the waiting time vector in heavy traffic. Both transient behaviour and the stationary regime are considered. Our analysis is based on the conception of ‘approximated functionals', which appeared to be fruitful in weak convergence theory of stochastic processes.

scholarly journals A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning

2014 ◽  
Vol 24 (4) ◽  
pp. 887-900 ◽  
Author(s):  
Marcin Woźniak ◽  
Wojciech M. Kempa ◽  
Marcin Gabryel ◽  
Robert K. Nowicki
Keyword(s):  
Busy Period ◽  
Optimization Problem ◽  
Analytical Study ◽  
Cost Optimization ◽  
Queueing Systems ◽  
Evolutionary Strategy ◽  
Finite Buffer ◽  
Single Vacation ◽  
Erlang Distributions ◽  
Finite Buffer Queue

Abstract In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

scholarly journals ON THE NUMBER OF REFUSALS IN A BUSY PERIOD

1999 ◽  
Vol 13 (1) ◽  
pp. 71-74 ◽  
Author(s):  
Erol A. Peköz
Keyword(s):  
Service Time ◽  
Busy Period ◽  
Queueing Systems ◽  
Interarrival Time ◽  
Direct Argument ◽  
The Mean ◽  
Interesting Special Case ◽  
Special Case

Formulas are derived for moments of the number of refused customers in a busy period for the M/GI/1/n and the GI/M/1/n queueing systems. As an interesting special case for the M/GI/1/n system, we note that the mean number is 1 when the mean interarrival time equals the mean service time. This provides a more direct argument for a result given in Abramov [1].

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